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Winter Academic Term 2002 Course Guide

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Courses in Mathematics


This page was created at 5:42 PM on Tue, Oct 30, 2001.

Winter Academic Term, 2002 (January 7 April 26)

Open courses in Mathematics
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Wolverine Access Subject listing for MATH

Winter Academic Term '02 Time Schedule for Mathematics.

What's New This Week in Mathematics.

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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 (except 385, 489 or 497).

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.

All elementary teaching certificate candidates are required to take two mathematics courses, Math 385 and Math 489, either before or after admission to the School of Education. Math 385 is offered in the Fall, Math 489 in the Winter. The next Spring Term offering of Math 489 will be in 2003. For further information, contact Prof. Krause at 763-1186 or at his office, 3086 East Hall.

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

Full QR

Credits: (4).

Course Homepage: http://www.math.lsa.umich.edu/courses/105/

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. Math 110 is a condensed half-term version of the same material offered as a self-study course through the Math Lab.

TEXT: Functions Modeling Change, Connally, Wiley Publishing.

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

MATH 107. Mathematics for the Information Age.

Section 001.

Instructor(s): Karen Rhea

Prerequisites & Distribution: Three to four years high school mathematics. (3). (MSA). (QR/1).

Full QR

Credits: (3).

Course Homepage: No homepage submitted.

From computers and the Internet to playing a CD or running an election, great progress in modern technology and science has come from understanding how information is exchanged, processed, and perceived. Typical topics: cryptography, error-correcting codes, data compression, fairness in politics, voting systems, population growth, and biological modeling. Grading will be based on homework, at least one written report, a midterm, and a final.

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

MATH 110. Pre-Calculus (Self-Study).

Instructor(s):

Prerequisites & Distribution: See Elementary Courses above. Enrollment in Math. 110 is by recommendation of Math. 115 instructor and override only. No credit granted to those who already have 4 credits for pre-calculus mathematics courses. (2). (Excl).

Credits: (2).

Course Homepage: http://www.math.lsa.umich.edu/~meggin/math110.html

The course covers data analysis by means of functions and graphs. Math 110 serves both as a preparatory class to the calculus sequences and as a terminal course for students who need only this level of mathematics. The course is a condensed, half-term version of Math 105 (Math 105 covers the same material in a traditional classroom setting) designed for students who appear to be prepared to handle calculus but are not able to successfully complete Math 115. Students who complete 110 are fully prepared for 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.

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).

Full QR

Credits: (4).

Course Homepage: http://www.math.lsa.umich.edu/courses/115/

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 uniform midterm and final exam. 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. Math 185 is a somewhat more theoretical course which covers some of the same material. Math 175 includes some of the material of Math 115 together with some combinatorial mathematics. A student whose preparation is insufficient for Math 115 should take Math 105 (Data, Functions, and Graphs). Math 116 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. 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, Wiley Publishing.
TI-83 Graphing Calculator, Texas Instruments.

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, 119, 156, 176, 186, and 296. (4). (MSA). (BS). (QR/1).

Full QR

Credits: (4).

Course Homepage: http://www.math.lsa.umich.edu/courses/116/

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.

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

MATH 127. Geometry and the Imagination.

Instructor(s):

Prerequisites & Distribution: 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. No credit granted to those who have completed a 200- (or higher) level mathematics course. (4). (MSA). (BS). (QR/1).

Full QR First-Year Seminar,

Credits: (4).

Course Homepage: No homepage submitted.

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 next topic is non-Euclidean geometry. This 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: coordinatization the mathematician's tool for studying higher dimensions; construction of higher-dimensional analogues of some familiar objects like spheres and cubes; discussion of the proper higher-dimensional analogues of some geometric notions (length, angle, orthogonality, etc.). This course is intended for students who want an introduction to mathematical ideas and culture. Emphasis on conceptual thinking students will do hands-on experimentation with geometric shapes, patterns, and ideas.

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

MATH 147. Introduction to Interest Theory.

Instructor(s):

Prerequisites & Distribution: Math. 112 or 115. No credit granted to those who have completed a 200- (or higher) level mathematics course. (3). (MSA). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

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. 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. This course is not part of a sequence. Students should possess financial calculators.

Text: Mathematics of Finance, Zima and Brown, McGraw Hill Publishing.

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

MATH 186. Honors Calculus II.

Instructor(s):

Prerequisites & Distribution: Permission of the Honors advisor. Credit is granted for only one course from among Math. 114, 116, 119, 156, 176, 186, and 296. (4). (MSA). (BS). (QR/1).

Full QR

Credits: (4).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 214. Linear Algebra and Differential Equations.

Instructor(s):

Prerequisites & Distribution: Math. 115 and 116. 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. (4). (MSA). (BS).

Credits: (4).

Course Homepage: No homepage submitted.

No Description Provided.

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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).

Full QR

Credits: (4).

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

No Description Provided.

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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).

Credits: (4).

Course Homepage: http://www.math.lsa.umich.edu/courses/216/

No Description Provided.

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MATH 217. Linear Algebra.

Instructor(s):

Prerequisites & Distribution: Math. 215, 255, or 285. 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. (4). (MSA). (BS). (QR/1).

Full QR

Credits: (4).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 255. Applied Honors Calculus III.

Instructor(s):

Prerequisites & Distribution: Math. 156. Credit can be earned for only one of Math. 215, 255, or 285. (4). (MSA). (BS).

Credits: (4).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 286. Honors Differential Equations.

Instructor(s):

Prerequisites & Distribution: Math. 285. Credit can be earned for only one of Math. 216, 256, 286, or 316. (3). (MSA). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 288. Math Modeling Workshop.

Instructor(s):

Prerequisites & Distribution: Math. 216 or 316, and Math. 217 or 417. (1). (Excl). (BS). Offered mandatory credit/no credit. May be repeated for a total of three credits.

Mini/Short course

Credits: (1).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 289. Problem Seminar.

Instructor(s):

Prerequisites & Distribution: (1). (Excl). (BS). May be repeated for credit with permission.

Mini/Short course

Credits: (1).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 296. Honors Mathematics II.

Instructor(s):

Prerequisites & Distribution: Prior knowledge of first year calculus and permission of the Honors advisor. Credit is granted for only one course from among Math. 116, 119, 156, 176, 186, and 296. (4). (Excl). (BS). (QR/1).

Full QR

Credits: (4).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 310. Elementary Topics in Mathematics.

Math Games & Theory of Games.

Instructor(s): Mort Brown (mbrown@umich.edu)

Prerequisites & Distribution: Two years of high school mathematics. (4). (Excl). (BS).

Credits: (4).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 312. Applied Modern Algebra.

Instructor(s):

Prerequisites & Distribution: Math. 217. Only one credit granted to those who have completed Math. 412. (3). (Excl). (BS).

Credits: (3).

Course Homepage: http://www.math.lsa.umich.edu/courses/312/

No Description Provided.

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MATH 316. Differential Equations.

Instructor(s):

Prerequisites & Distribution: Math. 215 and 217. Credit can be earned for only one of Math. 216, 256, 286, or 316. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 333. Directed Tutoring.

Instructor(s): Eugene F Krause

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.

Credits: (1-3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 354. Fourier Analysis and its Applications.

Instructor(s):

Prerequisites & Distribution: Math. 216, 256, 286, or 316. No credit granted to those who have completed or are enrolled in Math. 454. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 371 / ENGR 371. Numerical Methods for Engineers and Scientists.

Instructor(s):

Prerequisites & Distribution: Engineering 101; one of Math. 216, 256, 286, or 316. (3). (Excl). (BS). CAEN lab access fee required for non-Engineering students.

Credits: (3).

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

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 396. Honors Analysis II.

Instructor(s):

Prerequisites & Distribution: Math. 395. (4). (Excl). (BS).

Credits: (4).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 399. Independent Reading.

Instructor(s):

Prerequisites & Distribution: (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 Instructor

MATH 412. Introduction to Modern Algebra.

Instructor(s):

Prerequisites & Distribution: Math. 215, 255, or 285; and 217. 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. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 416. Theory of Algorithms.

Section 001.

Instructor(s):

Prerequisites & Distribution: Math. 312 or 412 or CS 203, and CS 281. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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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).

Credits: (3).

Course Homepage: http://www.math.lsa.umich.edu/courses/417/

No Description Provided.

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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).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 422 / BE 440. Risk Management and Insurance.

Instructor(s):

Prerequisites & Distribution: Math. 115, junior standing, and permission of instructor. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 423. Mathematics of Finance.

Instructor(s):

Prerequisites & Distribution: Math. 217 and 425; CS 183. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 424. Compound Interest and Life Insurance.

Instructor(s):

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

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 425 / STATS 425. Introduction to Probability.

Instructor(s):

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

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 425 / STATS 425. Introduction to Probability.

Instructor(s):

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

Credits: (3).

Course Homepage: No homepage submitted.

See Statistics 425.

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

MATH 427 / HB 603. Retirement Plans and Other Employee Benefit Plans.

Section 001.

Instructor(s):

Prerequisites & Distribution: Junior standing. (3). (Excl).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 450. Advanced Mathematics for Engineers I.

Instructor(s):

Prerequisites & Distribution: Math. 215, 255, or 285. (4). (Excl). (BS).

Credits: (4).

Course Homepage: No homepage submitted.

No Description Provided.

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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).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 452. Advanced Calculus II.

Instructor(s):

Prerequisites & Distribution: Math. 217, 417, or 419; and Math. 451. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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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. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 462. Mathematical Models.

Instructor(s):

Prerequisites & Distribution: Math. 216, 256, 286, or 316; and 217, 417, or 419. Students with credit for Math. 362 must have department permission to elect Math. 462. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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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. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 475. Elementary Number Theory.

Instructor(s):

Prerequisites & Distribution: At least three terms of college mathematics are recommended. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 476. Computational Laboratory in Number Theory.

Instructor(s):

Prerequisites & Distribution: Prior or concurrent enrollment in Math. 475 or 575. (1). (Excl). (BS).

Credits: (1).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 485. Mathematics for Elementary School Teachers and Supervisors.

Instructor(s): Eugene F Krause

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.

Credits: (3; 2 in the half-term).

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 or preparing to teach in the elementary school.

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

MATH 486. Concepts Basic to Secondary Mathematics.

Instructor(s): Eugene F Krause

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

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 489. Mathematics for Elementary and Middle School Teachers.

Instructor(s): Eugene F Krause

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

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 490. Introduction to Topology.

Instructor(s):

Prerequisites & Distribution: Math. 412 or 451 or equivalent experience with abstract mathematics. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 498. Topics in Modern Mathematics.

Markov Chains: Theory and Applications.

Instructor(s): Divakar Viswanath

Prerequisites & Distribution: Senior mathematics concentrators and Master Degree students in mathematical disciplines. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

Markov chain theory is an elegant subject. This course will begin with the essentials: stationary measures, ergodicity, recurrence, and rate of convergence. Discussion of the Metropolis method, card shuffling, coupling techniques, two dimensional Ising models, and random matrix theory will follow. The elegance of this subject is easily matched by the breadth of its applications, which span all the major disciplines from Computer Science and Physics to Biology and Economics. So the final project can be any field of interest. Prerequisites: Math 425 would be good but any math class numbered in the 400s may be enough; some programming can be useful.

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

MATH 501. Applied & Interdisciplinary Mathematics Student Seminar.

Instructor(s):

Prerequisites & Distribution: At least two 300 or above level math courses, and graduate standing; Qualified undergraduates with permission of instructor only. (1). (Excl). (BS). Offered mandatory credit/no credit. May be repeated for a total of 6 credits.

Credits: (1).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 512. Algebraic Structures.

Instructor(s):

Prerequisites & Distribution: Math. 451 or 513. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 513. Introduction to Linear Algebra.

Instructor(s):

Prerequisites & Distribution: Math. 412. Two credits granted to those who have completed Math. 214, 217, 417, or 419. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 521. Life Contingencies II.

Instructor(s):

Prerequisites & Distribution: Math. 520. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 523. Risk Theory.

Instructor(s):

Prerequisites & Distribution: Math. 425. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 525 / STATS 525. Probability Theory.

Instructor(s):

Prerequisites & Distribution: Math. 450 or 451. Students with credit for Math. 425/Stat. 425 can elect Math. 525/Stat. 525 for only one credit. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 526 / STATS 526. Discrete State Stochastic Processes.

Instructor(s):

Prerequisites & Distribution: Math. 525 or EECS 501. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 526 / STATS 526. Discrete State Stochastic Processes.

Section 001.

Instructor(s):

Prerequisites & Distribution: Math. 525 or EECS 501. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

See Statistics 526.001.

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

MATH 531. Transformation Groups in Geometry.

Instructor(s):

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

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 550 / CMPLXSYS 510. Introduction to Adaptive Systems.

Section 001 Introduction to Dynamical Systems for Biocomplexity.

Instructor(s): Carl P Simon

Prerequisites & Distribution: Math. 215, 255, or 285; Math. 217; and Math. 425, and Permission of instructor. Working knowledge of calculus, probability, and matrix algebra. (3). (Excl). (BS).

Credits: (3).

Course Homepage: http://precisione.physics.lsa.umich.edu/CSCS/education/CSCS-courses/cscs510-w01.html

See Complex Systems 510.001.

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

Instructor(s):

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

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 557. Methods of Applied Mathematics II.

Instructor(s):

Prerequisites & Distribution: Math. 217, 419, or 513; 451 and 555. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 558. Ordinary Differential Equations.

Instructor(s):

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

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 559. Selected Topics in Applied Mathematics.

Section 001 Advanced Mathematical Methods for the Biological Sciences.

Instructor(s): Trachette Jackson (tjacks@umich.edu)

Prerequisites & Distribution: Math. 451; and 217 or 419. (3). (Excl). (BS). May be repeated for a total of six credits.

Credits: (3).

Course Homepage: No homepage submitted.

Natural systems behave in a way that reflects an underlying spatial pattern. For example, on the molecular level, rarely do reactions occur in a homogenous environment and the spatial organization does somehow influence the way in which particles interact. In this course, we will discover the way in which spatial variation influences the motion, dispersion, and persistence of species. We shall become aware of the fine balance that exists between interdependent species and demonstrate that spatial diversity can have subtle, but important effects or can lead to the emergence of remarkable spatial patterns from a previously uniform state. The concepts underlying spatially dependent processes and the partial differential equations which model them will be discussed in a general manner with examples taken from the molecular, cellular, and population levels. We will then apply these ideas to more specific cases with the aim of understanding interesting biological phenomena. Topics include: Population dispersal based on diffusion models; Cell movements (e.g., chemotaxis and haptotaxis); Growth of branching organisms; Traveling waves in microorganisms; Transport of biological substances; Models for development and pattern formation; and Age-Structured models of HIV dynamics.

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

Instructor(s):

Prerequisites & Distribution: Math. 217, 417, or 419. (3). (Excl). (BS). CAEN lab access fee required for non-Engineering students.

Credits: (3).

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

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 567. Introduction to Coding Theory.

Instructor(s):

Prerequisites & Distribution: One of Math. 217, 419, 513. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 571. Numerical Methods for Scientific Computing I.

Instructor(s):

Prerequisites & Distribution: Math. 217, 417, 419, or 513; and one of Math. 450, 451, or 454. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 572. Numerical Methods for Scientific Computing II.

Instructor(s):

Prerequisites & Distribution: Math. 217, 417, 419, or 513; and one of Math. 450, 451, or 454. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 582. Introduction to Set Theory.

Instructor(s):

Prerequisites & Distribution: Math. 412 or 451 or equivalent experience with abstract mathematics. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 592. Introduction to Algebraic Topology.

Instructor(s):

Prerequisites & Distribution: Math. 591. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 594. Algebra II.

Instructor(s):

Prerequisites & Distribution: Math. 593. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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MATH 597. Analysis II.

Instructor(s):

Prerequisites & Distribution: Math. 451 and 513. (3). (Excl). (BS).

Credits: (3).

Course Homepage: No homepage submitted.

No Description Provided.

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Graduate Course Listings for MATH.


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