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Spring/Summer '99 Course Guide

Courses in Mathematics (Division 428)


Calendars

Spring Half-Term, 1999 (May 3 June 22, 1999)
Spring/Summer Term, 1999 (May 3 August 17, 1999)
Summer Half-Term, 1999 (June 28 August 17, 1999)


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Spring Half-Term

Spring/Summer Term

Summer Half-Term


Spring Half-Term Courses

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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 admissions 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 Math 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 through the Math Lab and directed towards students who are unable to complete a first calculus course successfully. A maximum total of 4 credits may be earned in courses numbered 110 and below. 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 received credit for a 200- (or higher) level mathematics course.

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

The sequences 156-255-256, 175-176-285-286, 185-186-285-286, and 295-296-395-396 are Honors sequences. All students must have the permission of an Honors advisor to enroll in any of these courses, but they need not be enrolled in the LS&A Honors Program. All students with strong preparation and interest in mathematics are encouraged to consider these courses; they are both more interesting and more challenging than the standard sequences.

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 175-176 assumes a knowledge of calculus roughly equivalent to Math 115 and covers a substantial amount of so-called combinatorial mathematics (see course description) as well as calculus-related topics not usually part of the calculus sequence. Math 175 and 176 are 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. The student who completes Math 396 is prepared to explore the world of mathematics at the advanced undergraduate and 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 are two courses expressly designed and recommended for students with one or two semesters of AP credit, Math 119 and Math 156. Both will review the basic concepts of calculus, cover integration and an introduction to differential equations, and introduce the student to the computer algebra system MAPLE. Math 119 will stress experimentation and computation, while 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 or 295 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, students 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 Math 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 for 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 Mathematics courses numbered 110 and below. 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.

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).

No Description Provided.

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Math. 116. Calculus II.

Prerequisites & Distribution: Math. 115. Credit is granted for only one course from among Math. 116, 119, 156, 176, 186, and 296. (4). (MSA). (BS). (QR/1).

No Description Provided.

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Math. 215. Calculus III.

Prerequisites & Distribution: Math. 116, 119, 156, 176, 186, or 296. (4). (MSA). (BS). (QR/1).

No Description Provided.

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Math. 215. Calculus III.

Section 102.

Instructor(s): John Dean

Prerequisites & Distribution: Math. 116, 119, 156, 176, 186, or 296. (4). (MSA). (BS). (QR/1).

Full QR

Credits: (4).

Course Homepage: http://www.math.lsa.umich.edu/~jdean/215/

Background and Goals. See Math 115. 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 lab using MAPLE.

LABORATORY: in the lab you will be using the computer program maple as a tool to visualize 2-d and 3-d geometric phenomena. Participation in the laboratory (which is required) will improve your understanding of the concepts as well as your overall performance in the course. Exams will include material that is closely tied to the lab work.

Part of your work in the lab will involve completing the projects described in the course pack. These projects are due at the beginning of your lab hour. No late lab projects will be accepted.

You must have the course pack when you attend the first lab meeting.

HOMEWORK: I will hand out a list of homework problems from the text. This daily homework will not be collected, but is an essential part of the course. Doing the homework conscientiously is the best way to learn the material.

GRADING: Your grade will be determined as follows:

EXAMS AND QUIZZES: The midterm exam will be given during class on Friday, May 28. The final exam is on Monday, June 21 from 4 to 6 p.m. There will be a short quiz at least once per week. The quizzes will be similar to the assigned homework problems.

Texts:

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Math. 216. Introduction to Differential Equations.

Prerequisites & Distribution: Math. 116, 119, 156, 176, 186, or 296. (4). (MSA). (BS).

No Description Provided.

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Math. 333. Directed Tutoring.

Section 101.

Prerequisites & Distribution: Math. 385 and enrollment in the Elementary Program in the School of Education. (1-3). (Excl). (EXPERIENTIAL). May be repeated for a total of three credits.

No Description Provided.

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Math. 399. Independent Reading.

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

No Description Provided.

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Math. 417. Matrix Algebra I.

Section 101.

Prerequisites & Distribution: Three courses beyond Math. 110. No credit granted to those who have completed or are enrolled in 217, 419, or 513. (3). (Excl). (BS).

No Description Provided.

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Math. 417. Matrix Algebra I.

Section 102.

Prerequisites & Distribution: Three courses beyond Math. 110. No credit granted to those who have completed or are enrolled in 217, 419, or 513. (3). (Excl). (BS).

No Description Provided.

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Math. 425/Stat. 425. Introduction to Probability.

Prerequisites & Distribution: Math. 215, 255, or 285. (3). (MSA). (BS).

No Description Provided.

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Math. 451. Advanced Calculus I.

Section 101.

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).

No Description Provided.

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Math. 454. Boundary Value Problems for Partial Differential Equations.

Section 101.

Prerequisites & Distribution: Math. 216, 256, 286, or 316. Students with credit for Math. 354 can elect Math. 454 for one credit. (3). (Excl). (BS).

No Description Provided.

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Math. 489. Mathematics for Elementary and Middle School Teachers.

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

No Description Provided.

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Math. 555. Introduction to Functions of a Complex Variable with Applications.

Section 101.

Prerequisites & Distribution: Math. 450 or 451. (3). (Excl). (BS).

No Description Provided.

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Math. 561/SMS 518 (Business Administration)/IOE 510. Linear Programming I.

Section 101.

Instructor(s): Jack Goldberg (jackgold@umich.edu)

Prerequisites & Distribution: Math. 217, 417, or 419. (3). (Excl). (BS).

No Description Provided.

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Spring/Summer Term Courses

Take me to the Spring/Summer Term '99 Time Schedule for Mathematics.


Math. 399. Independent Reading.

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

No Description Provided.

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Summer Half-Term Courses

Take me to the Summer Half-Term '99 Time Schedule for Mathematics.

Math. 103. Intermediate Algebra.

Section Math 103 Bridge Program Students only

Prerequisites & Distribution: Only open to designated summer half-term Bridge students. (2). (Excl).

No Description Provided.

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Math. 105. Data, Functions, and Graphs.

Section 201.

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. (4). (MSA). (QR/1).

No Description Provided.

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Math. 115. Calculus I.

Section 201.

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).

No Description Provided.

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Math. 116. Calculus II.

Section 201.

Prerequisites & Distribution: Math. 115. Credit is granted for only one course from among Math. 116, 119, 156, 176, 186, and 296. (4). (MSA). (BS). (QR/1).

No Description Provided.

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Math. 116. Calculus II.

Section 202.

Prerequisites & Distribution: Math. 115. Credit is granted for only one course from among Math. 116, 119, 156, 176, 186, and 296. (4). (MSA). (BS). (QR/1).

No Description Provided.

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Math. 215. Calculus III.

Section 201.

Prerequisites & Distribution: Math. 116, 119, 156, 176, 186, or 296. (4). (MSA). (BS). (QR/1).

No Description Provided.

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Math. 216. Introduction to Differential Equations.

Section 201.

Prerequisites & Distribution: Math. 116, 119, 156, 176, 186, or 296. (4). (MSA). (BS).

No Description Provided.

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Math. 216. Introduction to Differential Equations.

Section 202.

Prerequisites & Distribution: Math. 116, 119, 156, 176, 186, or 296. (4). (MSA). (BS).

No Description Provided.

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Math. 399. Independent Reading.

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

No Description Provided.

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Math. 417. Matrix Algebra I.

Section 201.

Prerequisites & Distribution: Three courses beyond Math. 110. No credit granted to those who have completed or are enrolled in 217, 419, or 513. (3). (Excl). (BS).

No Description Provided.

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Math. 419/EECS 400/CS 400. Linear Spaces and Matrix Theory.

Prerequisites & Distribution: Four terms of college mathematics beyond Math 110. No credit granted to those who have completed or are enrolled in 217 or 513. One credit granted to those who have completed Math. 417. (3). (Excl). (BS).

No Description Provided.

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Math. 425/Stat. 425. Introduction to Probability.

Section 201.

Prerequisites & Distribution: Math. 215, 255, or 285. (3). (MSA). (BS).

No Description Provided.

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Math. 450. Advanced Mathematics for Engineers I.

Section 201.

Prerequisites & Distribution: Math. 216, 256, 286, or 316. (4). (Excl). (BS).

No Description Provided.

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Math. 471. Introduction to Numerical Methods.

Section 201.

Prerequisites & Distribution: Math. 216, 256, 286, or 316; and 217, 417, or 419; and a working knowledge of one high-level computer language. (3). (Excl). (BS).

No Description Provided.

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Math. 485. Mathematics for Elementary School Teachers and Supervisors.

Section 201.

Instructor(s): Dana Winter

Prerequisites & Distribution: One year of high school algebra. No credit granted to those who have completed or are enrolled in 385. (2). (Excl). (BS). May not be included in a concentration plan in mathematics.

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