Information for Prospective Students Information for First-Year Students Information for Transfer Students Information for International Students Learning Communities, Study Abroad, Theme Semester Calendars Quick Reference Forms Listings Table of Contents SAA Search Feature Academic Advising, Concentration Advising, How-tos, and Degree Requirements Academic Standards Board, Academic Discipline, Petitions, and Appeals SAA Advisors and Support Staff


Spring/Summer Academic Term 2003 Course Guide

Note: You must establish a session for the correct term (Spring, Summer, or Spring/Summer Academic Term 2003) on wolverineaccess.umich.edu in order to use the link "Check Times, Location, and Availability". Once your session is established, the links will function.

Courses in Mathematics

This page was created at 8:18 PM on Mon, Jul 14, 2003.



Spring Half-Term Courses

Search the LS&ACourse Guide
(Advanced Search Page)


Elementary Mathematics Courses. In order to accommodate diverse backgrounds and interests, several course options are available to beginning mathematics students. All courses require three years of high school mathematics; four years are strongly recommended and more information is given for some individual courses below. Students with College Board Advanced Placement credit and anyone planning to enroll in an upper-level class should consider one of the Honors sequences and discuss the options with a mathematics advisor.

Students who need additional preparation for calculus are tentatively identified by a combination of the math placement test (given during orientation), college admission test scores (SAT or ACT), and high school grade point average. Academic advisors will discuss this placement information with each student and refer students to a special mathematics advisor when necessary.

Two courses preparatory to the calculus, MATH 105 and 110, are offered. MATH 105 is a course on data analysis, functions and graphs with an emphasis on problem solving. MATH 110 is a condensed half-term version of the same material offered as a self-study course taught through the Math Lab and is only open to students in MATH 115 who find that they need additional preparation to successfully complete the course. A maximum total of 4 credits may be earned in courses numbered 103, 105, and 110. MATH 103 is offered exclusively in the Summer half-term for students in the Summer Bridge Program.

MATH 127 and 128 are courses containing selected topics from geometry and number theory, respectively. They are intended for students who want exposure to mathematical culture and thinking through a single course. They are neither prerequisite nor preparation for any further course. No credit will be received for the election of MATH 127 or 128 if a student already has credit for a 200-(or higher) level MATH course.

Each of MATH 115, 185, and 295 is a first course in calculus. Generally credit can be received for only one of 115 or 185. The sequence MATH 115-116-215 is appropriate for must students who want a complete introduction to calculus. One of 215, 285, or 395 is prerequisite to most more advanced courses in Mathematics.

The sequences MATH 156-255-256, 175-186-285-286, 185-186-285-286, and 295-296-395-396 are Honors sequences. Students need not be enrolled in the LS&A Honors Program to enroll in any of these courses but must have the permission of an Honors advisor. Students with strong preparation and interest in mathematics are encouraged to consider these courses.

MATH 185-285 covers much of the material of MATH 115-215 with more attention to the theory in addition to applications. Most students who take MATH 185 have taken a high school calculus course, but it is not required. MATH 175-186 assumes a knowledge of calculus roughly equivalent to MATH 115 and covers a substantial amount of so-called combinatorial mathematics as well as calculus-related topics not usually part of the calculus sequence. MATH 175 is taught by the discovery method: students are presented with a great variety of problems and encouraged to experiment in groups using computers. The sequence MATH 295-396 provides a rigorous introduction to theoretical mathematics. Proofs are stressed over applications and these courses require a high level of interest and commitment. Most students electing MATH 295 have completed a thorough high school calculus course. MATH 295-396 is excellent preparation for mathematics at the advanced undergraduate and beginning graduate level.

Students with strong scores on either the AB or BC version of the College Board Advanced Placement exam may be granted credit and advanced placement in one of the sequences described above; a table explaining the possibilities is available from advisors and the Department. In addition, there is one course expressly designed and recommended for students with one or two semesters of AP credit, MATH 156. MATH 156 is an Honors course intended primarily for science and engineering concentrators and will emphasize both applications and theory. Interested students should consult a mathematics advisor for more details.

In rare circumstances and with permission of a Mathematics advisor, reduced credit may be granted for MATH 185 after MATH 115. A list of these and other cases of reduced credit for courses with overlapping material is available from the Department. To avoid unexpected reduction in credit, a student should always consult an advisor before switching from one sequence to another. In all cases a maximum total of 16 credits may be earned for calculus courses MATH 115 through 396, and no credit can be earned for a prerequisite to a course taken after the course itself.

Students completing MATH 116 who are principally interested in the application of mathematics to other fields may continue either to MATH 215 (Analytic Geometry and Calculus III) or to MATH 216 (Introduction to Differential Equations); these two courses may be taken in either order. Students who have greater interest in theory or who intend to take more advanced courses in mathematics should continue with MATH 215 followed by the sequence MATH 217-316 (Linear Algebra-Differential Equations). MATH 217 (or the Honors version, MATH 513) is required for a concentration in Mathematics; it both serves as a transition to the more theoretical material of advanced courses and provides the background required to optimal treatment of differential equations in MATH 316. MATH 216 is not intended for mathematics concentrators.

A maximum total of 4 credits may be earned in MATH 103, 105, and 110. A maximum total of 16 credits may be earned for calculus courses MATH 112 through MATH 396, and no credit can be earned for a prerequisite to a course taken after the course itself.


MATH 115. Calculus I.

Instructor(s):

Prerequisites & Distribution: Four years of high school mathematics. See Elementary Courses above. Credit usually is granted for only one course from among MATH 112, 115, 185, and 295. No credit granted to those who have completed MATH 175. (4). (MSA). (BS). (QR/1). May not be repeated for credit.

Full QR

Credits: (4).

Course Homepage: No homepage submitted.

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. 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. The cost for this course is over $100 since the student will need a text (to be used for 115 and 116) and a graphing calculator (the Texas Instruments TI-83 is recommended).

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

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 116. Calculus II.

Instructor(s):

Prerequisites & Distribution: MATH 115. Credit is granted for only one course from among MATH 116, 156, 176, 186, and 296. (4). (MSA). (BS). (QR/1). May not be repeated for credit.

Full QR

Credits: (4).

Course Homepage: No homepage submitted.

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, infinite series. Math 186 is a somewhat more theoretical course which covers much of the same material, offered only in the Winter term. 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, offered in the Fall term.

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

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 215. Calculus III.

Instructor(s):

Prerequisites & Distribution: MATH 116, 119, 156, 176, 186, or 296. Credit can be earned for only one of MATH 215, 255, or 285. (4). (MSA). (BS). (QR/1). May not be repeated for credit.

Full QR

Credits: (4).

Course Homepage: No homepage submitted.

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 concentrate 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 midterm and final exam.

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 software. Math 285 is a somewhat more theoretical course which covers the same material, offered only in the Fall term. For students intending to concentrate in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217. Students who intend to take only one further mathematics course and need differential equations should take Math 216.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 216. Introduction to Differential Equations.

Instructor(s):

Prerequisites & Distribution: MATH 116, 119, 156, 176, 186, or 296. Not intended for Mathematics concentrators. Credit can be earned for only one of MATH 216, 256, 286, or 316. (4). (MSA). (BS). May not be repeated for credit.

Credits: (4).

Course Homepage: No homepage submitted.

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 concentrators and other students who have some interest in the theory of mathematics should elect the sequence Math 217-316.

After an introduction to ordinary differential equations, the first half of the course is devoted to topics in linear algebra, including systems of linear algebraic equations, vector spaces, linear dependence, bases, dimension, matrix algebra, determinants, eigenvalues, and eigenvectors. In the second half these tools are applied to the solution of linear systems of ordinary differential equations. Topics include: oscillating systems, the Laplace transform, initial value problems, resonance, phase portraits, and an introduction to numerical methods. There is a weekly computer lab using MATLAB software. This course is not intended for mathematics concentrators, who should elect the sequence 217-316. Math 286 covers much of the same material in the honors sequence, offered in the Winter term. The sequence Math 217-316 covers all of this material and substantially more at greater depth and with greater emphasis on the theory. Math 404 covers further material on differential equations. Math 217 and 417 cover further material on linear algebra. Math 371 and 471 cover additional material on numerical methods.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 333. Directed Tutoring.

Instructor(s): Eugene F Krause

Prerequisites & Distribution: MATH 385 and enrollment in the Elementary Program in the School of Education. Permission of instructor required. (1-3). (Excl). (EXPERIENTIAL). May be repeated for credit for a maximum of 3 credits.

Credits: (1-3).

Course Homepage: No homepage submitted.

An experiential mathematics course for exceptional upper-level students in the elementary teacher certification program. Students tutor needy beginners enrolled in the introductory courses (Math 385 and Math 489) required of all elementary teachers.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Instructor

MATH 399. Independent Reading.

Instructor(s):

Prerequisites & Distribution: Permission of instructor required. (1-6). (Excl). (INDEPENDENT). May be repeated for credit.

Credits: (1-6).

Course Homepage: No homepage submitted.

Designed especially for Honors students.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Department

MATH 417. Matrix Algebra I.

Instructor(s):

Prerequisites & Distribution: 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 MATH 513. (3). (Excl). (BS). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

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 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.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 425 / STATS 425. Introduction to Probability.

Instructor(s):

Prerequisites & Distribution: MATH 215, 255, or 285. (3). (Excl). (BS). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

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. 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, and covariances. Different instructors will vary the emphasis. Math 525 is a similar course for students with stronger mathematical background and ability. Stat 426 is a natural sequel for students interested in statistics. Math 523 includes many applications of probability theory.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 425 / STATS 425. Introduction to Probability.

Instructor(s):

Prerequisites & Distribution: MATH 215, 255, or 285. (3). (Excl). (BS). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

See Statistics 425.001.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 451. Advanced Calculus I.

Instructor(s):

Prerequisites & Distribution: MATH 215 and one course beyond MATH 215; or MATH 255 or 285. Intended for concentrators; other students should elect MATH 450. (3). (Excl). (BS). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

Background and Goals. 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.

Content. Topics covered include: logic and techniques of proofs; sets, functions, and relations; cardinality; the real number system and its topology; infinite sequences, limits, and continuity; differentiation; integration; the Fundamental Theorem of Calculus; infinite series; and sequences and series of functions.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 454. Boundary Value Problems for Partial Differential Equations.

Instructor(s):

Prerequisites & Distribution: MATH 216, 256, 286, or 316. 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. (3). (Excl). (BS). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

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; 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.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 489. Mathematics for Elementary and Middle School Teachers.

Section 101.

Instructor(s): Eugene F Krause

Prerequisites & Distribution: MATH 385 or 485. May not be used in any graduate program in mathematics. (3). (Excl). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

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. 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.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 561 / IOE 510 / SMS 518. Linear Programming I.

Instructor(s): Jack L Goldberg

Prerequisites & Distribution: MATH 217, 417, or 419. (3). (Excl). (BS). CAEN lab access fee required for non-Engineering students. May not be repeated for credit.

Credits: (3).

Lab Fee: CAEN lab access fee required for non-Engineering students.

Course Homepage: No homepage submitted.

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; 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.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.


Spring/Summer Term Courses

Search the LS&ACourse Guide
(Advanced Search Page)



MATH 399. Independent Reading.

Instructor(s):

Prerequisites & Distribution: Permission of instructor required. (1-6). (Excl). (INDEPENDENT). May be repeated for credit.

Credits: (1-6).

Course Homepage: No homepage submitted.

Designed especially for Honors students.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Department


Summer Half-Term Courses

Search the LS&ACourse Guide
(Advanced Search Page)


Elementary Mathematics Courses. In order to accommodate diverse backgrounds and interests, several course options are available to beginning mathematics students. All courses require three years of high school mathematics; four years are strongly recommended and more information is given for some individual courses below. Students with College Board Advanced Placement credit and anyone planning to enroll in an upper-level class should consider one of the Honors sequences and discuss the options with a mathematics advisor.

Students who need additional preparation for calculus are tentatively identified by a combination of the math placement test (given during orientation), college admission test scores (SAT or ACT), and high school grade point average. Academic advisors will discuss this placement information with each student and refer students to a special mathematics advisor when necessary.

Two courses preparatory to the calculus, MATH 105 and 110, are offered. MATH 105 is a course on data analysis, functions and graphs with an emphasis on problem solving. MATH 110 is a condensed half-term version of the same material offered as a self-study course taught through the Math Lab and is only open to students in MATH 115 who find that they need additional preparation to successfully complete the course. A maximum total of 4 credits may be earned in courses numbered 103, 105, and 110. MATH 103 is offered exclusively in the Summer half-term for students in the Summer Bridge Program.

MATH 127 and 128 are courses containing selected topics from geometry and number theory, respectively. They are intended for students who want exposure to mathematical culture and thinking through a single course. They are neither prerequisite nor preparation for any further course. No credit will be received for the election of MATH 127 or 128 if a student already has credit for a 200-(or higher) level MATH course.

Each of MATH 115, 185, and 295 is a first course in calculus. Generally credit can be received for only one of 115 or 185. The sequence MATH 115-116-215 is appropriate for must students who want a complete introduction to calculus. One of 215, 285, or 395 is prerequisite to most more advanced courses in Mathematics.

The sequences MATH 156-255-256, 175-186-285-286, 185-186-285-286, and 295-296-395-396 are Honors sequences. Students need not be enrolled in the LS&A Honors Program to enroll in any of these courses but must have the permission of an Honors advisor. Students with strong preparation and interest in mathematics are encouraged to consider these courses.

MATH 185-285 covers much of the material of MATH 115-215 with more attention to the theory in addition to applications. Most students who take MATH 185 have taken a high school calculus course, but it is not required. MATH 175-186 assumes a knowledge of calculus roughly equivalent to MATH 115 and covers a substantial amount of so-called combinatorial mathematics as well as calculus-related topics not usually part of the calculus sequence. MATH 175 is taught by the discovery method: students are presented with a great variety of problems and encouraged to experiment in groups using computers. The sequence MATH 295-396 provides a rigorous introduction to theoretical mathematics. Proofs are stressed over applications and these courses require a high level of interest and commitment. Most students electing MATH 295 have completed a thorough high school calculus course. MATH 295-396 is excellent preparation for mathematics at the advanced undergraduate and beginning graduate level.

Students with strong scores on either the AB or BC version of the College Board Advanced Placement exam may be granted credit and advanced placement in one of the sequences described above; a table explaining the possibilities is available from advisors and the Department. In addition, there is one course expressly designed and recommended for students with one or two semesters of AP credit, MATH 156. MATH 156 is an Honors course intended primarily for science and engineering concentrators and will emphasize both applications and theory. Interested students should consult a mathematics advisor for more details.

In rare circumstances and with permission of a Mathematics advisor, reduced credit may be granted for MATH 185 after MATH 115. A list of these and other cases of reduced credit for courses with overlapping material is available from the Department. To avoid unexpected reduction in credit, a student should always consult an advisor before switching from one sequence to another. In all cases a maximum total of 16 credits may be earned for calculus courses MATH 115 through 396, and no credit can be earned for a prerequisite to a course taken after the course itself.

Students completing MATH 116 who are principally interested in the application of mathematics to other fields may continue either to MATH 215 (Analytic Geometry and Calculus III) or to MATH 216 (Introduction to Differential Equations); these two courses may be taken in either order. Students who have greater interest in theory or who intend to take more advanced courses in mathematics should continue with MATH 215 followed by the sequence MATH 217-316 (Linear Algebra-Differential Equations). MATH 217 (or the Honors version, MATH 513) is required for a concentration in Mathematics; it both serves as a transition to the more theoretical material of advanced courses and provides the background required to optimal treatment of differential equations in MATH 316. MATH 216 is not intended for mathematics concentrators.

A maximum total of 4 credits may be earned in MATH 103, 105, and 110. A maximum total of 16 credits may be earned for calculus courses MATH 112 through MATH 396, and no credit can be earned for a prerequisite to a course taken after the course itself.


MATH 101. Explorations in Algebra.

Instructor(s):

Prerequisites & Distribution: Students can get a total of only 4 credits for MATH courses numbered below 110. No credit granted to those who have completed or are enrolled in MATH 105. (2). (Excl). May not be repeated for credit.

Credits: (2 in the half-term).

Course Homepage: No homepage submitted.

No Description Provided. Contact the Department.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 103. Intermediate Algebra.

BRIDGE PROGRAM STUDENTS ONLY.

Instructor(s):

Prerequisites & Distribution: Only open to designated summer half-term Bridge students. A maximum of four credits may be earned in MATH 103, 105, and 110. (2). (Excl). May not be repeated for credit.

Credits: (2 in the half-term).

Course Homepage: No homepage submitted.

This course is an in-depth review of high school algebra. It covers linear, quadratic, and polynomial functions and their graphs. This course is restricted to students enrolled in the Bridge Program.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 105. Data, Functions, and Graphs.

Instructor(s):

Prerequisites & Distribution: 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 103, 105, and 110. (4). (MSA). (QR/1). May not be repeated for credit.

Full QR

Credits: (4).

Course Homepage: No homepage submitted.

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

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 115. Calculus I.

Instructor(s):

Prerequisites & Distribution: Four years of high school mathematics. See Elementary Courses above. Credit usually is granted for only one course from among MATH 112, 115, 185, and 295. No credit granted to those who have completed MATH 175. (4). (MSA). (BS). (QR/1). May not be repeated for credit.

Full QR

Credits: (4).

Course Homepage: No homepage submitted.

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. 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. The cost for this course is over $100 since the student will need a text (to be used for 115 and 116) and a graphing calculator (the Texas Instruments TI-83 is recommended).

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 116. Calculus II.

Instructor(s):

Prerequisites & Distribution: MATH 115. Credit is granted for only one course from among MATH 116, 156, 176, 186, and 296. (4). (MSA). (BS). (QR/1). May not be repeated for credit.

Full QR

Credits: (4).

Course Homepage: No homepage submitted.

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, infinite series. Math 186 is a somewhat more theoretical course which covers much of the same material, offered only in the Winter term. 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, offered in the Fall term.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 215. Calculus III.

Instructor(s):

Prerequisites & Distribution: MATH 116, 119, 156, 176, 186, or 296. Credit can be earned for only one of MATH 215, 255, or 285. (4). (MSA). (BS). (QR/1). May not be repeated for credit.

Full QR

Credits: (4).

Course Homepage: No homepage submitted.

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 concentrate 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 midterm and final exam.

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 software. Math 285 is a somewhat more theoretical course which covers the same material, offered only in the Fall term. For students intending to concentrate in mathematics or who have some interest in the theory of mathematics as well as its applications, the appropriate sequel is Math 217. Students who intend to take only one further mathematics course and need differential equations should take Math 216.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 216. Introduction to Differential Equations.

Instructor(s):

Prerequisites & Distribution: MATH 116, 119, 156, 176, 186, or 296. Not intended for Mathematics concentrators. Credit can be earned for only one of MATH 216, 256, 286, or 316. (4). (MSA). (BS). May not be repeated for credit.

Credits: (4).

Course Homepage: No homepage submitted.

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 concentrators and other students who have some interest in the theory of mathematics should elect the sequence Math 217-316.

After an introduction to ordinary differential equations, the first half of the course is devoted to topics in linear algebra, including systems of linear algebraic equations, vector spaces, linear dependence, bases, dimension, matrix algebra, determinants, eigenvalues, and eigenvectors. In the second half these tools are applied to the solution of linear systems of ordinary differential equations. Topics include: oscillating systems, the Laplace transform, initial value problems, resonance, phase portraits, and an introduction to numerical methods. There is a weekly computer lab using MATLAB software. This course is not intended for mathematics concentrators, who should elect the sequence 217-316. Math 286 covers much of the same material in the honors sequence, offered in the Winter term. The sequence Math 217-316 covers all of this material and substantially more at greater depth and with greater emphasis on the theory. Math 404 covers further material on differential equations. Math 217 and 417 cover further material on linear algebra. Math 371 and 471 cover additional material on numerical methods.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 399. Independent Reading.

Instructor(s):

Prerequisites & Distribution: Permission of instructor required. (1-6). (Excl). (INDEPENDENT). May be repeated for credit.

Credits: (1-6).

Course Homepage: No homepage submitted.

Designed especially for Honors students.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: 5, Permission of Department

MATH 417. Matrix Algebra I.

Instructor(s):

Prerequisites & Distribution: 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 MATH 513. (3). (Excl). (BS). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

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 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.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 419. Linear Spaces and Matrix Theory.

Instructor(s):

Prerequisites & Distribution: Four terms of college mathematics 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. (3). (Excl). (BS). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

Math 419 covers much of the same ground as Math 417 but presents the material in a somewhat more abstract way in terms of vector spaces and linear transformations instead of matrices. There is a mix of proofs, calculations, and applications with the emphasis depending somewhat on the instructor. A previous proof-oriented course is helpful but by no means necessary. Basic notions of vector spaces and linear transformations: spanning, linear independence, bases, dimension, and matrix representation of linear transformations; determinants; eigenvalues, eigenvectors, Jordan canonical form, and inner-product spaces; unitary, self-adjoint, and orthogonal operators and matrices, and applications to differential and difference equations.

Math 417 is less rigorous and theoretical and more oriented to applications. Math 217 is similar to Math 419 but slightly more proof-oriented. Math 513 is much more abstract and sophisticated. Math 420 is the natural sequel, but this course serves as prerequisite to several courses: Math 452, 462, 561, and 571.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 425 / STATS 425. Introduction to Probability.

Instructor(s):

Prerequisites & Distribution: MATH 215, 255, or 285. (3). (Excl). (BS). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

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. 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, and covariances. Different instructors will vary the emphasis. Math 525 is a similar course for students with stronger mathematical background and ability. Stat 426 is a natural sequel for students interested in statistics. Math 523 includes many applications of probability theory.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 450. Advanced Mathematics for Engineers I.

Instructor(s):

Prerequisites & Distribution: MATH 215, 255, or 285. No credit granted to those who have completed or are enrolled in MATH 454. (4). (Excl). (BS). May not be repeated for credit.

Credits: (4).

Course Homepage: No homepage submitted.

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.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 471. Introduction to Numerical Methods.

Instructor(s):

Prerequisites & Distribution: MATH 216, 256, 286, or 316; and 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. (3). (Excl). (BS). May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

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.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 485. Mathematics for Elementary School Teachers and Supervisors.

Section 201 — ELMAC 5B.

Instructor(s):

Prerequisites & Distribution: One year of high school algebra. No credit granted to those who have completed or are enrolled in MATH 385. (3). (Excl). (BS). May not be included in a concentration plan in mathematics. May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

The history, development, and logical foundations of the real number system and of numeration systems including scales of notation, cardinal numbers, and the cardinal concept; and the logical structure of arithmetic (field axioms) and relations to the algorithms of elementary school instruction. Simple algebra, functions, and graphs. Geometric relationships. For persons teaching in or preparing to teach in the elementary school.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.

MATH 485. Mathematics for Elementary School Teachers and Supervisors.

Section 202 — ELMAC 5A.

Instructor(s):

Prerequisites & Distribution: One year of high school algebra. No credit granted to those who have completed or are enrolled in MATH 385. (3). (Excl). (BS). May not be included in a concentration plan in mathematics. May not be repeated for credit.

Credits: (3).

Course Homepage: No homepage submitted.

The history, development, and logical foundations of the real number system and of numeration systems including scales of notation, cardinal numbers, and the cardinal concept; and the logical structure of arithmetic (field axioms) and relations to the algorithms of elementary school instruction. Simple algebra, functions, and graphs. Geometric relationships. For persons teaching in or preparing to teach in the elementary school.

Check Times, Location, and Availability Cost: No Data Given. Waitlist Code: No Data Given.


Graduate Course Listings for MATH.


Page


This page was created at 8:18 PM on Mon, Jul 14, 2003.

LSA

University of Michigan | College of LS&A | Student Academic Affairs | LS&A Bulletin Index | Department Homepage

This page maintained by LS&A Advising Technology (webmaster_saa@umich.edu), 1228 Angell Hall

Copyright © 2003 The Regents of the University of Michigan,
Ann Arbor, MI 48109 USA +1 734 764-1817

Trademarks of the University of Michigan may not be electronically or otherwise altered or separated from this document or used for any non-University purpose.