2072 East Hall

764-0337

Professor B. A. Taylor, Chair

David E. Barrett,

Andreas R. Blass,

Morton Brown,

Daniel M. Burns, Jr.,

Joseph G. Conlon,

Igor V. Dolgachev,

Peter L. Duren,

Paul G. Federbush,

John Erik Fornaess,

Robert L. Griess, Jr.,

Philip J. Hanlon,

Donald G. Higman,

Peter G. Hinman,

Melvin Hochster (R.W. and L.H. Browne Professor of Science),

Curtis Huntington,

James M. Kister,

Eugene F. Krause,

Donald J. Lewis,

James S. Milne,

Hugh L. Montgomery,

Gopal Prasad,

M. S. Ramanujan,

Jeffrey B. Rauch,

Frank A. Raymond,

G. Peter Scott,

Carl P. Simon,

Joel A. Smoller,

Ralf J. Spatzier,

J. Tobias Stafford,

John R. Stembridge,

Thomas F. Storer,

B. Alan Taylor,

Alejandro Uribe-Ahumada,

Arthur G. Wasserman,

Michael I. Weinstein,

David J. Winter,

Michael B. Woodroofe,

Anthony M. Bloch,

Christoph Borgers,

Jack L. Goldberg,

Thomas Hales,

Eduard Harabetian,

Juha Heinonen,

Robert Krasny,

Igor Kriz,

John W. Lott,

Robert Megginson,

Allen Moy,

Art J. Schwartz,

Chung-Tuo Shih,

Berit Stensones,

Trevor Wooley,

John N. Aarsvold,

Alexandre Barvinok,

Michael Bean

Michael Bennett,

Richard Canary,

Timothy Chow,

Donatella Delfino,

Vesselin Gasharov,

Rita Gitik,

Mark Gockenbach,

Lizhen Ji,

Richard Jordan,

Ruth Lawrence,

Liviu Nicolaescu,

Mingqing Ouyang,

Guillaume Sanje-Mpacko,

Nikolai Savaliev,

Peter Smereka,

Renming Song,

Joanna Staniszkis,

Edward Taylor,

Siu-Kei Tin,

Lan Wang,

Caryn Werner,

Glen Whitney,

Jeremy D. Avigad,

Ioannis Emmanouil,

Timothy Hsu,

Alexandru Nica,

Tonghai Yang,

Howard Young,

Patricia Shure,

Mathematics is sometimes called the Queen of the Sciences; because of its unforgiving insistence on accuracy and rigor it is a model for all of science. It is a field which serves science but also stands on its own as one of the greatest edifices of human thought. Much more than a collection of calculations, it is finally a system for the analysis of form. Alone among the sciences, it is a discipline where almost every fact can and must be proved.

The study of mathematics is an excellent preparation for many careers; the patterns of careful logical reasoning and analytical problem solving essential to mathematics are also applicable in contexts where quantity and measurement play only minor roles. Thus students of mathematics may go on to excel in medicine, law, politics, or business as well as any of a vast range of scientific careers. Special programs are offered for those interested in teaching mathematics at the elementary or high school level or in actuarial mathematics, the mathematics of insurance. The other programs split between those which emphasize mathematics as an independent discipline and those which favor the application of mathematical tools to problems in other fields. There is considerable overlap here, and any of these programs may serve as preparation for either further study in a variety of academic disciplines, including mathematics itself, or intellectually challenging careers in a wide variety of corporate and governmental settings.

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, 128, and 147 are courses containing selected topics from geometry number theory, and financial mathematics. 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, 128, or 147 if a student has already received credit for a 200(or higher)-level mathematics course.

Each of Math 112, 115, 185, and 295 is a first course in calculus and generally credit can be received for only one course from this list. Math 112 is designed for students of business and the social sciences who require only one term of calculus. It neither presupposes nor covers any trigonometry. The sequence 115-116-215 is appropriate for most students who want a complete introduction to calculus. Math 118 is an alternative to Math 116 intended for students of the social sciences who do not intend to continue to Math 215. One of Math 215, 285, or 395 is prerequisite to most more advanced courses in Mathematics. Math 112

Students planning a career in medicine should note that some medical schools require a course in calculus. Generally either Math 112 or 115 will satisfy this requirement, although most science concentrations require at least a year of calculus. Math 112 is accepted by the School of Business Administration, but Math 115 is prerequisite to concentration in Economics and further math courses are strongly recommended.

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. 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 semester of AP credit, Math 119 and Math 156 (Fall). Both will review the basic concepts of calculus, cover integration and an introduction to differential equations, and introduce the student to the use of the computer algebra system MAPLE. Math 119 will stress experimentation and computation, while Math 156 is intended primarily for engineering and science majors, and will emphasize both applications and theory. Interested students are advised to consult a mathematics advisor for more details.

In rare circumstances and

Students completing Math 215 may continue either to Math 216 (Introduction to Differential Equations) or to the sequence Math 217-316 (Linear Algebra-Differential Equations). Math 217-316 is

(Students should consult the pamphlet

a. Four basic courses (one course from each of the following four groups):

Modern Algebra: Math 412 or 512

Differential Equations: Math 286 or 316

Analysis: Math 451

Geometry/Topology: Math 432, 433, 490, 531 or 590

b. Four elective courses (mathematics) chosen from a list of approved electives and approved by a concentration advisor.

c. One cognate course outside the Mathematics Department, but having advanced mathematical content.

(Students should consult the pamphlet

Additional prerequisite: one term of computer programming (EECS 183 or the equivalent), and for the Numerical and Applied Analysis option, 8 credits of physics.

a. Four basic courses (one course from each of the following four groups):

Differential Equations: Math 286 or 316

Discrete Math/Modern Algebra: Math 312, 412 or 512

Analysis: Math 450 or 451

Probability: Math 425 or 525

b. At least three courses from ONE of the Program Options listed below (the list of possible electives for each option is given in the

Discrete and Algorithmic Methods

Numerical and Applied Analysis

Operations Research and Modelling

Probabilistic Methods

Mathematics of Finance and Risk Management

Mathematical Economics

Mathematical Physics

Control Systems

c. Two additional advanced mathematics (or related) courses, approved by a concentration advisor.

Outstanding students may elect an Honors concentration in Mathematics. The Honors Program is designed not only for students who expect to become mathematicians but also for students whose ultimate professional goal lies in the humanities, law, medicine or the sciences.

Students intending an Honors concentration are strongly advised to take one of the Honors introductory calculus sequences (175 or 185)-286 or 295-396, or some combination of the two. Eight credits of physics and familiarity with a high-level computer language are

(Students should consult the pamphlet

a. Four basic courses (one course from each of the following four groups):

Linear Algebra: Math 513

Modern Algebra: Math 512

Analysis: Math 451

Geometry/Topology: Math 433, 490, 590 or 531

b. Four elective (mathematics) courses, chosen with the approval of the Honors advisor.

c. One cognate course from outside the Mathematics department, but containing significant mathematical content, chosen with the approval of the Honors advisor.

Students who, in the judgment of the departmental Honors committee, have completed an Honors concentration with distinction are granted a citation upon graduating. Interested students should discuss their program and the specific requirements for obtaining the citation with a Mathematics Honors advisor (appointments scheduled in 2082 East Hall) no later than the second term of their sophomore year.

(Students should consult the pamphlet

Additional prerequisite: At least one course in each of the following fields: Accounting (271, 272, 471), Computer Science (183, 280), and Economics (201, 202, 400).

a. Five basic courses (one from each of the following five groups):

1. Differential Equations: Math 286 or 316

2. Probability: Math 425 or 525

3. Analysis: Math 450 or 451

4. Statistics: Stat 426

5. Numerical Analysis: Math 371 or 471 (preferred)

b. Three special actuarial courses, including Math 424 and 520, and one of Math 521 or 522.

c. Two additional courses in areas relating to Actuarial Science, approved by an advisor.

It is essential that students planning to obtain a teaching certificate consult a teaching certificate advisor, either Professor Krause (LS&A) or Professor Coxford (Education),

Additional prerequisite: One term of computer programming, EECS 183 or the equivalent.

(Students should consult the pamphlet

a. Four basic courses, one from each of the following four groups (chosen with the approval of a teaching certificate advisor):

1. Discrete Math/Modern Algebra: Math 312, 412, or 512

2. Geometry: Math 431, 432 or 531

3. Probability: Math 425 or 525

4. Secondary Mathematics: Math 486

b. Seven specific education courses, totaling 28 credits. Consult the

c. A major or minor in a second academic area (normally requires 20-24 credits in a structured program other than Mathematics. Consult the

d. Two additional courses, which must include a course in the Psychology Department, and a minimum of one additional mathematics course.

Students should consult with Professor Coxford in their sophomore year to be admitted to the certification program and to schedule practice teaching.

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