Mathematics Department

Here is a list of courses to be offered in Fall 2001. They are all offered Fall and Spring unless otherwise mentioned.

MAT 310 Linear Algebra - TuTh 9:50-11:10, (John Robertson)
Linear algebra, the study of vector spaces and linear transformations, is an essential tool in many areas of mathematics. For example, a substantial amount of calculus results from linearizing a function at a point and applying linear algebra. In differential equations, one views a linear equation as the result of applying a linear transformation to a vectorspace of functions. The subject also has wide applications to other disciplines, such as physics. This course emphasizes the development of mathematical theory and students will be taught how to write proofs. It is required for all math majors. Prerequisites: MAT 211 or AMS 210; some version of Calc III (ie MAT 203/205 or AMS 261)

MAT 312/AMS 351 Applied Algebra -- MWF 2:15-3:30 (Andrew McIntyre)
This is an introduction to congruences and group theory through applications. Although the course will emphasize applications (especially encryption methods and error-correcting codes), a fair amount of attention will be paid to the underlying theory. Students will also do some computer projects. Now offered Fall and Spring prereq: MAT 211 or AMS 210; some version of Calc III

MAT 313 Abstract Algebra - TuTh 11:20-12:40 (John Terilla)
This course introduces students to the basic algebraic structures which underlie all of modern mathematics. We begin with groups and group homomorphisms and then study the ring of integers and the fields formed by various kinds of numbers. This course is more abstract (and so for some students more difficult) than MAT 318 or 312, and has newly increased prerequisites. It is highly recommended for all students thinking of going to graduate school in a mathematics related discipline. Now Fall only. MAT 311 (Number theory) will be offered in the Spring. Prerequisites: MAT 310 or 312 or 318; some version of Calc III Students who have taken both MAT 310 and MAT 313 and who want to take a more advanced algebra class should consider the graduate class MAT 534: Algebra I

MAT 318 Classical Algebra MWF 10:30-11:25 (Siddartha Gadgil)
Reexamines algebra from a historical perspective. Properties of the integers (unique factorization, Euclidean division algorithm), complex numbers and polynomials; unsolvability of the three great problems (trisecting the angle, squaring the circle, solving quintics); modern perspectives. Students write an extended project. This is the most accessible of the 300 level algebra classes and is highly recommended to students in the teacher preparation program. Now offered Fall and Spring Prerequisites: MAT 211 or AMS 210.

MAT 320 Introduction to Analysis -- MWF 11:35-12:30 (Irwin Kra), recitation F 12:40-1:35 (W. Kim)
This is an introductory course in analysis, required for math majors. It provides a closer and more rigorous look at material which most students encountered on an informal level during their first two semesters of Calculus. There are two motivations to doing this. One is simply to gain an understanding of what a mathematical proof is about, and how the tools of calculus, such as real numbers, limits and derivatives, are really constructed and justified. The second motivation is to build up a robust framework on which the student can confidently hang more sophisticated tools, both pure and applied. For example, the concept of limit, which is logically subtle, can be related to the notion of estimation and control of errors in approximate calculations. This "practical" approach to the logic will be maintained as far as possible throughout the semester. At the same time the course will show with short but detailed examples how the ideas and techniques it presents apply to many different contexts in pure and applied mathematics. Prerequisites: MAT 203 or 205 or 211 or AMS 261 or A- or higher in MAT 127 or 132.

MAT 324 Introduction to Measure Theory MWF 11:35-12:30 (David Ebin)

MAT 331 Problem Solving using computers - Sec 01 TuTh 2:20-3:40 (Shafikov), Sec 02 MW 5:30-6:56 (Yankeelov)
The emphasis in this course is on the ``problem solving'' portion of the title -- we will take a series of problems and try to find solutions, keeping in mind that we have a computer at hand. For example, one such problem is the brachistocrone problem -- to find the curve along which a particle will slide (without friction) in the shortest time from one point to another. The discussion of the problems and development of the necessary mathematics will be done in the classroom, and then we will adjourn to the computers to work out solutions. These should be found by the class with a combination of experimentation and mathematical analysis (plus maybe some help from the instructor). Collaborations and classroom participation is STRONGLY encouraged, although the write-ups of the probelms should be done individually. We will use the math computer lab in S235, which is equipped with SUN workstations, and MAPLE. Contrary to popular belief, this is NOT a programming course, although we may do some simple programming. NO previous experience with computers is required. Prerequisites: some version of Calc III

MAT 341 Applied Real Analysis - TuTh 9:50-11:10 (Santiago Simanca)
The course begins with a discussion of the physical derivation and meaning of the classical PDE's: the heat equation, the wave equation and the equations of Laplace and Poisson. Then comes a discussion of which type of boundary conditions and/or initial conditions are appropriate for each of these equations. Examples and connections with heat conduction, diffusion, vibrating membranes, potential theory, and electrostatics are used to explain and motivate the notion of a well-posed problem. The main technique used to understand and solve these equations is Fourier series. Fall only Prerequisites: some version of Calc IV (ie MAT 303/305 or AMS 361)

MAT 364: Topology and Geometry TuTh 12:50-2:10 (Mikhail Lyubich)
A broadly based introduction to topology and geometry, the mathematical theories of shape, form, and rigid structure. Topics include intuitive knot theory, lattices and tilings, non-Euclidean geometry, smooth curves and surfaces in Euclidean 3-space, open sets and continuity, combinatorial and algebraic invariants of spaces, higher dimensional spaces. Fall only Prerequisite: some version of Calc III. Students who are ready for a more advanced topology course should consider taking the graduate course MAT 530.

MAT 373: Analysis of Algorithms MWF 10:30-11:25
Crosslisted with AMS 373 and CSE 373. Contact the CSE department for more information.

MAT 401: Mathematics Seminar TuTh 12:50-2:10 (Sorin Popescu) The mathematics seminar is offered each semester. Topics rotate, and students will be expected to make short presentations in class as well as to write a short project. For more detailed information, please see the separate sheet. Prerequisite: MAT 320 or permission of the instructor

MAT 475 Teaching Practicum HTBA

MAT 487 Independent Study Tutorial; by arrangement with instructor.

MAT 495 Honors Thesis Tutorial; by arrangement with instructor.