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LSA Course Guide Search Results: UG, GR, Winter 2007, Dept = MATH
 
Page 1 of 1, Results 1 — 246 of 246
Title
Section
Instructor
Term
Credits
Requirements
MATH 105 — Data, Functions, and Graphs
Section 001, LEC

Instructor: Jakus,Stephanie Julliette

WN 2007
Credits: 4
Reqs: MSA, QR/1

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

MATH 105 — Data, Functions, and Graphs
Section 002, LEC

WN 2007
Credits: 4
Reqs: MSA, QR/1

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

MATH 105 — Data, Functions, and Graphs
Section 003, LEC

Instructor: Kneezel,Daniel James

WN 2007
Credits: 4
Reqs: MSA, QR/1

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

MATH 105 — Data, Functions, and Graphs
Section 004, LEC

Instructor: Rooney,Darragh Patrick

WN 2007
Credits: 4
Reqs: MSA, QR/1

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

MATH 105 — Data, Functions, and Graphs
Section 005, LEC

Instructor: Selegue,Lindsey Ann

WN 2007
Credits: 4
Reqs: MSA, QR/1

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

MATH 105 — Data, Functions, and Graphs
Section 006, LEC

WN 2007
Credits: 4
Reqs: MSA, QR/1

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

MATH 105 — Data, Functions, and Graphs
Section 007, LEC

Instructor: Blakelock,Clara Rose Vogl

WN 2007
Credits: 4
Reqs: MSA, QR/1

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

MATH 105 — Data, Functions, and Graphs
Section 008, LEC

WN 2007
Credits: 4
Reqs: MSA, QR/1

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

MATH 105 — Data, Functions, and Graphs
Section 009, LEC

WN 2007
Credits: 4
Reqs: MSA, QR/1

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

MATH 105 — Data, Functions, and Graphs
Section 010, LEC

WN 2007
Credits: 4
Reqs: MSA, QR/1

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

MATH 105 — Data, Functions, and Graphs
Section 170, LEC
SECTION 170, 171, 173 ONLY BY PERMISSION OF CSP.

Instructor: Khumbah,Nkem-Amin N

WN 2007
Credits: 4
Reqs: MSA, QR/1

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

MATH 105 — Data, Functions, and Graphs
Section 173, LEC
SECTION 170, 171, 173 ONLY BY PERMISSION OF CSP.

WN 2007
Credits: 4
Reqs: MSA, QR/1

Credit Exclusions: Students with credit for MATH 103 can elect MATH 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: MATH 105 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. Students who successfully complete MATH 105 are fully prepared for MATH 115.

Content: This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are assessed during the term by periodic testing. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 110 (Pre-Calculus (Self-Paced)) is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

Subsequent Courses: The course prepares students for MATH 115.

MATH 107 — Mathematics for the Information Age
Section 001, LEC

Instructor: Winter,Dale John; homepage

WN 2007
Credits: 3
Reqs: MSA, QR/1

The course investigates topics relevant to the information age in which we live. Topics covered include cryptography, error-correcting codes, data compression, fairness in politics, voting systems, population growth, biological modeling.

Advisory Prerequisite: Three to four years high school mathematics.

MATH 110 — Pre-Calculus (Self-Study)
Section 001, LAB

WN 2007
Credits: 2

Credit Exclusions: No credit granted to those who already have 4 credits for pre-calculus mathematics courses. A maximum of four credits may be earned in MATH 101, 103, 105, and 110.

Background and Goals: Math 110 is a condensed, half-term version of Math 105 designed specifically to prepare students for Math 115. It is open only to students who have enrolled in Math 115 and whose performance on the first uniform examination indicates that they will have difficulty completing that course successfully. This self-study course begins shortly after the first uniform examination in Math 115, and is completed under the guidance of an instructor without regular classroom meetings. Students must receive permission from the Math 115 Course Director or other designated representative to enroll in the course, and must visit the Math Lab as soon as possible after enrolling to receive printed course information. Enrollment opens the day after the first Math 115 uniform examination, and must be completed by the Friday of the following week.

Content: The course is a condensed, half-term version of Math 105 designed for students who appear to be prepared to handle calculus but are not able to successfully complete Math 115. Students may enroll in Math 110 only on the recommendation of a mathematics instructor after the third week of classes in the Fall and must visit the Math Lab to complete paperwork and receive course materials. The course covers data analysis by means of functions and graphs.

Alternatives: Math 105 (Data, Functions and Graphs) covers the same material in a traditional classroom setting.

Subsequent Courses: The course prepares students for Math 115.

Advisory Prerequisite: MATH 110 is by recommendation or permission of MATH 115 instructor.

MATH 115 — Calculus I
Section 001, LEC

Instructor: Zeager,Crystal Anne

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 002, LEC

Instructor: McNulty,Gregory Francis

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 003, LEC

Instructor: Eisenstein,Eugene

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 004, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 005, LEC

Instructor: Twentyman,Elizabeth Lyell

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 006, LEC

Instructor: Xu,Zhengjie

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 007, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 008, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 009, LEC

Instructor: Sargsyan,Khachik Vahan

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 010, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 011, LEC

Instructor: Strauss,Martin J; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

MCSP has reserved ten spaces in Math 115.011. The advantage of registering for this section is that you will be in the same class with other MCSP students so it will be convenient for you to study with others. The instructor for this math section is selected by the math department, not MCSP, unlike all other MCSP courses. In addition, this class is not held in Couzens Hall.

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 012, LEC

Instructor: More,Ajinkya Ajay

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 013, LEC

Instructor: Selegue,Ashley Dianne

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 014, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 015, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 016, LEC

Instructor: Elsey,Matthew Rees

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 017, LEC

Instructor: Rhea,Karen; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 018, LEC

Instructor: Lozovanu,Victor

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 019, LEC

Instructor: Whitehead,Jared Pierce

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 020, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 021, LEC

Instructor: Sahattchieve,Jordan Antonov

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 022, LEC

Instructor: Chung,Sohhyun

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 023, LEC

Instructor: Wang,Ting

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 024, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 025, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 026, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 027, LEC

Instructor: Lee,Michelle Dongeun

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 028, LEC

Instructor: Totz,Nathan David

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 029, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 030, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 031, LEC

Instructor: Gomez Guerra,Jose Manuel

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 032, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 170, LEC
SECTION 170-173 ONLY BY PERMISSION OF CSP.

Instructor: Lofton,Shylynn N

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 171, LEC
SECTION 170-173 ONLY BY PERMISSION OF CSP.

Instructor: Lofton,Shylynn N

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 172, LEC
SECTION 170-173 ONLY BY PERMISSION OF CSP.

Instructor: Lee,Denise Michele

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 115 — Calculus I
Section 173, LEC
SECTION 170-173 ONLY BY PERMISSION OF CSP.

Instructor: Lee,Denise Michele

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course from among MATH 112, 115, and 185. No credit granted to those who have completed MATH 175.

Background and Goals: The sequence MATH 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof. All sections are given a uniform midterm and final exam.

Content: The course presents the concepts of calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students will develop their reading, writing and questioning skills. Topics include functions and graphs, derivatives and their applications to real-life problems in various fields, and definite integrals. The classroom atmosphere is interactive and cooperative and homework is done in groups.

Alternatives: MATH 185 (Honors Anal. Geom. and Calc. I ) is a somewhat more theoretical course which covers some of the same material. Math 175 (Combinatorics and Calculus) is a non-calculus alternative for students with a good command of first-semester calculus. MATH 295 (Honors Mathematics I) is a much more intensive and rigorous course. A student whose preparation is insufficient for MATH 115 should take MATH 105 (Data, Functions and Graphs).

Subsequent Courses: MATH 116 (Calculus II) is the natural sequel. A student who has done very well in this course could enter the honors sequence at this point by taking MATH 186 (Honors Anal. Geom. and Calc. II).

Advisory Prerequisite: Four years of high school mathematics.

MATH 116 — Calculus II
Section 001, LEC

Instructor: Spencer,Craig V

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 002, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 003, LEC

Instructor: Jurgelewicz,Brian S

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 004, LEC

Instructor: Ormsby,Kyle Michael

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 005, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 006, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 007, LEC

Instructor: Sierra,Susan Judith

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 008, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 009, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 010, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 011, LEC

Instructor: Dewitt,Elizabeth Angela

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 012, LEC

Instructor: Block,Florian Stefan

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 013, LEC

Instructor: Jacobson,Brian David

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 014, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 015, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 016, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 017, LEC

Instructor: Zupunski,Eric J

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 018, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 019, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 020, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 021, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 022, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 023, LEC

Instructor: Arakelian,Irina M; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 024, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 025, LEC

Instructor: Wojczyszyn,Szymon Jedrzej

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 026, LEC

Instructor: Crown,Sarah Anne

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 027, LEC

Instructor: Middleton,Ivan David

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 028, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 029, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 030, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 031, LEC

Instructor: Graves,Hester Katherine

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 032, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 033, LEC

Instructor: Arakelian,Irina M; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 034, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 035, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 036, LEC

Instructor: Robbins,Hannah Reid

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 037, LEC

Instructor: Izbicki,Geri Lyn

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 038, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 039, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 040, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 041, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 042, LEC

Instructor: Rupprecht,Nicholas Andrew

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 043, LEC

Instructor: Golman,Russell

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 044, LEC

Instructor: Kang,Hyosang

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 045, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 046, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 047, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 048, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 049, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 050, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 051, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 053, LEC

Instructor: Jimenez,Fidel Guillermo

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 054, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 055, LEC

Instructor: Mueller,Charles Christopher

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 056, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 057, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 058, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 059, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 060, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 061, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 062, LEC

Instructor: Krawitz,Marc

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 063, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 064, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 170, LEC
SECTION 170-171 ONLY BY PERMISSION OF CSP.

Instructor: Halpern,Jill Ellen

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 116 — Calculus II
Section 171, LEC
SECTION 170-171 ONLY BY PERMISSION OF CSP.

Instructor: Halpern,Jill Ellen

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit is granted for only one course among MATH 116, 119, 156, 176, and 186

See MATH 115 for a general description of the sequence MATH 115-116-215.

Topics include the indefinite integral, techniques of integration, introduction to differential equations, and infinite series. MATH 186 is a somewhat more theoretical course which covers much of the same material. MATH 215 is the natural sequel. A student who has done very well in this course could enter the Honors sequence at this point by taking MATH 285.

Text: Calculus, 3rd Edition, Hughes-Hallet/Gleason, Wiley Publishing. TI-83 Graphing Calculator, Texas Instruments.

Advisory Prerequisite: MATH 115.

MATH 127 — Geometry and the Imagination
Section 001, LEC

Instructor: Joukhovitski,Valentina; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1
Other: FYSem

Credit Exclusions: No credit granted to those who have completed a 200- (or higher) level mathematics course (except for MATH 385 and 485).

Background and Goals: This course introduces students to the ideas and some of the basic results in Euclidean and non-Euclidean geometry. Beginning with geometry in ancient Greece, the course includes the construction of new geometric objects from old ones by projecting and by taking slices. The course is intended for students who want an introduction to mathematical ideas and culture. Emphasis is on conceptual thinking — — students will do hands-on experimentation with geometric shapes, patterns and ideas.

Content: The section begins with the independence of Euclid's Fifth Postulate and with the construction of spherical and hyperbolic geometries in which the Fifth Postulate fails; how spherical and hyperbolic geometry differs from Euclidean geometry. The last topic is geometry of higher dimensions: coordinization — — the mathematician's tool for studying higher dimensions; construction of higher-dimension analogues of some familiar objects like spheres and cubes; discussion of the proper higher-dimensional analogues of some geometric notions (length, angle, orthogonality, etc.).

Alternatives: none Subsequent Courses: This course does not provide preparation for any further study of mathematics.

Advisory Prerequisite: Three years of high school mathematics including a geometry course. Only first-year students, including those with sophomore standing, may pre-register for First-Year Seminars. All others need permission of instructor.

MATH 146 — Houghton Scholars Calculus Workshop II
Section 001, LAB

Instructor: Mosher,Bryan D; homepage

WN 2007
Credits: 2

Each section of the two workshops for which course approval is requested will be limited to 18 students, who will be required to be concurrently enrolled in Math 115 or 116, respectively, for DHSP Workshops I and II. The students will work together in groups of size three or four on very challenging problems that will develop their conceptual understanding of calculus and skill at solving difficult multistep problems. The workshops will meet for four hours per week, in two class meetings of two hours each. As is common with the ESP model, little or no graded homework will be assigned, although the problems on which the students work will be challenging enough that they will not always finish them during class time. The experience of other ESP programs has been that in many, perhaps most, cases, they will continue to work on them outside of class rather than wait until the next class period to finish them. Grading will be CR/NC, with intensive participation in class being the key element in receiving credit. As Treisman himself has pointed out, implementation of this program at UM will have some particular challenges, since the standard UM calculus sequence has already incorporated some of the elements of ESP programs, particularly the group work in class on problems. However, the problems selected for the DHSP workshop sections will be particularly challenging, multistep exercises that will extend the students beyond what they will generally experience in their regular calculus sections. An extensive evaluation of the program, directed by mathematics educator Vilma Mesa of UMís School of Education, will be conducted, and the future direction of the program will be guided by the results of that evaluation.

Intended audience:Participants in the Douglass Houghton Scholars Program. Class Format: 2 lab meetings per week, lasting 2 hours each

Course Requirements:Students will be evaluated on the basis of attendance and participation in activities during scheduled sessions. Course is credit-no credit.

Advisory Prerequisite: Concurrent enrollment in MATH 116

MATH 146 — Houghton Scholars Calculus Workshop II
Section 002, LAB

Instructor: Mosher,Bryan D; homepage

WN 2007
Credits: 2

Each section of the two workshops for which course approval is requested will be limited to 18 students, who will be required to be concurrently enrolled in Math 115 or 116, respectively, for DHSP Workshops I and II. The students will work together in groups of size three or four on very challenging problems that will develop their conceptual understanding of calculus and skill at solving difficult multistep problems. The workshops will meet for four hours per week, in two class meetings of two hours each. As is common with the ESP model, little or no graded homework will be assigned, although the problems on which the students work will be challenging enough that they will not always finish them during class time. The experience of other ESP programs has been that in many, perhaps most, cases, they will continue to work on them outside of class rather than wait until the next class period to finish them. Grading will be CR/NC, with intensive participation in class being the key element in receiving credit. As Treisman himself has pointed out, implementation of this program at UM will have some particular challenges, since the standard UM calculus sequence has already incorporated some of the elements of ESP programs, particularly the group work in class on problems. However, the problems selected for the DHSP workshop sections will be particularly challenging, multistep exercises that will extend the students beyond what they will generally experience in their regular calculus sections. An extensive evaluation of the program, directed by mathematics educator Vilma Mesa of UMís School of Education, will be conducted, and the future direction of the program will be guided by the results of that evaluation.

Intended audience:Participants in the Douglass Houghton Scholars Program. Class Format: 2 lab meetings per week, lasting 2 hours each

Course Requirements:Students will be evaluated on the basis of attendance and participation in activities during scheduled sessions. Course is credit-no credit.

Advisory Prerequisite: Concurrent enrollment in MATH 116

MATH 147 — Introduction to Interest Theory
Section 001, LEC

Instructor: Lee,Sung-Hee Victor

WN 2007
Credits: 3
Reqs: BS, MSA

Credit Exclusions: No credit granted to those who have completed a 200- (or higher) level mathematics course.

Background and Goals: This course is designed for students who seek an introduction to the mathematical concepts and techniques employed by financial institutions such as banks, insurance companies, and pension funds. Actuarial students, and other mathematics concentrators, should elect Math 424 which covers the same topics but on a more rigorous basis requiring considerable use of calculus. The course is not part of a sequence. Students should possess financial calculators.

Content: Topics covered include: various rates of simple and compound interest, present and accumulated values based on these; annuity functions and their application to amortization, sinking funds and bond values; depreciation methods; introduction to life tables, life annuity, and life insurance values.

Alternatives: Math 424 (Compound Interest and Life Ins) covers the same material in greater depth and with a higher level of mathematical content.

Subsequent Courses: none

Advisory Prerequisite: Three to four years high school mathematics.

MATH 186 — Honors Calculus II
Section 001, LEC

Instructor: Lehavi,David; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1
Other: Honors

Credit Exclusions: Credit is granted for only one course from among MATH 116, 119, 156, 176, and 186

Background and Goals: The sequence Math 185-186-285-286 is the honors introduction to the calculus. It is taken by students intending to major in mathematics, science, or engineering as well as students heading for many other fields who want a somewhat more theoretical approach. Although much attention is paid to concepts and solving problems, the underlying theory and proofs of important results are also included. This sequence is not restricted to students enrolled in the LSA Honors Program.

Content: Topics covered include transcendental functions; techniques of integration; applications of calculus such as elementary differential equations, simple harmonic motion, and center of mass; conic sections; polar coordinates; infinite sequences and series including power series and Taylor series. Other topics, often an introduction to matrices and vector spaces, will be included at the discretion of the instructor.

Alternatives: Math 116 (Calculus II) is a somewhat less theoretical course which covers much of the same material. Math 156 (Applied Honors Calculus II) is more application based, but covers much of the same material.

Subsequent Courses: Math 285 (Honors Anal. Geom. and Calc. III) is the natural sequel.

Advisory Prerequisite: Permission of the Honors advisor.

MATH 186 — Honors Calculus II
Section 003, LEC

Instructor: Lehavi,David; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1
Other: Honors

Credit Exclusions: Credit is granted for only one course from among MATH 116, 119, 156, 176, and 186

Background and Goals: The sequence Math 185-186-285-286 is the honors introduction to the calculus. It is taken by students intending to major in mathematics, science, or engineering as well as students heading for many other fields who want a somewhat more theoretical approach. Although much attention is paid to concepts and solving problems, the underlying theory and proofs of important results are also included. This sequence is not restricted to students enrolled in the LSA Honors Program.

Content: Topics covered include transcendental functions; techniques of integration; applications of calculus such as elementary differential equations, simple harmonic motion, and center of mass; conic sections; polar coordinates; infinite sequences and series including power series and Taylor series. Other topics, often an introduction to matrices and vector spaces, will be included at the discretion of the instructor.

Alternatives: Math 116 (Calculus II) is a somewhat less theoretical course which covers much of the same material. Math 156 (Applied Honors Calculus II) is more application based, but covers much of the same material.

Subsequent Courses: Math 285 (Honors Anal. Geom. and Calc. III) is the natural sequel.

Advisory Prerequisite: Permission of the Honors advisor.

MATH 214 — Linear Algebra and Differential Equations
Section 001, LEC

Instructor: Branden,Petter J

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

Background and Goals: An introduction to matrices and linear algebra. This course covers the basics needed to understand a wide variety of applications that use the ideas of linear algebra, from linear programming to mathematical economics. The emphasis is on concepts and problem solving. The course is designed as an alternative to Math 216 for students who need more linear algebra and less differential equations background than provided in 216.

Content: An introduction to the main concepts of linear algebra… matrix operations, echelon form, solution of systems of linear equations, Euclidean vector spaces, linear combinations, independence and spans of sets of vectors in Euclidean space, eigenvectors and eigenvalues, similarity theory. There are applications to discrete Markov processes, linear programming, and solutions of linear differential equations with constant coefficients.

Alternatives: Math 419 (Linear Spaces and Matrix Theory) has a somewhat more theoretical emphasis. Math 217 is a more theoretical course which covers much of the material of Math 214 at a deeper level. Math 513 (Intro. to Linear Algebra) is a honors version of this course. Mathematics majors are required to take Math 217 or Math 513.

Subsequent Courses: Math 420 (Matrix algebra II), Linear programming (Math 561), Mathematical Modeling (Math 462), Math 571 (Numer. method. For Sci).

Advisory Prerequisite: MATH 115 and 116. Most students take only one course from among MATH 214, 217, 417, 419, and 513.

MATH 214 — Linear Algebra and Differential Equations
Section 002, LEC

Instructor: Branden,Petter J

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

Background and Goals: An introduction to matrices and linear algebra. This course covers the basics needed to understand a wide variety of applications that use the ideas of linear algebra, from linear programming to mathematical economics. The emphasis is on concepts and problem solving. The course is designed as an alternative to Math 216 for students who need more linear algebra and less differential equations background than provided in 216.

Content: An introduction to the main concepts of linear algebra… matrix operations, echelon form, solution of systems of linear equations, Euclidean vector spaces, linear combinations, independence and spans of sets of vectors in Euclidean space, eigenvectors and eigenvalues, similarity theory. There are applications to discrete Markov processes, linear programming, and solutions of linear differential equations with constant coefficients.

Alternatives: Math 419 (Linear Spaces and Matrix Theory) has a somewhat more theoretical emphasis. Math 217 is a more theoretical course which covers much of the material of Math 214 at a deeper level. Math 513 (Intro. to Linear Algebra) is a honors version of this course. Mathematics majors are required to take Math 217 or Math 513.

Subsequent Courses: Math 420 (Matrix algebra II), Linear programming (Math 561), Mathematical Modeling (Math 462), Math 571 (Numer. method. For Sci).

Advisory Prerequisite: MATH 115 and 116. Most students take only one course from among MATH 214, 217, 417, 419, and 513.

MATH 215 — Calculus III
Section 010, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 215, 255, or 285.

Background and Goals: The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.

Content: Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; line, surface, and volume integrals and applications; vector fields and integration; Green's Theorem and Stokes' Theorem. There is a weekly computer lab using MAPLE.

Alternatives: Math 285 (Honors Calculus III) is a somewhat more theoretical course which covers the same material. Math 255 (Applied Honors Calculus III) is also an alternative.

Subsequent Courses: For students intending to major in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217 (Linear Algebra). Students who intend to take only one further mathematics course and need differential equations should take Math 216 (Intro. to Differential Equations).

Advisory Prerequisite: MATH 116

MATH 215 — Calculus III
Section 020, LEC

Instructor: DeBacker,Stephen M; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 215, 255, or 285.

Background and Goals: The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.

Content: Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; line, surface, and volume integrals and applications; vector fields and integration; Green's Theorem and Stokes' Theorem. There is a weekly computer lab using MAPLE.

Alternatives: Math 285 (Honors Calculus III) is a somewhat more theoretical course which covers the same material. Math 255 (Applied Honors Calculus III) is also an alternative.

Subsequent Courses: For students intending to major in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217 (Linear Algebra). Students who intend to take only one further mathematics course and need differential equations should take Math 216 (Intro. to Differential Equations).

Advisory Prerequisite: MATH 116

MATH 215 — Calculus III
Section 030, LEC

Instructor: Kolesnikov,Alexei S; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 215, 255, or 285.

Background and Goals: The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.

Content: Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; line, surface, and volume integrals and applications; vector fields and integration; Green's Theorem and Stokes' Theorem. There is a weekly computer lab using MAPLE.

Alternatives: Math 285 (Honors Calculus III) is a somewhat more theoretical course which covers the same material. Math 255 (Applied Honors Calculus III) is also an alternative.

Subsequent Courses: For students intending to major in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217 (Linear Algebra). Students who intend to take only one further mathematics course and need differential equations should take Math 216 (Intro. to Differential Equations).

Advisory Prerequisite: MATH 116

MATH 215 — Calculus III
Section 040, LEC

Instructor: Kolesnikov,Alexei S; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 215, 255, or 285.

Background and Goals: The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.

Content: Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; line, surface, and volume integrals and applications; vector fields and integration; Green's Theorem and Stokes' Theorem. There is a weekly computer lab using MAPLE.

Alternatives: Math 285 (Honors Calculus III) is a somewhat more theoretical course which covers the same material. Math 255 (Applied Honors Calculus III) is also an alternative.

Subsequent Courses: For students intending to major in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217 (Linear Algebra). Students who intend to take only one further mathematics course and need differential equations should take Math 216 (Intro. to Differential Equations).

Advisory Prerequisite: MATH 116

MATH 215 — Calculus III
Section 050, LEC

Instructor: Lenzhen,Anna Borisovna; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 215, 255, or 285.

Background and Goals: The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.

Content: Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; line, surface, and volume integrals and applications; vector fields and integration; Green's Theorem and Stokes' Theorem. There is a weekly computer lab using MAPLE.

Alternatives: Math 285 (Honors Calculus III) is a somewhat more theoretical course which covers the same material. Math 255 (Applied Honors Calculus III) is also an alternative.

Subsequent Courses: For students intending to major in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217 (Linear Algebra). Students who intend to take only one further mathematics course and need differential equations should take Math 216 (Intro. to Differential Equations).

Advisory Prerequisite: MATH 116

MATH 215 — Calculus III
Section 060, LEC

Instructor: Huang,Zheng; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 215, 255, or 285.

Background and Goals: The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.

Content: Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; line, surface, and volume integrals and applications; vector fields and integration; Green's Theorem and Stokes' Theorem. There is a weekly computer lab using MAPLE.

Alternatives: Math 285 (Honors Calculus III) is a somewhat more theoretical course which covers the same material. Math 255 (Applied Honors Calculus III) is also an alternative.

Subsequent Courses: For students intending to major in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217 (Linear Algebra). Students who intend to take only one further mathematics course and need differential equations should take Math 216 (Intro. to Differential Equations).

Advisory Prerequisite: MATH 116

MATH 215 — Calculus III
Section 070, LEC

Instructor: Lenzhen,Anna Borisovna; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 215, 255, or 285.

Background and Goals: The sequence Math 115-116-215 is the standard complete introduction to the concepts and methods of calculus. It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.

Content: Topics include vector algebra and vector functions; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; line, surface, and volume integrals and applications; vector fields and integration; Green's Theorem and Stokes' Theorem. There is a weekly computer lab using MAPLE.

Alternatives: Math 285 (Honors Calculus III) is a somewhat more theoretical course which covers the same material. Math 255 (Applied Honors Calculus III) is also an alternative.

Subsequent Courses: For students intending to major in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217 (Linear Algebra). Students who intend to take only one further mathematics course and need differential equations should take Math 216 (Intro. to Differential Equations).

Advisory Prerequisite: MATH 116

MATH 216 — Introduction to Differential Equations
Section 010, LEC

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 216, 256, 286, or 316.

Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or MATH 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316.

Content: MATH 216 is a basic course on differential equations, intended for engineers and other scientists who need to apply the techniques in their work. The lectures are accompanied by a computer lab and recitation section where students have the opportunity to discuss problems and work through computer experiments to further develop their understanding of the concepts of the class. Topics covered include some material on complex numbers and matrix algebra, first and second order linear and non-linear systems with applications, introductory numerical methods, and elementary Laplace transform techniques.

Alternatives: MATH 286 (Honors Differential Equations) covers much of the same material in the honors sequence. The sequence MATH 217 (Linear Algebra)-MATH 316 (Differential Equations) covers all of this material and substantially more at greater depth and with greater emphasis on the theory. MATH 256 (Applied Honors Calculus IV) is also an alternative.

Subsequent Courses: MATH 404 (Intermediate Diff. Eq.) covers further material on differential equations. MATH 217 (Linear Algebra) and MATH 417 (Matrix Algebra I) cover further material on linear algebra. MATH 371 ((ENGR 303) Numerical Methods) and MATH 471 (Intro. To Numerical Methods) cover additional material on numerical methods.

Advisory Prerequisite: MATH 116, 119, 156, 176, 186, or 296.

MATH 216 — Introduction to Differential Equations
Section 020, LEC

Instructor: Zheng,Xiaoming; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 216, 256, 286, or 316.

Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or MATH 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316.

Content: MATH 216 is a basic course on differential equations, intended for engineers and other scientists who need to apply the techniques in their work. The lectures are accompanied by a computer lab and recitation section where students have the opportunity to discuss problems and work through computer experiments to further develop their understanding of the concepts of the class. Topics covered include some material on complex numbers and matrix algebra, first and second order linear and non-linear systems with applications, introductory numerical methods, and elementary Laplace transform techniques.

Alternatives: MATH 286 (Honors Differential Equations) covers much of the same material in the honors sequence. The sequence MATH 217 (Linear Algebra)-MATH 316 (Differential Equations) covers all of this material and substantially more at greater depth and with greater emphasis on the theory. MATH 256 (Applied Honors Calculus IV) is also an alternative.

Subsequent Courses: MATH 404 (Intermediate Diff. Eq.) covers further material on differential equations. MATH 217 (Linear Algebra) and MATH 417 (Matrix Algebra I) cover further material on linear algebra. MATH 371 ((ENGR 303) Numerical Methods) and MATH 471 (Intro. To Numerical Methods) cover additional material on numerical methods.

Advisory Prerequisite: MATH 116, 119, 156, 176, 186, or 296.

MATH 216 — Introduction to Differential Equations
Section 030, LEC

Instructor: Cadman,Charles D

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 216, 256, 286, or 316.

Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or MATH 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316.

Content: MATH 216 is a basic course on differential equations, intended for engineers and other scientists who need to apply the techniques in their work. The lectures are accompanied by a computer lab and recitation section where students have the opportunity to discuss problems and work through computer experiments to further develop their understanding of the concepts of the class. Topics covered include some material on complex numbers and matrix algebra, first and second order linear and non-linear systems with applications, introductory numerical methods, and elementary Laplace transform techniques.

Alternatives: MATH 286 (Honors Differential Equations) covers much of the same material in the honors sequence. The sequence MATH 217 (Linear Algebra)-MATH 316 (Differential Equations) covers all of this material and substantially more at greater depth and with greater emphasis on the theory. MATH 256 (Applied Honors Calculus IV) is also an alternative.

Subsequent Courses: MATH 404 (Intermediate Diff. Eq.) covers further material on differential equations. MATH 217 (Linear Algebra) and MATH 417 (Matrix Algebra I) cover further material on linear algebra. MATH 371 ((ENGR 303) Numerical Methods) and MATH 471 (Intro. To Numerical Methods) cover additional material on numerical methods.

Advisory Prerequisite: MATH 116, 119, 156, 176, 186, or 296.

MATH 216 — Introduction to Differential Equations
Section 040, LEC

Instructor: Joukhovitski,Valentina; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 216, 256, 286, or 316.

Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or MATH 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316.

Content: MATH 216 is a basic course on differential equations, intended for engineers and other scientists who need to apply the techniques in their work. The lectures are accompanied by a computer lab and recitation section where students have the opportunity to discuss problems and work through computer experiments to further develop their understanding of the concepts of the class. Topics covered include some material on complex numbers and matrix algebra, first and second order linear and non-linear systems with applications, introductory numerical methods, and elementary Laplace transform techniques.

Alternatives: MATH 286 (Honors Differential Equations) covers much of the same material in the honors sequence. The sequence MATH 217 (Linear Algebra)-MATH 316 (Differential Equations) covers all of this material and substantially more at greater depth and with greater emphasis on the theory. MATH 256 (Applied Honors Calculus IV) is also an alternative.

Subsequent Courses: MATH 404 (Intermediate Diff. Eq.) covers further material on differential equations. MATH 217 (Linear Algebra) and MATH 417 (Matrix Algebra I) cover further material on linear algebra. MATH 371 ((ENGR 303) Numerical Methods) and MATH 471 (Intro. To Numerical Methods) cover additional material on numerical methods.

Advisory Prerequisite: MATH 116, 119, 156, 176, 186, or 296.

MATH 216 — Introduction to Differential Equations
Section 050, LEC

Instructor: Siano,Anna; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 216, 256, 286, or 316.

Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or MATH 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316.

Content: MATH 216 is a basic course on differential equations, intended for engineers and other scientists who need to apply the techniques in their work. The lectures are accompanied by a computer lab and recitation section where students have the opportunity to discuss problems and work through computer experiments to further develop their understanding of the concepts of the class. Topics covered include some material on complex numbers and matrix algebra, first and second order linear and non-linear systems with applications, introductory numerical methods, and elementary Laplace transform techniques.

Alternatives: MATH 286 (Honors Differential Equations) covers much of the same material in the honors sequence. The sequence MATH 217 (Linear Algebra)-MATH 316 (Differential Equations) covers all of this material and substantially more at greater depth and with greater emphasis on the theory. MATH 256 (Applied Honors Calculus IV) is also an alternative.

Subsequent Courses: MATH 404 (Intermediate Diff. Eq.) covers further material on differential equations. MATH 217 (Linear Algebra) and MATH 417 (Matrix Algebra I) cover further material on linear algebra. MATH 371 ((ENGR 303) Numerical Methods) and MATH 471 (Intro. To Numerical Methods) cover additional material on numerical methods.

Advisory Prerequisite: MATH 116, 119, 156, 176, 186, or 296.

MATH 216 — Introduction to Differential Equations
Section 060, LEC

Instructor: Siano,Anna; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 216, 256, 286, or 316.

Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or MATH 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316.

Content: MATH 216 is a basic course on differential equations, intended for engineers and other scientists who need to apply the techniques in their work. The lectures are accompanied by a computer lab and recitation section where students have the opportunity to discuss problems and work through computer experiments to further develop their understanding of the concepts of the class. Topics covered include some material on complex numbers and matrix algebra, first and second order linear and non-linear systems with applications, introductory numerical methods, and elementary Laplace transform techniques.

Alternatives: MATH 286 (Honors Differential Equations) covers much of the same material in the honors sequence. The sequence MATH 217 (Linear Algebra)-MATH 316 (Differential Equations) covers all of this material and substantially more at greater depth and with greater emphasis on the theory. MATH 256 (Applied Honors Calculus IV) is also an alternative.

Subsequent Courses: MATH 404 (Intermediate Diff. Eq.) covers further material on differential equations. MATH 217 (Linear Algebra) and MATH 417 (Matrix Algebra I) cover further material on linear algebra. MATH 371 ((ENGR 303) Numerical Methods) and MATH 471 (Intro. To Numerical Methods) cover additional material on numerical methods.

Advisory Prerequisite: MATH 116, 119, 156, 176, 186, or 296.

MATH 216 — Introduction to Differential Equations
Section 070, LEC

Instructor: Sahutoglu,Sonmez; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 216, 256, 286, or 316.

Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or MATH 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316.

Content: MATH 216 is a basic course on differential equations, intended for engineers and other scientists who need to apply the techniques in their work. The lectures are accompanied by a computer lab and recitation section where students have the opportunity to discuss problems and work through computer experiments to further develop their understanding of the concepts of the class. Topics covered include some material on complex numbers and matrix algebra, first and second order linear and non-linear systems with applications, introductory numerical methods, and elementary Laplace transform techniques.

Alternatives: MATH 286 (Honors Differential Equations) covers much of the same material in the honors sequence. The sequence MATH 217 (Linear Algebra)-MATH 316 (Differential Equations) covers all of this material and substantially more at greater depth and with greater emphasis on the theory. MATH 256 (Applied Honors Calculus IV) is also an alternative.

Subsequent Courses: MATH 404 (Intermediate Diff. Eq.) covers further material on differential equations. MATH 217 (Linear Algebra) and MATH 417 (Matrix Algebra I) cover further material on linear algebra. MATH 371 ((ENGR 303) Numerical Methods) and MATH 471 (Intro. To Numerical Methods) cover additional material on numerical methods.

Advisory Prerequisite: MATH 116, 119, 156, 176, 186, or 296.

MATH 217 — Linear Algebra
Section 001, LEC

Instructor: Petersen,Thomas Kyle

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316. These courses are explicitly designed to introduce the student to both the concepts and applications of their subjects and to the methods by which the results are proved.

Content: The topics covered include: systems of linear equations; matrix algebra; vectors, vector spaces, and subspaces; geometry of Rn; linear dependence, bases, and dimension; linear transformations; Eigenvalues and Eigenvectors; diagonalization; inner products. Throughout there will be emphasis on the concepts, logic, and methods of theoretical mathematics.

Alternatives: MATH 214, 417 and 419 cover similar material with more emphasis on computation and applications and less emphasis on proofs. MATH 513 covers more in a much more sophisticated way.

Subsequent Courses: The intended course to follow MATH 217 is MATH 316 (Differential Equations). MATH 217 is also prerequisite for MATH 312 (Applied Modern Algebra), MATH 412 (Introduction to Modern Algebra) and all more advanced courses in mathematics.

Advisory Prerequisite: MATH 215, 255, or 285. Most students take only one course from MATH 214, 217, 417, 419, and 513.

MATH 217 — Linear Algebra
Section 002, LEC

Instructor: Pankka,Pekka Julius; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316. These courses are explicitly designed to introduce the student to both the concepts and applications of their subjects and to the methods by which the results are proved.

Content: The topics covered include: systems of linear equations; matrix algebra; vectors, vector spaces, and subspaces; geometry of Rn; linear dependence, bases, and dimension; linear transformations; Eigenvalues and Eigenvectors; diagonalization; inner products. Throughout there will be emphasis on the concepts, logic, and methods of theoretical mathematics.

Alternatives: MATH 214, 417 and 419 cover similar material with more emphasis on computation and applications and less emphasis on proofs. MATH 513 covers more in a much more sophisticated way.

Subsequent Courses: The intended course to follow MATH 217 is MATH 316 (Differential Equations). MATH 217 is also prerequisite for MATH 312 (Applied Modern Algebra), MATH 412 (Introduction to Modern Algebra) and all more advanced courses in mathematics.

Advisory Prerequisite: MATH 215, 255, or 285. Most students take only one course from MATH 214, 217, 417, 419, and 513.

MATH 217 — Linear Algebra
Section 003, LEC

Instructor: Milicevic,Djordje; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316. These courses are explicitly designed to introduce the student to both the concepts and applications of their subjects and to the methods by which the results are proved.

Content: The topics covered include: systems of linear equations; matrix algebra; vectors, vector spaces, and subspaces; geometry of Rn; linear dependence, bases, and dimension; linear transformations; Eigenvalues and Eigenvectors; diagonalization; inner products. Throughout there will be emphasis on the concepts, logic, and methods of theoretical mathematics.

Alternatives: MATH 214, 417 and 419 cover similar material with more emphasis on computation and applications and less emphasis on proofs. MATH 513 covers more in a much more sophisticated way.

Subsequent Courses: The intended course to follow MATH 217 is MATH 316 (Differential Equations). MATH 217 is also prerequisite for MATH 312 (Applied Modern Algebra), MATH 412 (Introduction to Modern Algebra) and all more advanced courses in mathematics.

Advisory Prerequisite: MATH 215, 255, or 285. Most students take only one course from MATH 214, 217, 417, 419, and 513.

MATH 217 — Linear Algebra
Section 004, LEC

Instructor: Schwede,Karl E; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

Background and Goals: For a student who has completed the calculus sequence, there are two sequences which deal with linear algebra and differential equations, MATH 216-417 (or 419) and MATH 217-316. The sequence MATH 216-417 emphasizes problem-solving and applications and is intended for students of Engineering and the sciences. Math majors and other students who have some interest in the theory of mathematics should elect the sequence MATH 217-316. These courses are explicitly designed to introduce the student to both the concepts and applications of their subjects and to the methods by which the results are proved.

Content: The topics covered include: systems of linear equations; matrix algebra; vectors, vector spaces, and subspaces; geometry of Rn; linear dependence, bases, and dimension; linear transformations; Eigenvalues and Eigenvectors; diagonalization; inner products. Throughout there will be emphasis on the concepts, logic, and methods of theoretical mathematics.

Alternatives: MATH 214, 417 and 419 cover similar material with more emphasis on computation and applications and less emphasis on proofs. MATH 513 covers more in a much more sophisticated way.

Subsequent Courses: The intended course to follow MATH 217 is MATH 316 (Differential Equations). MATH 217 is also prerequisite for MATH 312 (Applied Modern Algebra), MATH 412 (Introduction to Modern Algebra) and all more advanced courses in mathematics.

Advisory Prerequisite: MATH 215, 255, or 285. Most students take only one course from MATH 214, 217, 417, 419, and 513.

MATH 255 — Applied Honors Calculus III
Section 001, LEC

Instructor: Li,Peijun; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1
Other: Honors

Credit Exclusions: Credit can be earned for only one of MATH 215, 255, or 285.

Background and Goals: The sequence 156-255-256 is an honors calculus sequence intended for engineering and science majors who scored 4 or 5 on the AB or BC Advanced Placement calculus exam. Applications will be stressed, but some theory will also be included. Content: Topics include multivariable calculus, line, surface and volume integrals, vector fields, Green's theorem, Stokes' theorem, divergence theorem, applications (e.g. electromagnetic fields, fluid dynamics). MAPLE will be used throughout.

Alternatives: Math 215 (Calculus III) or Math 285 (Honors Anal. Geom. and Calc. III).

Subsequent Courses: Math 256 (Applied Honors Calculus IV) is the natural sequel.

Advisory Prerequisite: MATH 156.

MATH 255 — Applied Honors Calculus III
Section 002, LEC

Instructor: Li,Peijun; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1
Other: Honors

Credit Exclusions: Credit can be earned for only one of MATH 215, 255, or 285.

Background and Goals: The sequence 156-255-256 is an honors calculus sequence intended for engineering and science majors who scored 4 or 5 on the AB or BC Advanced Placement calculus exam. Applications will be stressed, but some theory will also be included. Content: Topics include multivariable calculus, line, surface and volume integrals, vector fields, Green's theorem, Stokes' theorem, divergence theorem, applications (e.g. electromagnetic fields, fluid dynamics). MAPLE will be used throughout.

Alternatives: Math 215 (Calculus III) or Math 285 (Honors Anal. Geom. and Calc. III).

Subsequent Courses: Math 256 (Applied Honors Calculus IV) is the natural sequel.

Advisory Prerequisite: MATH 156.

MATH 255 — Applied Honors Calculus III
Section 003, LEC

Instructor: Morier-Genoud,Sophie; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1
Other: Honors

Credit Exclusions: Credit can be earned for only one of MATH 215, 255, or 285.

Background and Goals: The sequence 156-255-256 is an honors calculus sequence intended for engineering and science majors who scored 4 or 5 on the AB or BC Advanced Placement calculus exam. Applications will be stressed, but some theory will also be included. Content: Topics include multivariable calculus, line, surface and volume integrals, vector fields, Green's theorem, Stokes' theorem, divergence theorem, applications (e.g. electromagnetic fields, fluid dynamics). MAPLE will be used throughout.

Alternatives: Math 215 (Calculus III) or Math 285 (Honors Anal. Geom. and Calc. III).

Subsequent Courses: Math 256 (Applied Honors Calculus IV) is the natural sequel.

Advisory Prerequisite: MATH 156.

MATH 255 — Applied Honors Calculus III
Section 004, LEC

Instructor: Esedoglu,Selim; homepage

WN 2007
Credits: 4
Reqs: BS, MSA, QR/1
Other: Honors

Credit Exclusions: Credit can be earned for only one of MATH 215, 255, or 285.

Background and Goals: The sequence 156-255-256 is an honors calculus sequence intended for engineering and science majors who scored 4 or 5 on the AB or BC Advanced Placement calculus exam. Applications will be stressed, but some theory will also be included. Content: Topics include multivariable calculus, line, surface and volume integrals, vector fields, Green's theorem, Stokes' theorem, divergence theorem, applications (e.g. electromagnetic fields, fluid dynamics). MAPLE will be used throughout.

Alternatives: Math 215 (Calculus III) or Math 285 (Honors Anal. Geom. and Calc. III).

Subsequent Courses: Math 256 (Applied Honors Calculus IV) is the natural sequel.

Advisory Prerequisite: MATH 156.

MATH 286 — Honors Differential Equations
Section 001, LEC

Instructor: Herbig,Anne-Katrin; homepage

WN 2007
Credits: 3
Reqs: BS, MSA, QR/1
Other: Honors

Credit Exclusions: Credit can be earned for only one of MATH 216, 256, 286, or 316.

Background and Goals: The sequence Math 185-186-285-286 is the honors introduction to the calculus. It is taken by students intending to major in mathematics, science, or engineering as well as students heading for many other fields who want a somewhat more theoretical approach. Although much attention is paid to concepts and solving problems, the underlying theory and proofs of important results are also included. This sequence is not restricted to students enrolled in the LSA Honors Program.

Content: Topics include first-order differential equations, higher-order linear differential equations with constant coefficients, an introduction to linear algebra, linear systems, the Laplace Transform, series solutions and other numerical methods (Euler, Runge-Kutta). If time permits, Picard's Theorem will be proved.

Alternatives: Math 216 (Intro. to Differential Equations) and Math 316 (Differential Equations) cover much of the same material. Math 256 (Applied Honors Calculus IV) is also an alternative.

Subsequent Courses: Math 471 (Intro. to Numerical Methods) and/or Math 572 (Numer. Meth. for Sci. Comput. II) are natural sequels in the area of differential equations, but Math 286 is also preparation for more theoretical courses such as Math 451 (Advanced Calculus I).

Advisory Prerequisite: MATH 285.

MATH 286 — Honors Differential Equations
Section 002, LEC

Instructor: Herbig,Anne-Katrin; homepage

WN 2007
Credits: 3
Reqs: BS, MSA, QR/1
Other: Honors

Credit Exclusions: Credit can be earned for only one of MATH 216, 256, 286, or 316.

Background and Goals: The sequence Math 185-186-285-286 is the honors introduction to the calculus. It is taken by students intending to major in mathematics, science, or engineering as well as students heading for many other fields who want a somewhat more theoretical approach. Although much attention is paid to concepts and solving problems, the underlying theory and proofs of important results are also included. This sequence is not restricted to students enrolled in the LSA Honors Program.

Content: Topics include first-order differential equations, higher-order linear differential equations with constant coefficients, an introduction to linear algebra, linear systems, the Laplace Transform, series solutions and other numerical methods (Euler, Runge-Kutta). If time permits, Picard's Theorem will be proved.

Alternatives: Math 216 (Intro. to Differential Equations) and Math 316 (Differential Equations) cover much of the same material. Math 256 (Applied Honors Calculus IV) is also an alternative.

Subsequent Courses: Math 471 (Intro. to Numerical Methods) and/or Math 572 (Numer. Meth. for Sci. Comput. II) are natural sequels in the area of differential equations, but Math 286 is also preparation for more theoretical courses such as Math 451 (Advanced Calculus I).

Advisory Prerequisite: MATH 285.

MATH 289 — Problem Seminar
Section 001, SEM

Instructor: Kollar,Richard; homepage

WN 2007
Credits: 1
Reqs: BS

Background and Goals: One of the best ways to develop mathematical abilities is by solving problems using a variety of methods. Familiarity with numerous methods is a great asset to the developing student of mathematics. Methods learned in attacking a specific problem frequently find application in many other areas of mathematics. In many instances an interest in and appreciation of mathematics is better developed by solving problems than by hearing formal lectures on specific topics. The student has an opportunity to participate more actively in his/her education and development. This course is intended for superior students who have exhibited both ability and interest in doing mathematics, but it is not restricted to honors students. This course is excellent preparation for the Putnam competition.

Content: Students and one or more faculty and graduate student assistants will meet in small groups to explore problems in many different areas of mathematics. Problems will be selected according to the interests and background of the students.

Alternatives: none

MATH 296 — Honors Mathematics II
Section 001, LEC

Instructor: Spatzier,Ralf J; homepage

WN 2007
Credits: 4
Reqs: BS, QR/1
Other: Honors

Credit Exclusions: Credit is granted for only one course from among MATH 156, 176, 186, and 296.

Background and Goals: Math 295-296-395-396 is the most theoretical and demanding honors calculus sequence. The emphasis is on concepts, problem solving, as well as the underlying theory and proofs of important results. It provides an excellent background for advanced courses in mathematics. The expected background is high school trigonometry and algebra (previous calculus not required, but helpful). This sequence is not restricted to students enrolled in the LSA Honors program.

Content: Infinite series, power series, metric spaces, some multivariable calculus, implicit functions, definite integrals, and applications. Alternatives: none Subsequent Courses: Math 395 (Honors Analysis I)

Advisory Prerequisite: MATH 295

MATH 310 — Elementary Topics in Mathematics
Section 001, LEC

Instructor: Montgomery,Hugh L; homepage

WN 2007
Credits: 3
Reqs: ULWR, BS

Background and Goals: The Elementary Topics course may focus on any one of several topics. The material is presented at a level appropriate for sophomores and juniors without extensive coursework in math. The current offering of the course focuses on game theory.

Content: Students study the strategy of several games where mathematical ideas and concepts can play a role. Most of the course will be occupied with the structure of a variety of two person games of strategy: tic tac toe, tic tac toe misère, the French military game, hex, nim, the penny dime game, and many others. If there is sufficient interest students can study: dots and boxes, go-moku, and some aspects of checkers and chess. There will also be a brief introduction to the classical Von Neuman/Morgenstern theory of mixed strategy games.

Alternatives: none

Subsequent Courses: none

Advisory Prerequisite: Two years of high school mathematics.

MATH 316 — Differential Equations
Section 001, LEC

Instructor: Wasserman,Arthur G; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: Credit can be earned for only one of MATH 216, 256, 286, or 316.

Background and Goals: This is an introduction to differential equations for students who have studied linear algebra (Math 217). It treats techniques of solution (exact and approximate), existence and uniqueness theorems, some qualitative theory, and many applications. Proofs are given in class; homework problems include both computational and more conceptually oriented problems.

Content: First-order equations: solutions, existence and uniqueness, and numerical techniques; linear systems: eigenvector-eigenvalue solutions of constant coefficient systems, fundamental matrix solutions, nonhomogeneous systems; higher-order equations, reduction of order, variation of parameters, series solutions; qualitative behavior of systems, equilibrium points, stability. Applications to physical problems are considered throughout.

Alternatives: Math 216 covers somewhat less material without presupposing linear algebra and with less emphasis on theory. Math 286 (Honors Differential Equations) is the honors version of Math 316.

Subsequent Courses: Math 471 (Intro. to Numerical Methods) and/or Math 572 (Numer. Meth. For Sci. Comput. III) are natural sequels in the area of differential equations, but Math 316 is also preparation for more theoretical courses such as Math 451 (Advanced Calculus I).

Advisory Prerequisite: MATH 215 and 217.

MATH 327 — Evolution of Mathematical Concepts
Section 001, LEC

Instructor: Uribe-Ahumada,Alejandro; homepage

WN 2007
Credits: 3
Reqs: ULWR, BS

Background and Goals: This course examines the evolution of major mathematical concepts form mathematical and historical points of view. The course's goal is to throw light on contemporary mathematics by retracing the history of some of the major mathematical discoveries.

Content: This course follows the evolution of three mathematical ideas in geometry, analysis and algebra. Typical choices of subject are: Euclid's parallel postulate and the development of non-Euclidean geometries, the notions of limit and infinitesimals, and the development of the theory of equations culminating with Galois theory.

Alternatives: none Subsequent Courses: none

Advisory Prerequisite: MATH 116 or 186.

MATH 333 — Directed Tutoring
Section 001, LEC

WN 2007
Credits: 1 — 3
Other: Expr

An experiential mathematics course for students enrolled in the Secondary Teaching Certificate Program with a concentration in mathematics. Students would tutor pre-calculus (MATH 105) or calculus (MATH 115) in the Math. Lab. They would also participate in a weekly seminar to discuss mathematical and methodological questions.

Advisory Prerequisite: Enrollment in the secondary teaching certificate program with concentration in Mathematics and permission of instructor.

MATH 351 — Principles of Analysis
Section 001, LEC

Instructor: Mummert,Carl Beckhorn; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 451.

Background and Goals: The course content is similar to that of Math 451, but Math 351 assumes less background. This course covers topics that might be of greater use to students considering a Mathematical Sciences concentration or a minor in Math.

Content: Analysis of the real line, rational and irrational numbers, infinity — large and small, limits, convergence, infinite sequences and series, continuous functions, power series, and differentiation.

Alternatives: Math 451 covers similar topics while assuming more background than 351.

Subsequent Courses: none

Advisory Prerequisite: MATH 215 and 217.

MATH 351 — Principles of Analysis
Section 002, LEC

Instructor: Mummert,Carl Beckhorn; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 451.

Background and Goals: The course content is similar to that of Math 451, but Math 351 assumes less background. This course covers topics that might be of greater use to students considering a Mathematical Sciences concentration or a minor in Math.

Content: Analysis of the real line, rational and irrational numbers, infinity — large and small, limits, convergence, infinite sequences and series, continuous functions, power series, and differentiation.

Alternatives: Math 451 covers similar topics while assuming more background than 351.

Subsequent Courses: none

Advisory Prerequisite: MATH 215 and 217.

MATH 354 — Fourier Analysis and its Applications
Section 001, LEC

Instructor: Sotirov,Alexander I; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 450 or 454.

Background and Goals: This course is an introduction to Fourier analysis with emphasis on applications. The course also can be viewed as a way of deepening one's understanding of the 100- and 200-level material by applying it in interesting ways.

Content: This is an introduction to Fourier analysis at an elementary level, emphasizing applications. The main topics are Fourier series, discrete Fourier transforms, and continuous Fourier transforms. A substantial portion of the time is spent on both scientific/technological applications (e.g. signal processing, Fourier optics), and applications in other branches of mathematics (e.g. partial differential equations, probability theory, number theory). Students will do some computer work, using MATLAB, an interactive programming tool that is easy to use, but no previous experience with computers is necessary.

Alternatives: Math 454 (Bound Val. Probs. for Part. Diff. Eq.) covers some of the same material with more emphasis on partial differential equations.

Subsequent Courses: This course is good preparation for Math 451 (Advanced Calculus I), which covers the theory of calculus in a mathematically rigorous way.

Advisory Prerequisite: MATH 216, 256, 286, or 316.

MATH 371 — Numerical Methods for Engineers and Scientists
Section 001, LEC

Instructor: Park,Frederick Erwin; homepage

WN 2007
Credits: 3

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 471 or 472.

Background and Goals: This is a survey course of the basic numerical methods which are used to solve practical scientific problems. Important concepts such as accuracy, stability, and efficiency are discussed. The course provides an introduction to MATLAB, an interactive program for numerical linear algebra, and may provide practice in FORTRAN programming and the use of a software library subroutine. Convergence theorems are discussed and applied, but the proofs are not emphasized.

Content: Floating point arithmetic, Gaussian elimination, polynomial interpolation, spline approximations, numerical integration and differentiation, solutions to non-linear equations, ordinary differential equations, polynomial approximations. Other topics may include discrete Fourier transforms, two-point boundary-value problems, and Monte-Carlo methods.

Alternatives: Alternatives: Math 471 (Numerical Analysis) provides a more in-depth study of the same topics, with a greater emphasis on analyzing the accuracy and stability of the numerical methods. Math 571 (Numerical Linear Algebra) is a detailed study of the solution of systems of linear equations and eigenvalue problems, with some emphasis on large-scale problems. Math 572 (Numerical Methods for Differential Equations) covers numerical methods for both ordinary and partial differential equations. (Math 571 and 572 can be taken in either order).

Subsequent Courses: This course is basic for many later courses in science and engineering. It is good background for 571 — 572.

Advisory Prerequisite: ENGR 101; one of MATH 216, 256, 286, or 316, and one of MATH 215, 217, 417, or 419.

MATH 371 — Numerical Methods for Engineers and Scientists
Section 002, LEC

WN 2007
Credits: 3

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 471 or 472.

Background and Goals: This is a survey course of the basic numerical methods which are used to solve practical scientific problems. Important concepts such as accuracy, stability, and efficiency are discussed. The course provides an introduction to MATLAB, an interactive program for numerical linear algebra, and may provide practice in FORTRAN programming and the use of a software library subroutine. Convergence theorems are discussed and applied, but the proofs are not emphasized.

Content: Floating point arithmetic, Gaussian elimination, polynomial interpolation, spline approximations, numerical integration and differentiation, solutions to non-linear equations, ordinary differential equations, polynomial approximations. Other topics may include discrete Fourier transforms, two-point boundary-value problems, and Monte-Carlo methods.

Alternatives: Alternatives: Math 471 (Numerical Analysis) provides a more in-depth study of the same topics, with a greater emphasis on analyzing the accuracy and stability of the numerical methods. Math 571 (Numerical Linear Algebra) is a detailed study of the solution of systems of linear equations and eigenvalue problems, with some emphasis on large-scale problems. Math 572 (Numerical Methods for Differential Equations) covers numerical methods for both ordinary and partial differential equations. (Math 571 and 572 can be taken in either order).

Subsequent Courses: This course is basic for many later courses in science and engineering. It is good background for 571 — 572.

Advisory Prerequisite: ENGR 101; one of MATH 216, 256, 286, or 316, and one of MATH 215, 217, 417, or 419.

MATH 389 — Explorations in Mathematics
Section 001, LEC

Instructor: Lagarias,Jeffrey C; homepage
Instructor: Chmutova,Tatyana; homepage

WN 2007
Credits: 3
Reqs: BS

This course is designed to show students how new mathematics is actually created: how to take a problem, make models and experiment with them, and search for underlying structure. The format involves limited formal lecturing, with much more laboratory work and student presentations of partial results and approaches. Problems for projects are drawn from a wide variety of mathematical areas, pure and applied. Problems are chosen on the basis of being accessible to undergraduates.

Course Requirements: No exams. Grades will be based on quality of team projects and the accompanying written and oral reports, weighted approximately equally. Each group will be expected to complete three lab projects during the term.

Intended Audience: Math and science students Class Format: Class will have 1 hour-long lecture per week. In addition there will be 3 hours per week of Lab work.

Advisory Prerequisite: MATH 215 and familiarity with Maple or other math modeling computer program

MATH 396 — Honors Analysis II
Section 001, LEC

Instructor: Barrett,David E; homepage

WN 2007
Credits: 4
Reqs: BS
Other: Honors

Background and Goals: This course is a continuation of Math 395 and has the same theoretical emphasis. Students are expected to understand and construct proofs.

Content: Differential and integral calculus of functions on Euclidean spaces.

Alternatives: none Subsequent Courses: Students who have successfully completed the sequence Math 295-396 are generally prepared to take a range of advanced undergraduate and graduate courses such as Math 512 (Algebraic Structures), Math 525 (Probability Theory), Math 590 (Intro. to Topology), and many others.

Advisory Prerequisite: MATH 395.

MATH 399 — Independent Reading
Section 001, IND

WN 2007
Credits: 1 — 6
Other: Honors, Indpnt Study

Designed especially for Honors students.

Advisory Prerequisite: Permission of instructor.

MATH 404 — Intermediate Differential Equations and Dynamics
Section 001, LEC

Instructor: Karni,Smadar; homepage

WN 2007
Credits: 3
Reqs: BS

This is a course oriented to the solutions and applications of differential equations. Numerical methods and computer graphics are incorporated to varying degrees depending on the instructor. There are relatively few proofs. Some background in linear algebra is strongly recommended. First-order equations, second and higher-order linear equations, Wronskians, variation of parameters, mechanical vibrations, power series solutions, regular singular points, Laplace transform methods, eigenvalues and eigenvectors, nonlinear autonomous systems, critical points, stability, qualitative behavior, application to competing-species and predator-prey models, numerical methods. MATH 454 is a natural sequel.

Advisory Prerequisite: MATH 216, 256 or 286, or 316.

MATH 412 — Introduction to Modern Algebra
Section 001, LEC

Instructor: Mustata,Mircea Immanuel; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 512. Students with credit for MATH 312 should take MATH 512 rather than 412. One credit granted to those who have completed MATH 312.

This course is designed to serve as an introduction to the methods and concepts of abstract mathematics. A typical student entering this course has substantial experience in using complex mathematical (calculus) calculations to solve physical or geometrical problems, but is unused to analyzing carefully the content of definitions or the logical flow of ideas which underlie and justify these calculations. Although the topics discussed here are quite distinct from those of calculus, an important goal of the course is to introduce the student to this type of analysis. Much of the reading, homework exercises, and exams consists of theorems (propositions, lemmas, etc.) and their proofs. MATH 217 or equivalent required as background. The initial topics include ones common to every branch of mathematics: sets, functions (mappings), relations, and the common number systems (integers, rational numbers, real numbers, and complex numbers). These are then applied to the study of particular types of mathematical structures such as groups, rings, and fields. These structures are presented as abstractions from many examples such as the common number systems together with the operations of addition or multiplication, permutations of finite and infinite sets with function composition, sets of motions of geometric figures, and polynomials. Notions such as generator, subgroup, direct product, isomorphism, and homomorphism are defined and studied.

MATH 312 is a somewhat less abstract course which substitutes material on finite automata and other topics for some of the material on rings and fields of MATH 412. MATH 512 is an Honors version of MATH 412 which treats more material in a deeper way. A student who successfully completes this course will be prepared to take a number of other courses in abstract mathematics: MATH 416, 451, 475, 575, 481, 513, and 582. All of these courses will extend and deepen the student's grasp of modern abstract mathematics.

Advisory Prerequisite: Math. 215,255 or 285; and 217; only 1 credit after Math. 312.

MATH 412 — Introduction to Modern Algebra
Section 002, LEC

Instructor: Mustata,Mircea Immanuel; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 512. Students with credit for MATH 312 should take MATH 512 rather than 412. One credit granted to those who have completed MATH 312.

This course is designed to serve as an introduction to the methods and concepts of abstract mathematics. A typical student entering this course has substantial experience in using complex mathematical (calculus) calculations to solve physical or geometrical problems, but is unused to analyzing carefully the content of definitions or the logical flow of ideas which underlie and justify these calculations. Although the topics discussed here are quite distinct from those of calculus, an important goal of the course is to introduce the student to this type of analysis. Much of the reading, homework exercises, and exams consists of theorems (propositions, lemmas, etc.) and their proofs. MATH 217 or equivalent required as background. The initial topics include ones common to every branch of mathematics: sets, functions (mappings), relations, and the common number systems (integers, rational numbers, real numbers, and complex numbers). These are then applied to the study of particular types of mathematical structures such as groups, rings, and fields. These structures are presented as abstractions from many examples such as the common number systems together with the operations of addition or multiplication, permutations of finite and infinite sets with function composition, sets of motions of geometric figures, and polynomials. Notions such as generator, subgroup, direct product, isomorphism, and homomorphism are defined and studied.

MATH 312 is a somewhat less abstract course which substitutes material on finite automata and other topics for some of the material on rings and fields of MATH 412. MATH 512 is an Honors version of MATH 412 which treats more material in a deeper way. A student who successfully completes this course will be prepared to take a number of other courses in abstract mathematics: MATH 416, 451, 475, 575, 481, 513, and 582. All of these courses will extend and deepen the student's grasp of modern abstract mathematics.

Advisory Prerequisite: Math. 215,255 or 285; and 217; only 1 credit after Math. 312.

MATH 417 — Matrix Algebra I
Section 001, LEC

Instructor: Stembridge,John R; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled MATH 513.

Many problems in science, engineering, and mathematics are best formulated in terms of matrices — rectangular arrays of numbers. This course is an introduction to the properties of and operations on matrices with a wide variety of applications. The main emphasis is on concepts and problem-solving, but students are responsible for some of the underlying theory. Diversity rather than depth of applications is stressed. This course is not intended for mathematics concentrators, who should elect MATH 217 or 513 (Honors). Topics include matrix operations, echelon form, general solutions of systems of linear equations, vector spaces and subspaces, linear independence and bases, linear transformations, determinants, orthogonality, characteristic polynomials, eigenvalues and eigenvectors, and similarity theory. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations.

MATH 419 is an enriched version of MATH 417 with a somewhat more theoretical emphasis. MATH 217 (despite its lower number) is also a more theoretical course which covers much of the material of MATH 417 at a deeper level. MATH 513 is an Honors version of this course, which is also taken by some mathematics graduate students. MATH 420 is the natural sequel, but this course serves as prerequisite to several courses: MATH 452, 462, 561, and 571.

Advisory Prerequisite: MATH,Three courses beyond MATH 110. Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

MATH 417 — Matrix Algebra I
Section 002, LEC

Instructor: Stembridge,John R; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled MATH 513.

Many problems in science, engineering, and mathematics are best formulated in terms of matrices — rectangular arrays of numbers. This course is an introduction to the properties of and operations on matrices with a wide variety of applications. The main emphasis is on concepts and problem-solving, but students are responsible for some of the underlying theory. Diversity rather than depth of applications is stressed. This course is not intended for mathematics concentrators, who should elect MATH 217 or 513 (Honors). Topics include matrix operations, echelon form, general solutions of systems of linear equations, vector spaces and subspaces, linear independence and bases, linear transformations, determinants, orthogonality, characteristic polynomials, eigenvalues and eigenvectors, and similarity theory. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations.

MATH 419 is an enriched version of MATH 417 with a somewhat more theoretical emphasis. MATH 217 (despite its lower number) is also a more theoretical course which covers much of the material of MATH 417 at a deeper level. MATH 513 is an Honors version of this course, which is also taken by some mathematics graduate students. MATH 420 is the natural sequel, but this course serves as prerequisite to several courses: MATH 452, 462, 561, and 571.

Advisory Prerequisite: MATH,Three courses beyond MATH 110. Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

MATH 417 — Matrix Algebra I
Section 003, LEC

Instructor: Dontchev,Assen L

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled MATH 513.

Many problems in science, engineering, and mathematics are best formulated in terms of matrices — rectangular arrays of numbers. This course is an introduction to the properties of and operations on matrices with a wide variety of applications. The main emphasis is on concepts and problem-solving, but students are responsible for some of the underlying theory. Diversity rather than depth of applications is stressed. This course is not intended for mathematics concentrators, who should elect MATH 217 or 513 (Honors). Topics include matrix operations, echelon form, general solutions of systems of linear equations, vector spaces and subspaces, linear independence and bases, linear transformations, determinants, orthogonality, characteristic polynomials, eigenvalues and eigenvectors, and similarity theory. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations.

MATH 419 is an enriched version of MATH 417 with a somewhat more theoretical emphasis. MATH 217 (despite its lower number) is also a more theoretical course which covers much of the material of MATH 417 at a deeper level. MATH 513 is an Honors version of this course, which is also taken by some mathematics graduate students. MATH 420 is the natural sequel, but this course serves as prerequisite to several courses: MATH 452, 462, 561, and 571.

Advisory Prerequisite: MATH,Three courses beyond MATH 110. Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

MATH 417 — Matrix Algebra I
Section 004, LEC

Instructor: Nguyen,Lan The; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled MATH 513.

Many problems in science, engineering, and mathematics are best formulated in terms of matrices — rectangular arrays of numbers. This course is an introduction to the properties of and operations on matrices with a wide variety of applications. The main emphasis is on concepts and problem-solving, but students are responsible for some of the underlying theory. Diversity rather than depth of applications is stressed. This course is not intended for mathematics concentrators, who should elect MATH 217 or 513 (Honors). Topics include matrix operations, echelon form, general solutions of systems of linear equations, vector spaces and subspaces, linear independence and bases, linear transformations, determinants, orthogonality, characteristic polynomials, eigenvalues and eigenvectors, and similarity theory. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations.

MATH 419 is an enriched version of MATH 417 with a somewhat more theoretical emphasis. MATH 217 (despite its lower number) is also a more theoretical course which covers much of the material of MATH 417 at a deeper level. MATH 513 is an Honors version of this course, which is also taken by some mathematics graduate students. MATH 420 is the natural sequel, but this course serves as prerequisite to several courses: MATH 452, 462, 561, and 571.

Advisory Prerequisite: MATH,Three courses beyond MATH 110. Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

MATH 419 — Linear Spaces and Matrix Theory
Section 001, LEC

Instructor: Dean,Carolyn A; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

Finite dimensional linear spaces and matrix representation of linear transformations; bases, subspaces, determinants, eigenvectors, and canonical forms; and structure of solutions of systems of linear equations. Applications to differential and difference equations. The course provides more depth and content than MATH 417. MATH 513 is the proper election for students contemplating research in mathematics.

Advisory Prerequisite: MATH,Four courses beyond MATH 110. Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513. Students take only one course from among MATH 214, 217, 417, 419, and 513

MATH 419 — Linear Spaces and Matrix Theory
Section 002, LEC

Instructor: Dean,Carolyn A; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513.

Finite dimensional linear spaces and matrix representation of linear transformations; bases, subspaces, determinants, eigenvectors, and canonical forms; and structure of solutions of systems of linear equations. Applications to differential and difference equations. The course provides more depth and content than MATH 417. MATH 513 is the proper election for students contemplating research in mathematics.

Advisory Prerequisite: MATH,Four courses beyond MATH 110. Credit can be earned for only one of MATH 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in MATH 513. Students take only one course from among MATH 214, 217, 417, 419, and 513

MATH 422 — Risk Management and Insurance
Section 001, LEC
If you are interested in this class, please put your name on the waitlist and email Prof. Huntington (chunt@umich.edu).

Instructor: Huntington,Curtis E; homepage

WN 2007
Credits: 3
Reqs: ULWR, BS

Background and Goals: This course is designed to allow students to explore the insurance mechanism as a means of replacing uncertainty with certainty. A main goal of the course is to explain, using mathematical models from the theory of interest, risk theory, credibility theory and ruin theory, how mathematics underlies many important individual and societal problems.

Content: We will explore how much insurance affects the lives of students (automobile insurance, social security, health insurance, theft insurance) as well as the lives of other family members (retirements, life insurance, group insurance). While the mathematical models are important, an ability to articulate why the insurance options exist and how they satisfy the consumer's needs are equally important. In addition, there are different options available (e.g. in social insurance programs) that offer the opportunity of discussing alternative approaches. This course may be used to satisfy the LSA upper-level writing requirement.

Alternatives: none Subsequent Courses: none

Advisory Prerequisite: MATH 115, junior standing, and permission of instructor.

MATH 423 — Mathematics of Finance
Section 001, LEC

Instructor: Duran,Ahmet; homepage

WN 2007
Credits: 3
Reqs: BS

This course is an introduction to the mathematical models used in finance and economics with particular emphasis on models for pricing derivative instruments such as options and futures. The goal is to understand how the models reflect observed market features, and to provide the necessary mathematical tools for their analysis and implementation. The course will introduce the stochastic processes used for modeling particular financial instruments. However, the students are expected to have a solid background in basic probability theory.

Specific Topics

  1. Review of basic probability.
  2. The one-period binomial model of stock prices used to price futures.
  3. Arbitrage, equivalent portfolios, and risk-neutral valuation.
  4. Multiperiod binomial model.
  5. Options and options markets; pricing options with the binomial model.
  6. Early exercise feature (American options).
  7. Trading strategies; hedging risk.
  8. Introduction to stochastic processes in discrete time. Random walks.
  9. Markov property, martingales, binomial trees.
  10. Continuous-time stochastic processes. Brownian motion.
  11. Black-Scholes analysis, partial differential equation, and formula.
  12. Numerical methods and calibration of models.
  13. Interest-rate derivatives and the yield curve.
  14. Limitations of existing models. Extensions of Black-Scholes.

Advisory Prerequisite: MATH 217 and 425; EECS 183 or equivalent.

MATH 423 — Mathematics of Finance
Section 002, LEC

Instructor: Duran,Ahmet; homepage

WN 2007
Credits: 3
Reqs: BS

This course is an introduction to the mathematical models used in finance and economics with particular emphasis on models for pricing derivative instruments such as options and futures. The goal is to understand how the models reflect observed market features, and to provide the necessary mathematical tools for their analysis and implementation. The course will introduce the stochastic processes used for modeling particular financial instruments. However, the students are expected to have a solid background in basic probability theory.

Specific Topics

  1. Review of basic probability.
  2. The one-period binomial model of stock prices used to price futures.
  3. Arbitrage, equivalent portfolios, and risk-neutral valuation.
  4. Multiperiod binomial model.
  5. Options and options markets; pricing options with the binomial model.
  6. Early exercise feature (American options).
  7. Trading strategies; hedging risk.
  8. Introduction to stochastic processes in discrete time. Random walks.
  9. Markov property, martingales, binomial trees.
  10. Continuous-time stochastic processes. Brownian motion.
  11. Black-Scholes analysis, partial differential equation, and formula.
  12. Numerical methods and calibration of models.
  13. Interest-rate derivatives and the yield curve.
  14. Limitations of existing models. Extensions of Black-Scholes.

Advisory Prerequisite: MATH 217 and 425; EECS 183 or equivalent.

MATH 424 — Compound Interest and Life Insurance
Section 001, LEC

Instructor: Sezer,Semih Onur; homepage

WN 2007
Credits: 3
Reqs: BS

This course explores the concepts underlying the theory of interest and then applies them to concrete problems. The course also includes applications of spreadsheet software. The course is a prerequisite to advanced actuarial courses. It also helps students prepare for the Part 4A examination of the Casualty Actuarial Society and the Course 140 examination of the Society of Actuaries. The course covers compound interest (growth) theory and its application to valuation of monetary deposits, annuities, and bonds. Problems are approached both analytically (using algebra) and geometrically (using pictorial representations). Techniques are applied to real-life situations: bank accounts, bond prices, etc. The text is used as a guide because it is prescribed for the Society of Actuaries exam; the material covered will depend somewhat on the instructor. MATH 424 is required for students concentrating in actuarial mathematics; others may take MATH 147, which deals with the same techniques but with less emphasis on continuous growth situations. MATH 520 applies the concepts of MATH 424 together with probability theory to the valuation of life contingencies (death benefits and pensions).

Advisory Prerequisite: MATH 215, 255, or 285 or permission of instructor.

MATH 424 — Compound Interest and Life Insurance
Section 002, LEC

Instructor: Sezer,Semih Onur; homepage

WN 2007
Credits: 3
Reqs: BS

This course explores the concepts underlying the theory of interest and then applies them to concrete problems. The course also includes applications of spreadsheet software. The course is a prerequisite to advanced actuarial courses. It also helps students prepare for the Part 4A examination of the Casualty Actuarial Society and the Course 140 examination of the Society of Actuaries. The course covers compound interest (growth) theory and its application to valuation of monetary deposits, annuities, and bonds. Problems are approached both analytically (using algebra) and geometrically (using pictorial representations). Techniques are applied to real-life situations: bank accounts, bond prices, etc. The text is used as a guide because it is prescribed for the Society of Actuaries exam; the material covered will depend somewhat on the instructor. MATH 424 is required for students concentrating in actuarial mathematics; others may take MATH 147, which deals with the same techniques but with less emphasis on continuous growth situations. MATH 520 applies the concepts of MATH 424 together with probability theory to the valuation of life contingencies (death benefits and pensions).

Advisory Prerequisite: MATH 215, 255, or 285 or permission of instructor.

MATH 425 — Introduction to Probability
Section 001, LEC

Instructor: Ziegler,Tamar; homepage

WN 2007
Credits: 3
Reqs: BS

Background and Goals: This course introduces students to useful and interesting ideas of the mathematical theory of probability and to a number of applications of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of MATH 116 and 215.

Content: Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. Different instructors will vary the emphasis.

Alternatives: MATH 525 (Probability Theory) is a similar course for students with stronger mathematical background and ability.

Subsequent Courses: STATS 426 (Intro. To Math. Stat.) is a natural sequel for students. MATH 423 (Mathematics of Finance) and MATH 523 (Risk Theory) include many applications of probability theory.

Advisory Prerequisite: MATH 215

MATH 425 — Introduction to Probability
Section 002, LEC

Instructor: Ziegler,Tamar; homepage

WN 2007
Credits: 3
Reqs: BS

Background and Goals: This course introduces students to useful and interesting ideas of the mathematical theory of probability and to a number of applications of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of MATH 116 and 215.

Content: Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. Different instructors will vary the emphasis.

Alternatives: MATH 525 (Probability Theory) is a similar course for students with stronger mathematical background and ability.

Subsequent Courses: STATS 426 (Intro. To Math. Stat.) is a natural sequel for students. MATH 423 (Mathematics of Finance) and MATH 523 (Risk Theory) include many applications of probability theory.

Advisory Prerequisite: MATH 215

MATH 425 — Introduction to Probability
Section 003, LEC

Instructor: Dean,Carolyn A; homepage

WN 2007
Credits: 3
Reqs: BS

Background and Goals: This course introduces students to useful and interesting ideas of the mathematical theory of probability and to a number of applications of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of MATH 116 and 215.

Content: Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. Different instructors will vary the emphasis.

Alternatives: MATH 525 (Probability Theory) is a similar course for students with stronger mathematical background and ability.

Subsequent Courses: STATS 426 (Intro. To Math. Stat.) is a natural sequel for students. MATH 423 (Mathematics of Finance) and MATH 523 (Risk Theory) include many applications of probability theory.

Advisory Prerequisite: MATH 215

MATH 425 — Introduction to Probability
Section 004, LEC

Instructor: Amirdjanova,Anna

WN 2007
Credits: 3
Reqs: BS

Background and Goals: This course introduces students to useful and interesting ideas of the mathematical theory of probability and to a number of applications of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of MATH 116 and 215.

Content: Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. Different instructors will vary the emphasis.

Alternatives: MATH 525 (Probability Theory) is a similar course for students with stronger mathematical background and ability.

Subsequent Courses: STATS 426 (Intro. To Math. Stat.) is a natural sequel for students. MATH 423 (Mathematics of Finance) and MATH 523 (Risk Theory) include many applications of probability theory.

Advisory Prerequisite: MATH 215

MATH 425 — Introduction to Probability
Section 005, LEC

Instructor: Atchade,Yves A

WN 2007
Credits: 3
Reqs: BS

Background and Goals: This course introduces students to useful and interesting ideas of the mathematical theory of probability and to a number of applications of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of MATH 116 and 215.

Content: Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. Different instructors will vary the emphasis.

Alternatives: MATH 525 (Probability Theory) is a similar course for students with stronger mathematical background and ability.

Subsequent Courses: STATS 426 (Intro. To Math. Stat.) is a natural sequel for students. MATH 423 (Mathematics of Finance) and MATH 523 (Risk Theory) include many applications of probability theory.

Advisory Prerequisite: MATH 215

MATH 425 — Introduction to Probability
Section 006, LEC

Instructor: Thelen,Brian J; homepage

WN 2007
Credits: 3
Reqs: BS

Background and Goals: This course introduces students to useful and interesting ideas of the mathematical theory of probability and to a number of applications of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of MATH 116 and 215.

Content: Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. Different instructors will vary the emphasis.

Alternatives: MATH 525 (Probability Theory) is a similar course for students with stronger mathematical background and ability.

Subsequent Courses: STATS 426 (Intro. To Math. Stat.) is a natural sequel for students. MATH 423 (Mathematics of Finance) and MATH 523 (Risk Theory) include many applications of probability theory.

Advisory Prerequisite: MATH 215

MATH 425 — Introduction to Probability
Section 007, LEC

Instructor: Petrakiev,Ivan Georgiev; homepage

WN 2007
Credits: 3
Reqs: BS

Background and Goals: This course introduces students to useful and interesting ideas of the mathematical theory of probability and to a number of applications of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of MATH 116 and 215.

Content: Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. Different instructors will vary the emphasis.

Alternatives: MATH 525 (Probability Theory) is a similar course for students with stronger mathematical background and ability.

Subsequent Courses: STATS 426 (Intro. To Math. Stat.) is a natural sequel for students. MATH 423 (Mathematics of Finance) and MATH 523 (Risk Theory) include many applications of probability theory.

Advisory Prerequisite: MATH 215

MATH 425 — Introduction to Probability
Section 008, LEC

Instructor: Smereka,Peter S; homepage

WN 2007
Credits: 3
Reqs: BS

Background and Goals: This course introduces students to useful and interesting ideas of the mathematical theory of probability and to a number of applications of probability to a variety of fields including genetics, economics, geology, business, and engineering. The theory developed together with other mathematical tools such as combinatorics and calculus are applied to everyday problems. Concepts, calculations, and derivations are emphasized. The course will make essential use of the material of MATH 116 and 215.

Content: Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. Different instructors will vary the emphasis.

Alternatives: MATH 525 (Probability Theory) is a similar course for students with stronger mathematical background and ability.

Subsequent Courses: STATS 426 (Intro. To Math. Stat.) is a natural sequel for students. MATH 423 (Mathematics of Finance) and MATH 523 (Risk Theory) include many applications of probability theory.

Advisory Prerequisite: MATH 215

MATH 429 — Internship
Section 001, IND

WN 2007
Credits: 1
Other: Expr

Credits is granted for a full-time internship of at least eight weeks that is used to enrich a student's academic experience and/or allows the student to explore careers related to his/her academic studies.

Advisory Prerequisite: Concentration in Mathematics.

MATH 429 — Internship
Section 046, IND

Instructor: Huntington,Curtis E; homepage

WN 2007
Credits: 1
Other: Expr

Credits is granted for a full-time internship of at least eight weeks that is used to enrich a student's academic experience and/or allows the student to explore careers related to his/her academic studies.

Advisory Prerequisite: Concentration in Mathematics.

MATH 450 — Advanced Mathematics for Engineers I
Section 001, LEC

Instructor: Balbás,Jorge; homepage

WN 2007
Credits: 4
Reqs: BS

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 354 or 454.

Although this course is designed principally to develop mathematics for application to problems of science and engineering, it also serves as an important bridge for students between the calculus courses and the more demanding advanced courses. Students are expected to learn to read and write mathematics at a more sophisticated level and to combine several techniques to solve problems. Some proofs are given, and students are responsible for a thorough understanding of definitions and theorems. Students should have a good command of the material from MATH 215, and 216 or 316, which is used throughout the course. A background in linear algebra, e.g. MATH 217, is highly desirable, as is familiarity with Maple software. Topics include a review of curves and surfaces in implicit, parametric, and explicit forms; differentiability and affine approximations; implicit and inverse function theorems; chain rule for 3-space; multiple integrals; scalar and vector fields; line and surface integrals; computations of planetary motion, work, circulation, and flux over surfaces; Gauss' and Stokes' Theorems; and derivation of continuity and heat equation. Some instructors include more material on higher dimensional spaces and an introduction to Fourier series. MATH 450 is an alternative to MATH 451 as a prerequisite for several more advanced courses. MATH 454 and 555 are the natural sequels for students with primary interest in engineering applications.

Advisory Prerequisite: MATH 215, 255, or 285.

MATH 450 — Advanced Mathematics for Engineers I
Section 002, LEC

Instructor: Cheskidov,Alexey P; homepage

WN 2007
Credits: 4
Reqs: BS

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 354 or 454.

Although this course is designed principally to develop mathematics for application to problems of science and engineering, it also serves as an important bridge for students between the calculus courses and the more demanding advanced courses. Students are expected to learn to read and write mathematics at a more sophisticated level and to combine several techniques to solve problems. Some proofs are given, and students are responsible for a thorough understanding of definitions and theorems. Students should have a good command of the material from MATH 215, and 216 or 316, which is used throughout the course. A background in linear algebra, e.g. MATH 217, is highly desirable, as is familiarity with Maple software. Topics include a review of curves and surfaces in implicit, parametric, and explicit forms; differentiability and affine approximations; implicit and inverse function theorems; chain rule for 3-space; multiple integrals; scalar and vector fields; line and surface integrals; computations of planetary motion, work, circulation, and flux over surfaces; Gauss' and Stokes' Theorems; and derivation of continuity and heat equation. Some instructors include more material on higher dimensional spaces and an introduction to Fourier series. MATH 450 is an alternative to MATH 451 as a prerequisite for several more advanced courses. MATH 454 and 555 are the natural sequels for students with primary interest in engineering applications.

Advisory Prerequisite: MATH 215, 255, or 285.

MATH 451 — Advanced Calculus I
Section 001, LEC

Instructor: Duren,Peter L; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 351.

This course has two complementary goals: (1) a rigorous development of the fundamental ideas of calculus, and (2) a further development of the student's ability to deal with abstract mathematics and mathematical proofs. The key words here are "rigor" and "proof"; almost all of the material of the course consists in understanding and constructing definitions, theorems (propositions, lemmas, etc.) and proofs. This is considered one of the more difficult among the undergraduate mathematics courses, and students should be prepared to make a strong commitment to the course. In particular, it is strongly recommended that some course which requires proofs (such as MATH 412) be taken before MATH 451. Topics include: logic and techniques of proof; sets, functions, and relations; cardinality; the real number system and its topology; infinite sequences, limits, and continuity; differentiation; integration, and the Fundamental Theorem of Calculus; infinite series; and sequences and series of functions.

There is really no other course which covers the material of MATH 451. Although MATH 450 is an alternative prerequisite for some later courses, the emphasis of the two courses is quite distinct. The natural sequel to MATH 451 is 452, which extends the ideas considered here to functions of several variables. In a sense, MATH 451 treats the theory behind MATH 115-116, while MATH 452 does the same for MATH 215 and a part of MATH 216. MATH 551 is a more advanced version of Math 452. MATH 451 is also a prerequisite for several other courses: MATH 575, 590, 596, and 597.

Advisory Prerequisite: Previous exposure to abstract mathematics, e.g. MATH 217 and 412

MATH 451 — Advanced Calculus I
Section 002, LEC

Instructor: Stensønes,Berit; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 351.

This course has two complementary goals: (1) a rigorous development of the fundamental ideas of calculus, and (2) a further development of the student's ability to deal with abstract mathematics and mathematical proofs. The key words here are "rigor" and "proof"; almost all of the material of the course consists in understanding and constructing definitions, theorems (propositions, lemmas, etc.) and proofs. This is considered one of the more difficult among the undergraduate mathematics courses, and students should be prepared to make a strong commitment to the course. In particular, it is strongly recommended that some course which requires proofs (such as MATH 412) be taken before MATH 451. Topics include: logic and techniques of proof; sets, functions, and relations; cardinality; the real number system and its topology; infinite sequences, limits, and continuity; differentiation; integration, and the Fundamental Theorem of Calculus; infinite series; and sequences and series of functions.

There is really no other course which covers the material of MATH 451. Although MATH 450 is an alternative prerequisite for some later courses, the emphasis of the two courses is quite distinct. The natural sequel to MATH 451 is 452, which extends the ideas considered here to functions of several variables. In a sense, MATH 451 treats the theory behind MATH 115-116, while MATH 452 does the same for MATH 215 and a part of MATH 216. MATH 551 is a more advanced version of Math 452. MATH 451 is also a prerequisite for several other courses: MATH 575, 590, 596, and 597.

Advisory Prerequisite: Previous exposure to abstract mathematics, e.g. MATH 217 and 412

MATH 454 — Boundary Value Problems for Partial Differential Equations
Section 001, LEC

Instructor: Buckingham,Robert J; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: Students with credit for MATH 354 can elect MATH 454 for one credit. No credit granted to those who have completed or are enrolled in MATH 450.

This course is devoted to the use of Fourier series and other orthogonal expansions in the solution of boundary-value problems for second-order linear partial differential equations. Emphasis is on concepts and calculation. The official prerequisite is ample preparation. Classical representation and convergence theorems for Fourier series; method of separation of variables for the solution of the one-dimensional heat and wave equation; the heat and wave equations in higher dimensions; spherical and cylindrical Bessel functions; Legendre polynomials; methods for evaluating asymptotic integrals (Laplace's method, steepest descent); Fourier and Laplace transforms; and applications to linear input-output systems, analysis of data smoothing and filtering, signal processing, time-series analysis, and spectral analysis. Both MATH 455 and 554 cover many of the same topics but are very seldom offered. MATH 454 is prerequisite to MATH 571 and 572, although it is not a formal prerequisite, it is good background for MATH 556.

Advisory Prerequisite: 216,316/286

MATH 454 — Boundary Value Problems for Partial Differential Equations
Section 002, LEC

Instructor: Kollar,Richard; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: Students with credit for MATH 354 can elect MATH 454 for one credit. No credit granted to those who have completed or are enrolled in MATH 450.

This course is devoted to the use of Fourier series and other orthogonal expansions in the solution of boundary-value problems for second-order linear partial differential equations. Emphasis is on concepts and calculation. The official prerequisite is ample preparation. Classical representation and convergence theorems for Fourier series; method of separation of variables for the solution of the one-dimensional heat and wave equation; the heat and wave equations in higher dimensions; spherical and cylindrical Bessel functions; Legendre polynomials; methods for evaluating asymptotic integrals (Laplace's method, steepest descent); Fourier and Laplace transforms; and applications to linear input-output systems, analysis of data smoothing and filtering, signal processing, time-series analysis, and spectral analysis. Both MATH 455 and 554 cover many of the same topics but are very seldom offered. MATH 454 is prerequisite to MATH 571 and 572, although it is not a formal prerequisite, it is good background for MATH 556.

Advisory Prerequisite: 216,316/286

MATH 462 — Mathematical Models
Section 001, LEC

Instructor: Conrad,Emery D; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: Students with credit for MATH 362 must have department permission to elect MATH 462.

Background and Goals: The focus of this course is the application of a variety of mathematical techniques to solve real-world problems. Students will learn how to model a problem in mathematical terms and use mathematics to gain insight and eventually solve the problem. Concepts and calculations, using applied analysis and numerical simulations, are emphasized.

Content: Construction and analysis of mathematical models in physics, engineering, economics, biology, medicine, and social sciences. Content varies considerably with instructor. Recent versions: Use and theory of dynamical systems (chaotic dynamics, ecological and biological models, classical mechanics), and mathematical models in physiology and population biology.

Alternatives: Students who are particularly interested in biology should considered Math 463 (Math Modeling in Biology).

Subsequent Courses: any higher-level course in differential equations

Advisory Prerequisite: MATH 216, 256, 286, or 316; and MATH 214, 217, 417, or 419. Students with credit for MATH 362 must have department permission to elect MATH 462.

MATH 471 — Introduction to Numerical Methods
Section 001, LEC

Instructor: Barannyk,Lyudmyla; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 371 or 472.

This is a survey of the basic numerical methods which are used to solve scientific problems. The emphasis is evenly divided between the analysis of the methods and their practical applications. Some convergence theorems and error bounds are proven. The course also provides an introduction to MATLAB, an interactive program for numerical linear algebra, as well as practice in computer programming. One goal of the course is to show how calculus and linear algebra are used in numerical analysis. Topics may include computer arithmetic, Newton's method for non-linear equations, polynomial interpolation, numerical integration, systems of linear equations, initial value problems for ordinary differential equations, quadrature, partial pivoting, spline approximations, partial differential equations, Monte Carlo methods, 2-point boundary value problems, and the Dirichlet problem for the Laplace equation. MATH 371 is a less sophisticated version intended principally for sophomore and junior engineering students; the sequence MATH 571-572 is mainly taken by graduate students, but should be considered by strong undergraduates. MATH 471 is good preparation for MATH 571 and 572, although it is not prerequisite to these courses.

Advisory Prerequisite: MATH 216, 256, 286, or 316; and 214, 217, 417, or 419; and a working knowledge of one high-level computer language. No credit granted to those who have completed or are enrolled in MATH 371 or 472.

MATH 471 — Introduction to Numerical Methods
Section 002, LEC

Instructor: Gammack,David; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: No credit granted to those who have completed or are enrolled in MATH 371 or 472.

This is a survey of the basic numerical methods which are used to solve scientific problems. The emphasis is evenly divided between the analysis of the methods and their practical applications. Some convergence theorems and error bounds are proven. The course also provides an introduction to MATLAB, an interactive program for numerical linear algebra, as well as practice in computer programming. One goal of the course is to show how calculus and linear algebra are used in numerical analysis. Topics may include computer arithmetic, Newton's method for non-linear equations, polynomial interpolation, numerical integration, systems of linear equations, initial value problems for ordinary differential equations, quadrature, partial pivoting, spline approximations, partial differential equations, Monte Carlo methods, 2-point boundary value problems, and the Dirichlet problem for the Laplace equation. MATH 371 is a less sophisticated version intended principally for sophomore and junior engineering students; the sequence MATH 571-572 is mainly taken by graduate students, but should be considered by strong undergraduates. MATH 471 is good preparation for MATH 571 and 572, although it is not prerequisite to these courses.

Advisory Prerequisite: MATH 216, 256, 286, or 316; and 214, 217, 417, or 419; and a working knowledge of one high-level computer language. No credit granted to those who have completed or are enrolled in MATH 371 or 472.

MATH 486 — Concepts Basic to Secondary Mathematics
Section 001, LEC

Instructor: Spice,Loren R; homepage

WN 2007
Credits: 3

Background and Goals: This course is designed for students who intend to teach junior high or high school mathematics. It is advised that the course be taken relatively early in the program to help the student decide whether or not this is an appropriate goal. Concepts and proofs are emphasized over calculation. The course is conducted in a discussion format. Class participation is expected and constitutes a significant part of the course grade. Content: Topics covered have included problem solving; sets, relations and functions; the real number system and its subsystems; number theory; probability and statistics; difference sequences and equations; interest and annuities; algebra; and logic. This material is covered in the course pack and scattered points in the text book. Alternatives: There is no real alternative, but the requirement of Math 486 may be waived for strong students who intend to do graduate work in mathematics.

Subsequent Courses: Prior completion of Math 486 may be of use for some students planning to take Math 312, 412, or 425.

Advisory Prerequisite: MATH 215, 255, or 285.

MATH 489 — Mathematics for Elementary and Middle School Teachers
Section 001, LEC

Instructor: Mosher,Bryan D; homepage
Instructor: Aaron,Wendy Rose

WN 2007
Credits: 3

Credit Exclusions: May not be used in any Graduate program in Mathematics.

Background and Goals: This course, together with its predecessor Math 385, provides a coherent overview of the mathematics underlying the elementary and middle school curriculum. It is required of all students intending to earn an elementary teaching certificate and is taken almost exclusively by such students. Concepts are heavily emphasized with some attention given to calculation and proof. The course is conducted using a discussion format. Class participation is expected and constitutes a significant part of the course grade. Enrollment is limited to 30 students per section. Although only two years of high school mathematics are required, a more complete background including pre-calculus or calculus is desirable.

Content: Topics covered include fractions and rational numbers, decimals and real numbers, probability and statistics, geometric figures, and measurement. Algebraic techniques and problem-solving strategies are used throughout the course. The material is contained in Chapters 7 — 12 of Krause.

Alternatives: There is no alternative course.

Subsequent Courses: Math 497 (Topics in Elementary Mathematics)

Advisory Prerequisite: 385/485/P.I.

MATH 489 — Mathematics for Elementary and Middle School Teachers
Section 002, LEC

Instructor: Lozano,Guadalupe Ines
Instructor: Aaron,Wendy Rose

WN 2007
Credits: 3

Credit Exclusions: May not be used in any Graduate program in Mathematics.

Background and Goals: This course, together with its predecessor Math 385, provides a coherent overview of the mathematics underlying the elementary and middle school curriculum. It is required of all students intending to earn an elementary teaching certificate and is taken almost exclusively by such students. Concepts are heavily emphasized with some attention given to calculation and proof. The course is conducted using a discussion format. Class participation is expected and constitutes a significant part of the course grade. Enrollment is limited to 30 students per section. Although only two years of high school mathematics are required, a more complete background including pre-calculus or calculus is desirable.

Content: Topics covered include fractions and rational numbers, decimals and real numbers, probability and statistics, geometric figures, and measurement. Algebraic techniques and problem-solving strategies are used throughout the course. The material is contained in Chapters 7 — 12 of Krause.

Alternatives: There is no alternative course.

Subsequent Courses: Math 497 (Topics in Elementary Mathematics)

Advisory Prerequisite: 385/485/P.I.

MATH 490 — Introduction to Topology
Section 001, LEC

Instructor: Cavalieri,Renzo; homepage

WN 2007
Credits: 3
Reqs: BS

Background and Goals: Topology is the study of a class of interesting spaces, geometric examples of which are knots and surfaces. We focus on those properties of such spaces which don't change if the space is deformed. Much of the course is devoted to understanding particular spaces, such as Möbius strips and Klein bottles. The material in this course has a wide range of applications. Most of the material is theoretical, but it is well-suited for developing intuition and giving convincing proofs which are pictorial or geometric rather than completely rigorous.

Content: Knots, orientable and non-orientable surfaces, Euler characteristic, open sets, connectedness, compactness, metric spaces. The topics covered are fairly constant but the presentation and emphasis will vary significantly with the instructor.

Alternatives: MATH 590 (Intro. to Topology) is a deeper and more difficult presentation of much of the same material. Math 433 (Intro. to Differential Geometry) is a related course at about the same level.

Subsequent Courses: MATH 490 is not prerequisite for any later course but provides good background for MATH 591 (General and Differential Topology) or any of the other courses in geometry or topology.

Advisory Prerequisite: MATH 451 or equivalent experience with abstract mathematics.

MATH 499 — Independent Reading
Section 001, IND

WN 2007
Credits: 1 — 4

This course is intended for graduate students in fields other than mathematics who require mathematical skills not otherwise available though existing courses.

Advisory Prerequisite: Graduate standing in a field other than Mathematics and permission of instructor.

MATH 501 — Applied & Interdisciplinary Mathematics Student Seminar
Section 001, SEM

Instructor: Doering,Charles R; homepage

WN 2007
Credits: 1

The AIM Student Seminar (Math 501) is a student-focused seminar series directed by core AIM faculty, worth one credit each term (S/U grading). The class meets once a week for an hour and then again the same day for another hour in the weekly AIM Research Seminar.

The purpose of the AIM Student Seminar is to:

  1. Present background and basic foundational material for the work that will be discussed at a more advanced level in the subsequent AIM Research Seminar;
  2. Put the subject of the Research Seminar in a broader scientific and technological context and discuss its significance and importance;
  3. Provide AIM students with an opportunity to ask general or background questions in order to derive greater benefit from the research seminar;
  4. Practice communicating new — and often unfamiliar — mathematical and scientific ideas to a broad audience.

Item (4) is addressed by having each student writing a journalistic style recap of one of the semester's AIM Research Seminars. These short non-technical review reports are be prepared in consultation with the Research Seminar speaker and course director for distribution to the Student Seminar participants.

Attendance at research seminars, even when the topic is not clearly of immediate interest, is a vital part of general interdisciplinary training and ongoing research. Students (and faculty!) are exposed to the currents of modern research, and seminar participation fosters important interactions among AIM students, faculty and researchers.

Requirements: Weekly attendance in the Student and Research Seminars, and successful completion of a research review report.

Advisory Prerequisite: At least two 300 or above level math courses, and Graduate standing; Qualified undergraduates with permission of instructor only.

MATH 512 — Algebraic Structures
Section 001, LEC

Instructor: Griess Jr,Robert L; homepage

WN 2007
Credits: 3
Reqs: BS

Textbook: Abstract Algebra, latest edition (there are at least three editions)David S. Dummit, Richard M. Foote

This course will cover introductory topics in group theory and ring theory with emphasis on mathematical rigor. MATH 312 and MATH 412 give different introductions to abstract algebra. A MATH 512 student should have experience with writing proofs and know some linear algebra (one of our introductory courses will suffice) since I use linear algebra for examples. Subgroups, subrings and quotients. Homomorphism theorems. Permutation representations for groups. Symmetric and alternating groups. Ideals and modules for rings. Composition series, nilpotence, solvability, simplicity. Sylow theorems for finite groups. Matrix rings, idempotents, polynomial rings, rings of operators, factorizations, geometry. Field theory. Examples will accompany the theory.

Advisory Prerequisite: MATH 451 or 513 or permission of instructor.

MATH 513 — Introduction to Linear Algebra
Section 001, LEC

Instructor: Winter,David J; homepage

WN 2007
Credits: 3
Reqs: BS

Credit Exclusions: Two credits granted to those who have completed MATH 214, 217, 417, or 419.

This is an introduction to the theory of abstract vector spaces and linear transformations. The emphasis is on concepts and proofs with some calculations to illustrate the theory. For students with only the minimal prerequisite, this is a demanding course; at least one additional proof-oriented course e.g., MATH 451 or 512) is recommended. Topics are selected from: vector spaces over arbitrary fields (including finite fields); linear transformations, bases, and matrices; eigenvalues and eigenvectors; applications to linear and linear differential equations; bilinear and quadratic forms; spectral theorem; Jordan Canonical Form. MATH 419 covers much of the same material using the same text, but there is more stress on computation and applications. MATH 217 is similarly proof-oriented but significantly less demanding than MATH 513. MATH 417 is much less abstract and more concerned with applications. The natural sequel to MATH 513 is 593. Math 513 is also prerequisite to several other courses (MATH 537, 551, 571, and 575) and may always be substituted for MATH 417 or 419.

Advisory Prerequisite: MATH 412 or equivalent experience with abstract mathematics

MATH 521 — Life Contingencies II
Section 001, LEC

Instructor: Young,Virginia R; homepage

WN 2007
Credits: 3
Reqs: BS

Background and Goals: This course extends the single decrement and single life ideas of MATH 520 to multi-decrement and multiple-life applications directly related to life insurance. The sequence MATH 520-521 covers the Part 4A examination of the Casualty Actuarial Society and covers the syllabus of the Course 150 examination of the Society of Actuaries. Concepts and calculation are emphasized over proof. Content: Topics include multiple life models — joint life, last survivor, contingent insurance; multiple decrement models — disability, withdrawal, retirement, etc.; and reserving models for life insurance. This corresponds to chapters 7-10, 14, and 15 of Bowers et al.

Alternatives: MATH 522 (Act. Theory of Pensions and Soc. Sec) is a parallel course covering mathematical models for prefunded retirement benefit programs.

Subsequent Courses: none

Advisory Prerequisite: MATH 520 or permission of instructor.

MATH 523 — Risk Theory
Section 001, LEC

Instructor: Moore,Kristen S; homepage

WN 2007
Credits: 3
Reqs: BS

Risk management is of major concern to all financial institutions and is an active area of modern finance. This course is relevant for students with interests in finance, risk management, or insurance and provides background for the professional examinations in Risk Theory offered by the Society of Actuaries and the Casualty Actuary Society. Students should have a basic knowledge of common probability distributions (Poisson, exponential, gamma, binomial, etc.) and have at least junior standing. Two major problems will be considered: (1) modeling of payouts of a financial intermediary when the amount and timing vary stochastically over time; and (2) modeling of the ongoing solvency of a financial intermediary subject to stochastically varying capital flow. These topics will be treated historically beginning with classical approaches and proceeding to more dynamic models. Connections with ordinary and partial differential equations will be emphasized. Classical approaches to risk including the insurance principle and the risk-reward tradeoff. Review of probability. Bachelier and Lundberg models of investment and loss aggregation. Fallacy of time diversification and its generalizations. Geometric Brownian motion and the compound Poisson process. Modeling of individual losses which arise in a loss aggregation process. Distributions for modeling size loss, statistical techniques for fitting data, and credibility. Economic rationale for insurance, problems of adverse selection and moral hazard, and utility theory. The three most significant results of modern finance: the Markowitz portfolio selection model, the capital asset pricing model of Sharpe, Lintner and Moissin, and (time permitting) the Black-Scholes option pricing model.

Advisory Prerequisite: MATH 425.

MATH 525 — Probability Theory
Section 001, LEC

Instructor: Fomin,Sergey; homepage

WN 2007
Credits: 3
Reqs: BS

This course is a thorough and fairly rigorous study of the mathematical theory of probability. There is substantial overlap with MATH 425, but here more sophisticated mathematical tools are used and there is greater emphasis on proofs of major results. MATH 451 is preferable to MATH 450 as preparation, but either is acceptable. Topics include the basic results and methods of both discrete and continuous probability theory. Different instructors will vary the emphasis between these two theories. EECS 501 also covers some of the same material at a lower level of mathematical rigor. MATH 425 is a course for students with substantially weaker background and ability. MATH 526, STATS 426, and the sequence STATS 610-611 are natural sequels.

Advisory Prerequisite: STATS,MATH 451 (strongly recommended). MATH 425/STATS 425 would be helpful.

MATH 526 — Discrete State Stochastic Processes
Section 001, LEC

Instructor: Ludkovski,Michael; homepage

WN 2007
Credits: 3
Reqs: BS

Background and Goals: The theory of stochastic processes is concerned with systems which change in accordance with probability laws. It can be regarded as the 'dynamic' part of statistic theory. Many applications occur in physics, engineering, computer sciences, economics, financial mathematics and biological sciences, as well as in other branches of mathematical analysis such as partial differential equations. The purpose of this course is to provide an introduction to the many specialized treatise on stochastic processes. Most of this course is on discrete state spaces. It is a second course in probability which should be of interest to students of mathematics and statistics as well as students from other disciplines in which stochastic processes have found significant applications. Special efforts will be made to attract and interest students in the rich diversity of applications of stochastic processes and to make them aware of the relevance and importance of the mathematical subtleties underlying stochastic processes.

Content: The material is divided between discrete and continuous time processes. In both, a general theory is developed and detailed study is made of some special classes of processes and their applications. Some specific topics include generating functions; recurrent events and the renewal theorem; random walks; Markov chains; limit theorems; Markov chains in continuous time with emphasis on birth and death processes and queueing theory; an introduction to Brownian motion; stationary processes and martingales. Significant applications will be an important feature of the course.

Coursework: weekly or biweekly problem sets and a midterm exam will each count for 30% of the grade. The final will count for 40%.

Advisory Prerequisite: MATH 525 or EECS 501

MATH 526 — Discrete State Stochastic Processes
Section 002, LEC

Instructor: Egami,Masahiko; homepage

WN 2007
Credits: 3
Reqs: BS

Background and Goals: The theory of stochastic processes is concerned with systems which change in accordance with probability laws. It can be regarded as the 'dynamic' part of statistic theory. Many applications occur in physics, engineering, computer sciences, economics, financial mathematics and biological sciences, as well as in other branches of mathematical analysis such as partial differential equations. The purpose of this course is to provide an introduction to the many specialized treatise on stochastic processes. Most of this course is on discrete state spaces. It is a second course in probability which should be of interest to students of mathematics and statistics as well as students from other disciplines in which stochastic processes have found significant applications. Special efforts will be made to attract and interest students in the rich diversity of applications of stochastic processes and to make them aware of the relevance and importance of the mathematical subtleties underlying stochastic processes.

Content: The material is divided between discrete and continuous time processes. In both, a general theory is developed and detailed study is made of some special classes of processes and their applications. Some specific topics include generating functions; recurrent events and the renewal theorem; random walks; Markov chains; limit theorems; Markov chains in continuous time with emphasis on birth and death processes and queueing theory; an introduction to Brownian motion; stationary processes and martingales. Significant applications will be an important feature of the course.

Coursework: weekly or biweekly problem sets and a midterm exam will each count for 30% of the grade. The final will count for 40%.

Advisory Prerequisite: MATH 525 or EECS 501

MATH 542 — Financial Engineering Seminar I
Section 001, LEC

Instructor: Keppo,Jussi Samuli; homepage

WN 2007
Credits: 3

Outline: The objective of the course is to present arbitrage theory and its applications to pricing for financial derivatives. The main mathematical tool used in the course is the theory of stochastic differential equations (SDEs). We treat basic SDE techniques, including martingales, Feynman-Kac representation, and the Kolmogorov equations. We also consider, in some detail, stochastic optimal control.

The mathematical models are applied to the arbitrage pricing of financial instruments. We consider Black-Scholes theory and its extensions, as well as incomplete markets. We cover several interest rate theories.

Course Material:

  • Lecture notes
  • Björk, T.: Arbitrage Theory in Continuous Time, 2nd edition, Oxford University Press.

Homework Problems: Students are expected to solve the selected homework problems. Homework must be submitted individually.

Grading: Exam 60% (closed book; midterm 20% and final 40%), homework 40%. If you believe an exam question was graded in error and wish to have the exam regraded, you must submit the exam to the GSI together with a written explanation for requesting the regrade. This must be done within one week from the date the exam was returned.

Schedule:

 
Date Topic 					Chapters 
1/10 Introduction and binomial trees 		1, 2, 3 
1/17 Stochastic calculus 			4, 5 
1/24 Arbitrage pricing 				6, 7 
1/31 Hedging 					8, 9 
2/7  Several underlying assets 			13 
2/14 Incomplete markets 			15 
2/21 Dividends and foreign exchange rates 	16, 17 
2/28 Spring break 
3/7  Midterm 
3/14 Exotic options 				18 
3/21 Optimal portfolio selection 		19 
3/28 Bonds and interest rates	 		20 
4/4  Short rate models 				21, 22 
4/11 Short rate models and review 		21, 22 
4/18 Final   

Advisory Prerequisite: MATH,IOE 453 or MATH 423. Business School students: FIN 580 or 618 or BA 855

MATH 555 — Introduction to Functions of a Complex Variable with Applications
Section 001, LEC

Instructor: Laza,Radu Mihai; homepage

WN 2007
Credits: 3
Reqs: BS

Background and Goals: This course is an introduction to the theory of complex valued functions of a complex variable with substantial attention to applications in science and engineering. Concepts, calculations, and the ability to apply principles to physical problems are emphasized over proofs, but arguments are rigorous. The prerequisite of a course in advanced calculus is essential. This course is a core course for the Applied and Interdisciplinary Mathematics (AIM) graduate program. Content: Differentiation and integration of complex valued functions of a complex variable, series, mappings, residues, applications. Evaluation of improper real integrals, fluid dynamics. This corresponds to Chapters 1-9 of Churchill.

Alternatives: MATH 596 (Analysis I (Complex)) covers all of the theoretical material of MATH 555 and usually more at a higher level and with emphasis on proofs rather than applications.

Subsequent Courses: MATH 555 is prerequisite to many advanced courses in science and engineering fields.

Advisory Prerequisite: MATH 451 or equivalent experience with abstract mathematics

MATH 557 — Methods of Applied Mathematics II
Section 001, LEC
Asymptotic Methods

Instructor: Doering,Charles R; homepage

WN 2007
Credits: 3
Reqs: BS

Text: Asymptotic Analysis, J.D. Murray (Springer)

Audience: Applied mathematics, science & engineering graduate students. Math 557 is a core course for the graduate program in Applied & Interdisciplinary Mathematics.

Background and Goals: We often try to understand phenomena by formulating and analyzing models that consist of differential equations with initial and/or boundary conditions. Often — and especially if the equations are nonlinear — explicit solutions are not available. And even if we are clever enough or lucky enough to find an explicit formula or integral representation, it may still be difficult to extract useful information. In practice we frequently study such problems via approximate solutions obtained by asymptotic analysis. Asymptotic analysis is a collection of mathematical methods developed to systematically produce accurate approximations together with rigorous error estimates. Asymptotic approximations can be remarkably accurate and useful. This course is an introduction to asymptotic analysis with a focus on differential equations. Substantial attention is given to problems arising in the context of scientific and engineering applications. Murray's compact text will be covered during about the first 2/3 of the course, and in the remaining time we will develop examples from fluid dynamics, chemical reaction kinetics, etc. The prerequisite of a complex variables course such as MATH 555 is absolutely essential. (Note: MATH 556 is not a prerequisite for MATH 557.) The material in MATH 557 is itself prerequisite to many advanced topics in applied mathematics, science and engineering.

Course content: Asymptotic sequences and (divergent) series; asymptotic expansions of integrals and Laplace's method; the methods of steepest descents and stationary phase; asymptotic evaluation of inverse Fourier and Laplace transforms; asymptotic solutions for linear (non-constant coefficient) differential equations; WBK expansions; singular perturbation theory; boundary, initial and internal layers; method of multiple scales and nonlinear oscillations; selected applications.

Homework, tests & grading: Attendance and participation in lectures is expected. Grades based on weekly or biweekly problem assignments (60%) and a comprehensive final exam (40%).

Advisory Prerequisite: MATH 217, 419, or 513; 451 and 555.

MATH 561 — Linear Programming I
Section 001, LEC

Instructor: Cohn,Amy Ellen Mainville

WN 2007
Credits: 3

Background and Goals: A fundamental problem is the allocation of constrained resources such as funds among investment possibilities or personnel among production facilities. Each such problem has as it's goal the maximization of some positive objective such as investment return or the minimization of some negative objective such as cost or risk. Such problems are called Optimization Problems. Linear Programming deals with optimization problems in which both the objective and constraint functions are linear (the word "programming" is historical and means "planning" rather that necessarily computer programming). In practice, such problems involve thousands of decision variables and constraints, so a primary focus is the development and implementation of efficient algorithms. However, the subject also has deep connections with higher-dimensional convex geometry. A recent survey showed that most Fortune 500 companies regularly use linear programming in their decision making. This course will present both the classical and modern approaches to the subject and discuss numerous applications of current interest.

Content: Formulation of problems from the private and public sectors using the mathematical model of linear programming. Development of the simplex algorithm; duality theory and economic interpretations. Postoptimality (sensitivity) analysis; algorithmic complexity; the ellipsoid method; scaling algorithms; applications and interpretations. Introduction to transportation and assignment problems; special purpose algorithms and advanced computational techniques. Students have opportunities to formulate and solve models developed from more complex case studies and use various computer programs.

Alternatives: Cross-listed as IOE 510.

Subsequent Courses: IOE 610 (Linear Programming II) and IOE 611 (Nonlinear Programming)

Advisory Prerequisite: MATH 217, 417, or 419

MATH 563 — Advanced Mathematical Methods for the Biological Sciences
Section 001, LEC
Advanced Mathematical Methods For the Biological Sciences

Instructor: Forger,Daniel Barclay; homepage

WN 2007
Credits: 3
Reqs: BS

Grading: 50% Final Project, 40% problem sets and computer labs, 10% class participation

Background and Goals: Many processes within the body are complex. Mathematical models can help understand these processes by piecing together diverse data, determining underlying principles and predicting future behavior. The goal of this course will be to teach students how to take real biological data, convert it to a system of equations and simulate and/or analyze these equations. All theory will be presented in the context of trying to understand specific processes within the human body.

Content: Models and analysis will be presented in three main topics: Computational Neuroscience, Cell Biology and Fluid Flow in the Human Body. Subtopics include: computation within a single neuron, visual signal processing in the retina and brain, reaction-diffusion and stochasticity in genetic networks, propagation of pulses in arteries, "heart attacks" and the spread of urinary tract infections. Models will typically use partial differential equations. Consideration will be given in the problem sets and course project to interdisciplinary student backgrounds. Teamwork will be encouraged.

Text: Mathematical Physiology, Keener and Sneyd

The basic readings are shown on the right in brackets. These readings will be supplemented by lecture notes and papers. Chapters refer to Keener and Sneyd.

Overview of topics, why model?

Introduction to Mathematica and numerical computing

Topic 1: Computational Neuroscience

  • Passive electric flow in dendrites [ch. 8]
  • Introduction to the Hodgkin-Huxley model [ch. 4]
  • Active spread of electrical signals [ch. 9]
  • Neuroscience computer lab
  • Signal processing in the retina [ch. 22]
  • Large scale modeling of vision [papers of Shelley and McLaughlin]

Topic 2: Cell Biology

  • Reaction diffusion and calcium waves [ch. 12]
  • Stochasticity of biological networks and Fokker-Planck [papers by Elston and notes]
  • Computer Lab

Topic 3: Fluid Flow in the Human Body

  • System wide modeling of the circulatory system [ch. 15.1-15.7]
  • Signal propagation in the heart [ch. 11]
  • Pulse propagation in arteries [ch. 15.8 and notes]
  • Peristaltic pumping in the developing heart and urinary tract infections (Shapiro et al. JFM 37:799)
  • Computer Lab

    Topic 4: Student Presentations

    Advisory Prerequisite: Graduate standing.

  • MATH 567 — Introduction to Coding Theory
    Section 001, LEC

    Instructor: Derksen,Hendrikus Gerardus; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    Background and Goals: This course is designed to introduce math majors to an important area of applications in the communications industry. From a background in linear algebra it will cover the foundations of the theory of error-correcting codes and prepare a student to take further EECS courses or gain employment in this area. For EECS students it will provide a mathematical setting for their study of communications technology.

    Content: Introduction to coding theory focusing on the mathematical background for error-correcting codes. Shannon's Theorem and channel capacity. Review of tools from linear algebra and an introduction to abstract algebra and finite fields. Basic examples of codes such and Hamming, BCH, cyclic, Melas, Reed-Muller, and Reed-Solomon. Introduction to decoding starting with syndrome decoding and covering weight enumerator polynomials and the Mac-Williams Sloane identity. Further topics range from asymptotic parameters and bounds to a discussion of algebraic geometric codes in their simplest form.

    Alternatives: none Subsequent Courses: Math 565 (Combinatorics and Graph Theory) and Math 556 (Methods of Applied Math I) are natural sequels or predecessors. This course also complements Math 312 (Applied Modern Algebra) in presenting direct applications of finite fields and linear algebra.

    Advisory Prerequisite: One of MATH 217, 419, 513.

    MATH 571 — Numerical Methods for Scientific Computing I
    Section 001, LEC

    Instructor: Viswanath,Divakar; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    This course is an introduction to numerical linear algebra, which is at the foundation of much of scientific computing. Numerical linear algebra deals with

    1. the solution of linear systems of equations,
    2. computation of eigenvalues and eigenvectors, and
    3. least squares problems.

    We will study accurate, efficient, and stable algorithms for matrices that could be dense, or large and sparse, or even highly ill-conditioned. The course will emphasize both theory and practical implementation.

    Textbook: L.N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM.

    From the preface: "The field of numerical linear algebra is more beautiful, and more fundamental, than its name may suggest... It is here that one finds the essential ideas that every mathematical scientist needs to know to work effectively with matrices and vectors."

    Topics:

    1. background, orthogonal matrices, vector and matrix norms, singular value decomposition;
    2. least squares problems, QR factorization, normal equations, projection matrices, Gram-Schmidt orthogonalization, Householder triangularization;
    3. stability, condition number, floating point arithmetic, backward error analysis;
    4. iterative methods, classical iterative methods (Jacobi, Gauss-Seidel, SOR), conjugate gradient method, Lánczos iteration, Krylov subspace methods, Arnoldi iteration, GMRES, preconditioning;
    5. direct methods, Gaussian elimination, LU factorization, pivoting, Cholesky factorization;
    6. eigenvalues and eigenvectors, Schur factorization, reduction to Hessenberg and tridiagonal form, power method, QR algorithm.

    Advisory Prerequisite: MATH 214, 217, 417, 419, or 513; and one of MATH 450, 451, or 454.

    MATH 572 — Numerical Methods for Scientific Computing II
    Section 001, LEC

    Instructor: Karni,Smadar; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    Background and Goals: This is one of the basic courses for students beginning study towards the Ph.D. degree in mathematics. Graduate students from engineering and science departments and strong undergraduates are also welcome. The course is an introduction to numerical methods for solving ordinary differential equations and hyperbolic and parabolic partial differential equations. Fundamental concepts and methods of analysis are emphasized. Students should have a strong background in linear algebra and analysis, and some experience with computer programming. This course is a core course for the Applied and Interdisciplinary Mathematics (AIM) graduate program. Content: Content varies somewhat with the instructor. Numerical methods for ordinary differential equations; Lax's equivalence theorem; finite difference and spectral methods for linear time dependent PDEs: diffusion equations, scalar first order hyperbolic equations, symmetric hyberbolic systems.

    Alternatives: There is no real alternative; MATH 471 (Intro to Numerical Methods) covers a small part of the same material at a lower level. MATH 571 and 572 may be taken in either order.

    Subsequent Courses: MATH 671 (Analysis of Numerical Methods I) is an advanced course in numerical analysis with varying topics chosen by the instructor.

    Advisory Prerequisite: MATH 214, 217, 417, 419, or 513; and one of MATH 450, 451, or 454.

    MATH 592 — Introduction to Algebraic Topology
    Section 001, LEC

    Instructor: Scott,G Peter; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    This is a first course in algebraic topology. The topics include the fundamental group, covering spaces, simplicial complexes, graphs and trees, applications to group theory, singular and simplicial homology, Eilenberg-Steenrod axioms, and Brouwer's and Lefschetz' fixed-point theorems. This covers the material from this area that appears on the topology qualifying review exam.

    Text: "Algebraic Topology" by Allen Hatcher, Cambridge University Press

    As an additional (non-required) text I recommend:

    "Elements of Algebraic Topology" by James R. Munkres, Addison-Wesley

    Advisory Prerequisite: MATH 591.

    MATH 594 — Algebra II
    Section 001, LEC

    Instructor: Stafford,J Tobias; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    Background and Goals: This is one of the two basic algebra courses for students beginning study towards a Ph.D. in mathematics (the other being MATH 593). Between them they provide a preparation for the Qualifying Review Exam in Algebra.

    Contents: The course will cover the basic theory of groups and fields (Galois theory). A comprehensive description can be found on the web page for the qualifying review exams:

    http://www.math.lsa.umich.edu/graduate/qualifiers/index.shtml

    but in outline is as follows:

    1. Group theory: Groups acting on sets, Sylow's theorems, solvable and nilpotent groups, free groups and presentations.

    2. Field extensions: algebraic and transcendental extensions, separable and purely inseparable extensions, norms, algebraic closures.

    3. Galois theory: splitting fields, the Galois correspondence, solution of equations by radicals and computation of Galois groups.

    Texts: There will be no formal set text, but if you want to read ahead, I recommend:

    M. Artin, Algebra, Prentice Hall, Englewood Cliffs, N.J 1991.

    This does not cover everything in the course, but is an interesting text. For more detailed books, try

    P. M. Cohn, Basic Algebra I,II or N. Jacobson, Basic Algebra I,II

    or more specialist books like:

    I. Macdonald, The theory of groups; J. Rotman, Group theory; I. T. Adamson, Introduction to field theory; I. Stewart, Galois theory.

    Advisory Prerequisite: MATH 593.

    MATH 597 — Analysis II
    Section 001, LEC

    Instructor: Duren,Peter L; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    Textbook: Gerald B. Folland, "Real Analysis: Modern Techniques and Their Applications", Second Edition, Wiley-Interscience, 1999.

    Contents: Lebesgue measure and integration theory, with applications to selected topics in functional analysis, Fourier analysis, and probability. We will aim to cover the topics listed in the Math Department syllabus for the course, plus some optional material as time permits.

    Prerequisites: Basic undergraduate analysis MATH 451 or equivalent) is essential. Students are assumed to be familiar with limits and continuity, sequences and series, uniform convergence, Riemann integrals, etc.

    Advisory Prerequisite: MATH 451 and 513.

    MATH 605 — Several Complex Variables
    Section 001, LEC
    Introduction to Several Complex Variables.

    Instructor: Stensønes,Berit; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    We will cover the basic topics in Several Complex Variables. Starting with a careful study of sub harmonic and plurisubharminic functions. Next we will move on to looking at several notions of pseudo convexity including solving the so called Levi problem. From here we will move on to the topic of envelopes of holomorphy. Finally we shall see how one can use integral kernels so solve the d- bar equation.

    We will not use one textbook but several, depending on the topic we are covering at the time.

    Among the books we will use are:" An introduction to Several Complex Variable." Lars Hormader, "Function theory of Several Complex Variables." Steven G. Krantz " Lectures on counterexamples in Several Complex Variables" John Erik Fornaess and Berit Stensones

    Advisory Prerequisite: MATH 596 and 597. Graduate standing.

    MATH 615 — Commutative Algebra II
    Section 001, LEC
    commutative Noetherian rings

    Instructor: Hochster,Melvin; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    The course will deal with several distinct topics in the theory of commutative Noetherian rings. These will include:

    1. The structure of complete local rings, including the structure of homomorphisms of complete local rings.

    2. Grobner bases.

    3. Aspects of the theory of tight closure.

    4. The method of reduction of problems to positive characteristic.

    There will be an emphasis throughout on the discussion of open questions and possible approaches to them.

    The prerequisite is MATH 614. Occasionally other background will be needed, and the necessary material will be sketched.

    There will be no text: lecture notes will be provided.

    Advisory Prerequisite: MATH 614 or permission of instructor. Graduate standing.

    MATH 623 — Computational Finance
    Section 001, LEC

    Instructor: Conlon,Joseph G; homepage

    WN 2007
    Credits: 3

    This course is a course on mathematical finance with an emphasis on numerical and statistical methods. It is assumed that the student is familiar with basic theory of arbitrage pricing, equity and fixed income (interest rate) derivatives in discrete and continuous time. The course will focus on numerical implementations of these models as well as statistical methods for calibration, i.e., obtaining the parameters of the models. Specific topics include finite-difference methods, trees and lattices and Monte Carlo simulations with extensions.

    Texts:

    1. James and Webber: Interest Rate Modelling, Wiley, 2000.
    2. Wilmott, Howison, Dewynne: The Mathematics of Financial Derivatives, Cambridge, 1995.
    3. Jaeckel: Monte Carlo Methods in Finance, Wiley, 2002.

    Advisory Prerequisite: MATH,MATH 316 and MATH 425 or 525.

    MATH 625 — Probability and Random Processes I
    Section 002, LEC

    Instructor: Bayraktar,Erhan; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    A graduate level introduction to probability theory and stochastic processes: measure theory and integration; Kolmogorov Extension Theorem; conditional expectation; characteristic functions; convergence concepts; limit theorems; stochastic processes, Poisson random measures, Brownian motion, Levy processes and martingales.

    Required Textbooks
    Book 1:
    AUTHOR: Williams
    TITLE: Probability with Martingales
    ISBN: 0521406056
    BINDING: paper
    PUBLISHER: Cambridge University Press
    Book 2:
    AUTHOR: Protter and Jacod
    TITLE: Probability Essentials
    ISBN: 3540438718
    BINDING: paper
    PUBLISHER: Springer

    Recommended Textbooks
    Book 1:
    AUTHOR: Varadhan
    TITLE: Probability Theory
    ISBN: 0821828525
    BINDING: paper
    PUBLISHER: Courant Institute of Mathemetical Sciences
    Book 2:
    AUTHOR: Shiryaev
    TITLE: Probability
    ISBN: 0387945490
    BINDING: hard
    PUBLISHER: Springer (Tentative) Syllabus:

    Measure and Integration
    1) Measurable Spaces 		 	 	January	5
    2) Measurable Functions		  	 	  	8
    3) Measures 					 	10
    4) Integration 					 	12
    5) Radon Nikodym Theorem 			 	 	17
    6) Kernels and Product Spaces 			 	19
    
    Probability Spaces
    7) Probability Spaces and Random Var.  	 	 	22
    8) Expectations 				 	 	24
    9) L^p Spaces 					 	26
    10) Information and Determinability 		 		29
    11) Independence 				 		31 
    
    Convergence
    12) Almost Sure Convergence 	 	      February 	2
    13) Convergence in Probability 			 	5
    14) Convergence in L^p 			 	 	7
    15) Weak Convergence 				 	9
    16) Laws of Large Numbers 			 		12
    17) Convergence of Series 			 		14
    18) Central Limit Theorems 			 		16 
    
    Conditioning
    19) Conditional Expectations 			 	19
    20) Conditional Probabilities and Distributions 		21
    21) Midterm 					 	23
    22) Construction of Probability Spaces 	 	  March	5
    23) Special Constructions 			 		7 
    
    Martingales
    24) Filtrations and Stopping Times 		 		9
    25) Martingales 						12
    26) Martingale Transformations 			 	14
    27) Martingale Convergence 			 		16, 19
    28) Martingales in Continuous Time 		 		21
    29) Martingale Inequalities 			 	23
    30) Martingale Characterizations of Wiener 	 		26 
          and Poisson
    31) Regularity of Filtrations 			 	28 
    
    Poisson Random Measures
    32) Random Measures 				 	30
    33) Poisson Random Measures 		 	 April 	2, 4
    34) Transforms and Magnifications 		 		6
    35) Levy Random Measures 			 		9
    36) Poisson Processes 				 	11
    37) Levy Processes 				 	13
    38) Review 					 	16

    Advisory Prerequisite: MATH 597 and Graduate standing.

    MATH 632 — Algebraic Geometry II
    Section 001, LEC
    cohomology of sheaves

    Instructor: Lazarsfeld,Robert K; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    This will be a second-semester course in algebraic geometry. We will focus on one of the most basic and powerful tools in the subject, namely the cohomology of sheaves. This is covered in Chapter III of Hartshorne's text, but we will take a much more concrete and down-to-earth approach than Hartshorne does. Along the way there will be lots of applications, including De Rham's theorem, Bezout's theorem, Noether's AF + BG theorem, etc.

    Advisory Prerequisite: MATH 631 and Graduate standing.

    MATH 635 — Differential Geometry
    Section 001, LEC

    Instructor: Ji,Lizhen; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    Riemannian manifolds are fundamental objects in modern mathematics. Methods and techniques from differential geometry have been used successfully to study problems in topology, analysis, algebraic geometry, Lie group theory et al. For example, the known result that any two maximal compact subgroups of a noncompact semiaimple Lie group are conjugate follows from general properties of manifolds of nonpositive curvature.

    In this course, we will cover basic concepts in differential geometry such as geodesics, the exponential map, connection, various notions of curvature, basic results such as the Rauch comparison theorem, important results relating geometry to topology such as the Meyers theorem. To understand better manifolds of nonpositively curved Riemannian manifolds, CAT(0)-spaces will be studied as well.

    Since Riemannian symmetric spaces and more generally homogeneous Riemannian manifolds are particularly important examples of Riemannian manifolds, they will be covered too.

    Besides these manifolds from Lie groups, smooth projective varieties provide important class of Kahler manifolds. In the latter part of the course, we will discuss complex differential geometry.

    If time permits, we will also discuss some topics from the theory of transformation groups.

    The basic reference is "Riemannian Geometry" by M.P. Do Carmo, published by Brikhauser, and a recommended book on complex manifolds is "Complex differential geometry" by Fangyang Zheng, published by AMS-IP.

    Advisory Prerequisite: MATH 537 or permission of instructor. Graduate standing.

    MATH 636 — Topics in Differential Geometry
    Section 001, LEC
    Complex and Symplectic Geometry.

    Instructor: Burns Jr,Daniel M; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    We will study special examples of complex algebraic varieties, emphasizing those which are particularly interesting to both algebraic geometers and symplectic geometers. These include the hyperk _ahler manifolds of Calabi, and the Calabi-Yau manifolds. We will also study the basics of symplectic manifolds, including special cases of Mirror Symmetry, but especially locally toric manifolds and their complex analytic and Hamiltonian properties. K3 surfaces will be studied from both perspectives.

    This is a continuation of Math 703: Hodge Theory from the Fall term. In particular, we will assume the results of Hodge's representation of cohomology classes by harmonic forms. Every effort will be made to make the course accessible to students who want to join the course this term. In particular, results used from the first term will be quoted explicitly, though they won't necessarily be proved again. There are several books which would be useful as references. I would recommend the following items:

    1. C. Voisin, Hodge Theory and Complex Algebraic Geometry, vols I and II, Cambridge University Press 2004.

    2. C. Voisin, Recent progress in Kaehler and complex algebraic geometry, in Proc. IV Eur. Cong. Math., Stockholm 2004, pp. 787-807, Eur. Math. Soc. 2005.

    3. P. Griffiths, Hodge theory and geometry, Bull. London Math. Soc. 36 (2004), 721-757.

    4. M. Gross, D. Huybrechts and D. Joyce, Calabi-Yau Manifolds and Related Geometries, Springer Verlag 2003.

    Advisory Prerequisite: MATH 635 and Graduate standing.

    MATH 637 — Lie Groups
    Section 001, LEC

    Instructor: Prasad,Gopal; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    This will be a comprehensive introduction to the theory of Lie groups. I will prove the basic results, describe the structure of nilpotent and solvable Lie groups. I will present the results on tori in compact Lie groups and use them to describe their topological and group-theoretic structure and their classification. I will study noncompact semi-simple Lie groups in considerable detail: Look at their maximal compact subgroups, prove their conjugacy, and prove the Cartan, Iwasawa (and possibly Bruhat) decompositions.

    I will assume some familiarity with differentiable manifolds. Results on Lie algebras will be used. I will give precise definitions, statements and references. Prior knowledge of Lie Algebras is therefore not required. The course should be useful for anyone interested in pursuing Differential or Algebraic Geometry, Topology, Representation Theory or Number Theory. I specially recommend it to those currently taking Professor Lizen Ji's Math 612 course.

    Advisory Prerequisite: MATH 635 and Graduate standing.

    MATH 638 — Introduction to Representation Theory
    Section 001, LEC

    WN 2007
    Credits: 3
    Reqs: BS

    A course on representation theory. Content varies by term and instructor.

    Advisory Prerequisite: MATH 597 and Graduate standing.

    MATH 650 — Fourier Analysis
    Section 001, LEC

    Instructor: Gilbert,Anna Catherine; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    Textbook: Stephane Mallat, A Wavelet Tour of Signal Processing.

    Website: http://www.math.lsa.umich.edu/_annacg/courses/m650-w07/

    Appointments will only be accepted via email with advance notice of one business day.

    Grading: The course grade will be determined as an average of the homework score (50%) and the final project (50%).

    Final Project: I will divide the class into four groups, each group containing students from different departments. Each group will present a final project based upon a paper we choose together. The report will include an implemention of any algorithms presented in the paper, a presentation of some example computations, and a discussion of theoretical results in the paper. The group will have 25 minutes to present the report to the rest of the class.

    Project presentation dates: Friday, April 13 and Monday, April 16.

    Homework policy: There will be approximately five homework assignments. Homework will be assigned on Friday and collected two weeks hence. Homework will be graded on a simple 3 point scale. You are encouraged to collaborate with other students to solve homework problems, but each student must write up and turn in his or her own assignment independently. No late homework will be accepted (homework must be turned in during class to obtain credit).

    Background and Goals: This course will cover the modern renaissance in Fourier analysis that is wavelet analysis and its applications. We will begin with Fourier analysis on the line and in the plane and move to discrete settings with Fourier analysis and its applications to signal processing.

    Next, we will spend a significant portion of the course on the development of orthonormal wavelet bases for the line and the plane, including compactly supported wavelets, the discrete wavelet transform, and multiresolution analysis. The final part of the course will include the application of wavelet analysis to three scientific areas: approximation theory (mathematics), signal estimation (statistics), and to transform coding (electrical engineering).

    Content: An approximate list of topics follows. (1) Fourier analysis in R, Z, Z/N
    (2) Multiresolution analysis and orthonormal wavelet bases
    (3) Compactly supported wavelets
    (4) Discrete wavelet transform
    (5) Wavelet packets and redundant transforms
    (6) Approximation
    (7) Estimation
    (8) Compression

    Advisory Prerequisite: MATH 596, 602, and Graduate standing.

    MATH 657 — Nonlinear Partial Differential Equations
    Section 001, LEC

    Instructor: Wu,Sijue; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    References:
    L.C. Evans: Partial Differential Equations. Graduate Studies in Mathematics, 19. AMS 1998. ISBN: 0-8218-0772-2
    R. C. McOwen: Partial Differential Equations
    J. Smoller: Shock waves and reaction- diffusion equations
    Whitham: Linear and nonlinear waves

    Partial Differential Equations are mathematical structures for models in science and technology. It is of fundamental importance in physics, biology and engineering design with connections to analysis, geometry, probability and many other subjects. The goal of this course is to introduce students (both pure and applied) to the basic concepts and methods that mathematicians have developed to understand and analyze the properties of solutions to partial differential equations.

    Topics covered include linear functional analysis, differential calculus method, semigroup method, and their applications to linear and nonlinear elliptic equations, parabolic equations, and wave equations.

    Course work: Attend lectures and complete several problem sets.

    Advisory Prerequisite: MATH 656.

    MATH 669 — Topics in Combinatorial Theory
    Section 001, LEC
    Combinatorics of Perfect Matchings

    Instructor: Speyer,David E

    WN 2007
    Credits: 3
    Reqs: BS

    Prerequisites: Comfort with Linear Algebra

    Student work expected: I will give problem sets every other week.

    Summary: Let G be a graph, then a perfect matching of G is a collection of edges of G such that every vertex lies on exactly one edge. The study of perfect matchings goes back to McMahon in the nineteenth century and goes forward to current papers of Richard Kenyon and recent Fields medalist Andrei Okounkov. Perfect matchings occur in applied mathematics when studying the entropy of large carbon structures or the formation of crystals and, more generally, form an excellent test case for methods of statistical mechanics. In pure mathematics, perfect matchings can be related to the combinatorics of Young Tableux and to the enumerative geometry of curves in three-folds.

    The first question to ask about perfect matchings is how many there are. We will introduce several techniques for answering this question in various cases. Next, we will show how to study the structure of the collection of perfect matchings, showing that it is possible to move between any two matchings via a series of simple restructuring moves and we will bound the number of moves which are needed. To do this, we will show how to put a lattice structure on the collection of perfect matchings of a planar graph and exploit it. We will show how to encode the perfect matchings of a graph into a generating function from which most statistics of matchings are easily extracted. In particular, we will be able to explain why the number of perfect matchings of families of plane graphs are often perfect powers. If time permits, we will discuss how this generating function can be used to give combinatorial proofs of various Laurentness theorems.

    We will then shift from studying exact enumerative questions to studying the statistical properties of a randomly chosen perfect matching in a large graph. We will begin by presenting algorithms to efficiently and uniformly sample from the space of perfect matchings. We will then describe Kenyon and Okounkov's elegant description of the local properties of a random matching in terms of amoebae of algebraic curves (which we will define).

    For most of the course, we will use nothing more than basic combinatorial arguments and some linear algebra. In the last weeks, we will use some standard facts from complex analysis.

    Advisory Prerequisite: MATH. 565, 566, or 664 or permission of instructor. Graduate standing.

    MATH 671 — Analysis of Numerical Methods I
    Section 001, LEC
    Particle Methods in Scientific Computing

    Instructor: Krasny,Robert; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    Topics: fast Fourier transform, potential theory, particle-particle method, particle-mesh methods (PIC, P3M), particle-cluster methods, Barnes-Hut treecode, Greengard-Rokhlin fast multipole method, Ewald summation, time permitting: radial basis functions

    Text: no required text, lecture notes will be available online, however, a recommended text is "Computer Simulation Using Particles", R.W. Hockney & J.W. Eastwood (1988) Taylor & Francis, ISBN: 0852743920

    Course Grade: based on homework

    The course will survey particle methods in scientific computing, an active area in applications and research. Particle methods are an alternative to traditional mesh-based methods for solving differential equations. The course will examine fast methods, i.e. methods that require fewer operations than the obvious straightforward approach. A well-known example is the fast Fourier transform (FFT) which reduces the operation count for computing the discrete Fourier transform of a vector of length N from O(N^2) to O(N log N). This has a huge impact in practice, and as a result, the FFT is a basic tool in signal processing and spectral analysis. We'll start by deriving an FFT algorithm and look at applications to interpolation and boundary value problems. Much of the course will deal with methods for evaluating the potential energy and forces due to long-range particle interactions, an important component in molecular dynamics and Monte-Carlo simulations. Applications arise in many fields including astrophysics (gravitational interaction), chemistry, materials science, and plasma dynamics (electrostatic interaction), and fluid dynamics (vortex interaction). In a system with N particles, O(N^2) operations are required to evaluate the pairwise interactions by direct summation. The FFT can be applied when the particles are uniformly spaced, but different ideas are needed to gain a speedup to O(N log N) for nonuniform particle distributions. First we'll consider particle-mesh algorithms such as particle-in-cell (PIC) and P3M (Hockney-Eastwood). We'll also derive the Ewald summation technique and consider particle-mesh Ewald (Darden-York-Pedersen). Then we'll discuss particle-cluster algorithms including hierarchical treecodes (Barnes-Hut) and the fast multipole method (Greengard-Rokhlin). We'll derive the spherical harmonics expansion for the Coulomb potential on which these methods are based. There's great interest in optimizing the performance of particle-cluster algorithms and I'll present some recent developments.

    Advisory Prerequisite: MATH. 571, 572, or permission of instructor. Graduate standing.

    MATH 677 — Diophantine Problems
    Section 001, LEC

    Instructor: Wooley,Trevor D; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    Text: Class notes and problem sheets will be self-contained and comprehensive. Some standard sources:

    The Hardy-Littlewood method (R. C. Vaughan, Cambridge Tract No. 125, Cambridge University Press, 1997), Analytic methods for Diophantine equations and Diophantine inequalities (H. Davenport, 2nd Edition, Cambridge Math. Library, Cambridge University Press, Cambridge, 2005), Diophantine Inequalities (R. C. Baker, London Mathematical Society Monographs, No. 1, Oxford University Press, 1986),

    About the course: The ancient mystic art of diophantine problems, practiced by the ancient Greeks and Egyptians, burnished by the brilliant Gauss, and built into a magnificent edifice of modern mathematical achievement by the master craftsmen of the 19th and 20th Centuries, most recently with work of Wiles on Fermat's Last Theorem and Gowers, Green and Tao on systems of quasi-linear equations .... Math 677 takes you on an epic journey through the fertile valleys of this subject.

    Content: The course begins with an introduction to exponential sums and the Hardy-Littlewood method, with a discussion of Weyl's inequality, Hua's Lemma, and the simplest treatment of Waring's problem and diagonal diophantine equations (with a discussion of the associated p-adic solubility problem). We discuss also distribution modulo 1 of sequences of the shape _nk, and related problems. Next we discuss Freeman's variant of the Davenport-Heilbronn method for solving diagonal diophantine inequalities.

    The second half of the course will be devoted to two modern applications of the circle method that intersect with arithmetic combinatorics and with arithmetic geometry. In one direction we will provide an account of Szemeredi's Theorem on the existence of long arithmetic progressions via a variant of Gowers' higher degree uniformity methods interpreted by means of the circle method. In a second direction we will combine the circle method with some descent arguments from arithmetic geometry so as to analyse the Hasse principle (and Brauer-Manin obstruction) for some low dimensional varieties via the circle method. If time permits, we may discuss the Green-Tao theorem on long arithmetic progressions in the primes, and further descent problems.

    Exams: There will be no exams.

    Coursework: Approximately one assignment every two weeks, containing both easier and more challenging problems.

    Advisory Prerequisite: MATH 575 and Graduate standing.

    MATH 684 — Recursion Theory
    Section 001, LEC
    computability and provability

    Instructor: Blass,Andreas R; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    This course is about two fundamental concepts of mathematics: computability and provability.

    The first topic to be covered is a precise definition of computability in principle, where "in principle" means that a computation must give a result after finitely many steps but we place no specific bounds on the number of steps or the amount of memory used. In fact, several precise definitions of computability have been proposed, but they all turn out to be equivalent. We shall discuss a few of them and develop the tools needed to prove their equivalence. We shall also discuss the connection between computability and definability, giving specific examples of definable but uncomputable functions.

    The second part of the course, building on the concepts and techniques of the first part, explores the limits of provability in axiomatic systems. It includes the proof of Goedel's incompleteness theorems — — that reasonable axiomatic systems cannot exactly capture truth, even in the limited domain of the arithmetic of natural numbers, and that they cannot prove their own consistency.

    The final part of the course is a deeper study of computability, and in particular a classification of uncomputable functions according to a criterion of the form "if we had access to values of f then we could compute values of g." The analysis of this relation has led to some deep and elegant arguments, the simplest of which will be covered in this course.

    Recommended book: "Fundamentals of Mathematical Logic" by Peter Hinman.

    Advisory Prerequisite: MATH 681 or equivalent.

    MATH 697 — Topics in Topology
    Section 001, LEC

    WN 2007
    Credits: 3
    Reqs: BS

    An intermediate level topics course.

    Advisory Prerequisite: Graduate standing.

    MATH 700 — Directed Reading and Research
    Section 001, IND

    WN 2007
    Credits: 1 — 3

    Designed for individual students who have an interest in a specific topic (usually that has stemmed from a previous course). An individual instructor must agree to direct such a reading, and the requirements are specified when approval is granted.

    Advisory Prerequisite: Graduate standing and permission of instructor.

    MATH 704 — Topics in Complex Function Theory II
    Section 001, LEC
    analysis and geometry of fractal spaces

    Instructor: Bonk,Mario; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    In this course we will discuss the analysis and geometry of fractal spaces. This is intended as a continuation and complement of a similar course that I taught in Winter 2006. The knowledge of the material of this course is no prerequisite for this class though. The necessary concepts from the analysis of metric spaces, geometric group theory, and the theory of quasiconformal and quasisymmetric maps will be reviewed.

    A fundamental problem in this area is to develop a uniformization theory for general classes of metric spaces that is similar to the classical uniformization theory for Riemann surfaces. This is partially motivated by questions in geometric group theory, and particularly relevant for fractal 2-spheres and Sierpinski carpets.

    For general background see my survey article on "Quasiconformal geometry of fractals" http://www.math.lsa.umich.edu/~mbonk/

    Advisory Prerequisite: MATH 703 and Graduate standing.

    MATH 710 — Topics in Modern Analysis II
    Section 001, LEC
    The Mathematical Theory of Shock Waves

    Instructor: Smoller,Joel A; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    Shock waves are violent physical processes which are ubiquitous in nature. They appear on many different scales, from combustion processes to the flight of supersonic jet planes, to atomic bombs, to volcanic eruptions, to supernova explosions of distant stars. These processes take the form of "shock fronts" across which the medium undergoes sudden and often large ganges in pressure, density, temperature, and velocity. Furthermore, these fronts can often arise spontaneously. The behavior of these violent processes is governed by first order nonlinear systems of hyperbolic partial differential equations, which describe the three conservation laws of mass, momentum, and energy; it is for this reason that the resulting PDE's are often referred to as "systems of conservation laws." Due to the nonlinearity of the equations, waves of different types can interact with each other, often resulting in huge increases in the physical quantities.

    The theory of propagation of shock waves is one of a small class of mathematical topics whose basic problems are easy to explain but hard to resolve. This course is a mathematical introduction to the subject : we shall describe the general mathematical form of the equations, some of the striking phenomena, and a few of the mathematical tools used to analyze them.

    The course will be entirely self-contained, and there are no formal prerequisites, save a little "mathematical maturity."

    Advisory Prerequisite: MATH 597 and Graduate standing.

    MATH 711 — Advanced Algebra
    Section 001, LEC

    WN 2007
    Credits: 3
    Reqs: BS

    Topics of current research interest, such as groups, rings, lattices, etc., including a thorough study of one such topic.

    Advisory Prerequisite: MATH 594 or 612 or permission of instructor. Graduate standing.

    MATH 715 — Advanced Topics in Algebra
    Section 001, LEC
    Noncommutative Algebraic Geometry

    Instructor: Stafford,J Tobias; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    Noncommutative algebraic geometry seeks to use the intuition and techniques from classical algebraic geometry to understand the strucuture of noncommutative algebras. This course will describe some of the main techniques and applications of this subject. Although the precise topics will depend upon the background and interests of the people attending the course, the emphasis will be on "noncommutative projective geometry.''

    In more detail, one has to accept that noncommutative algebraic varieties/schemes do not exist, but regarding a noncommutative algebra as the ring of functions on that imaginary space can give a very useful intuition. (Manin summed this up well in his book Quantum Groups and Noncommutative Geometry: ``In short, as A. Grothendieck taught us, to do geometry you don't really need a space, all you need is a category of sheaves on this would-be space.'') More importantly, associated to many noncommutative algebras one can construct schemes that determine the structure of those algebras (for example, the classification of ``noncommutative projective planes'' occurs this way and leads to some remarkable algebras known as Sklyanin algebras). In other cases the noncommutative algebra leads to a better understanding of or a generalization of important classical varieties (for example, in trying to understand or resolve singular varieties it seems that there are often substantial advantages to working with noncommutative algebras).

    To here more about either of the topics mentioned in the last paragraph, come to the course!

    Text: There are as yet no books on noncommutative projective geometry, but an outline of my view of the subject can be obtained from the survey article http://www.arxiv.org/pdf/math.RA/0304210

    For different views of noncommutative geometry, you could look at Manin's book mentioned above or Le Bruyn's book "Noncommutative geometry at n'' available at his web site http://www.math.ua.ac.be/~lebruyn/

    If you would like more information about the course, or whether you have an adequate background to take the course, please email me as I am out of town for the Fall semester.

    Prerequisites: A good knowledge of algebraic geometry certainly Math 613. If you have not had Math 632, then some working knowledge of schemes and sheaves would be desirable. Otherwise there are no formal requirements apart from a general algebraic sophistication.

    Advisory Prerequisite: MATH 594, 612, and Graduate standing.

    MATH 732 — Topics in Algebraic Geometry II
    Section 001, LEC
    McKay correspondence

    Instructor: Dolgachev,Igor; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    The subject can be described as the study of a relationship between the G-equivariant geometry of an algebraic variety X together with a group G acting on it and the geometry of a resolution of singularities of the orbit space X/G. The striking example of such a relationship is an observation of John McKay in the seventies that the set of irreducible representations of a finite subgroup G of SL(2,C) acting on C2 describing the G-equivariant theory of vector bundles on X = C2 is in a bijective correspondence with the set of irreducible components of the exceptional locus of a minimal resolution of singularities of C2/G. It was observed much earlier by Patrick Du Val that the geometry of the latter set is described by an affine Dynkin diagram of type A,D,E. More precisely, using the theory of linear representations, McKay attached a graph to any finite group and showed that the graph of a binary polyhedral group G is an affine Dynkin diagram, for instance of type E8 if the group is the binary icosahedral group.

    The Coxeter-Dynkin diagrams of types A,D,E appear in many classification problems in mathematics. For instance:

    • classification of simple Lie algebras and simple Lie groups;
    • classification of the platonic solids in R3, as in the Mckay correspondence;
    • classification of singularities of algebraic surfaces (rational Gorenstein singularities);
    • classification of critical points of polynomials (0-modal critical points); • classification of finite reflection groups;
    • classification of representations of quivers;
    • classification of singularities of closures of conjugacy classes in linear groups;
    • classification of representations of finite-dimensional algebras.

    The common origin of all the ADE-classifications is a still unsolved mystery in mathematics.

    The recent development in the theory of McKay correspondences use different modern constructions in algebraic geometry. Among them are punctual Hilbert schemes, the theory of derived categories, stringy cohomology, orbitfolds, quiver varieties, motivic integration. If time permits we plan to discuss them all.

    The literature on the McKay correspondence is enormous but no text-book is available. As an introduction I can recommend Miles Reid's talk at Bourbaki seminar. Lecture notes will appear on my web site.

    Advisory Prerequisite: MATH 631 or 731.

    MATH 776 — Topics in Algebraic Number Theory
    Section 001, LEC
    Introduction to Class Field Theory

    Instructor: Lagarias,Jeffrey C; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    Anyone seriously intending seriously to pursue algebraic number theory or arithmetic geometry should be familiar with the elements of Class Field Theory. Class Field Theory concerns the description of properties of abelian Galois extensions of a field k in terms of invariants of k. Global class field theory concerns k a number field or function field over finite field, and the invariants of k are (ray) class groups and units. Local class field theory concerns k a one-dimensional local field, such as a p-adic field, and invariants are field elements and norm groups. These two theories embody the GL(1) part of the (local and global) Langlands program. The course will describe some history and the main theorems, in both ideal theory version and idelic version, and their relation to Langlands program. The current plan for proofs is to take a classical approach, favoring analytic invariants (L-functions), based on the book of Janusz, for global class field theory, supplemented by Milne's notes (http:/www.jmilne.org/math/)

    Advisory Prerequisite: MATH 676 and Graduate standing.

    MATH 797 — Advanced Topics in Topology
    Section 001, LEC
    The geometry of conformal field theory

    Instructor: Kriz,Igor; homepage

    WN 2007
    Credits: 3
    Reqs: BS

    In this course, I will attempt to give a *mathematical* introduction to topics in conformal field theory and string theory. Topics will include discussion of Riemann surfaces, supersymmetry, the mathematical definitions of conformal field theory and known examples. A definition of superstring theory and its types will be also given. Possible discussion of more advanced topics such as D-branes or deformations may also be included according to time.

    Recommended text: Quantum Fields and Strings: A course for mathematicians, Vol. 1 and 2

    Advisory Prerequisite: Graduate standing and permission of instructor.

    MATH 821 — Actuarial Math
    Section 001, SEM

    Instructor: Huntington,Curtis E; homepage
    Instructor: Dong,Hua

    WN 2007
    Credits: 1

    MATH 821 — Actuarial Math
    Section 002, SEM

    Instructor: Huntington,Curtis E; homepage
    Instructor: Dong,Hua

    WN 2007
    Credits: 1

    MATH 990 — Dissertation/Precandidate
    Section 001, IND

    WN 2007
    Credits: 1 — 8

    Election for dissertation work by doctoral student not yet admitted as a Candidate.

    Advisory Prerequisite: Election for dissertation work by doctoral student not yet admitted as a Candidate. Graduate standing.

    MATH 995 — Dissertation/Candidate
    Section 001, IND

    WN 2007
    Credits: 8

    Graduate School authorization for admission as a doctoral Candidate. N.B. The defense of the dissertation (the final oral examination) must be held under a full term Candidacy enrollment period.

    Enforced Prerequisites: Graduate School authorization for admission as a doctoral Candidate

     
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