Mathematics Department

The most accessible classes are: MAT 318, 312, 303/305, and 360 and it is recommended that students start by taking some of these before trying other 300 level classes. The most advanced classes are MAT 313, 311, 322, 362 and 401/402. Students thinking about going to graduate school are highly recommended to take beginning graduate classes such as Topology/Geometry I (MAT 530) and Algebra I (MAT 534).

Algebra

MAT 318 (Classical Algebra) -- goes deeply into the topics of high school algebra from a historical perspective: prime numbers, complex numbers, constructible numbers and polynomials. Students write a project. An accessible class. (Fall and Spring)

MAT 312 (Applied Algebra) -- studies number congruences, groups and codes. A mixture of theory and applications, with some computer projects on public key cryptography and error correcting codes. An accessible class. (Fall and Spring)

MAT 310 (Linear Algebra) -- develops the basic theory of linear algebra. It is one of the two courses (MAT 320 is the other) in which students are taught how to write proofs, and is required for math majors. (Fall and Spring)

MAT 313 (Abstract Algebra) -- develops the abstract theory of groups, rings and fields. Highly recommended for those planning to go to graduate school. Prerequisite: MAT 310 or 312 or 318. (Fall only)

MAT 311 (Number theory) -- this classical and beautiful subject has surprising applications. This class has newly increased prerequisites, and so will be able to go fairly deeply into this subject. Prerequisite: MAT 312 or 313 or 318. (Spring)

Differential equations

MAT 303 and 305 (Calculus IV) -- a basic introduction to differential equations; prerequisite for all subsequent courses in this area.

MAT 341 (Applied Real Analysis) -- a study of the classical equations governing the flow of heat, the motion of waves, and the distribution of electric charge. (Fall)

MAT 351 (Differential equations: Dynamics and Chaos) -- studies systems which evolve with time, sometimes in a chaotic manner. Involves short computer projects. (Spring)

Analysis

MAT 342 (Applied complex analysis) -- studies complex valued functions of a complex variable. These functions have many beautiful and unexpected properties, as well as many applications, for example in physics. Prerequisite: Calc IV. (Spring)

MAT 320 (Introduction to Analysis) -- 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. Students learn how to write proofs. Students (especially those thinking of going to graduate school) should take this as early as possible. However students who find abstract reasoning hard are advised to take Calculus IV (MAT 303/305) first.

MAT 322 (Analysis in several dimensions) -- continues MAT 320, revisiting and developing the basic ideas of many-variable calculus. Since most applications of calculus involve working in more than one dimension, this is essential preparation for graduate level mathematics, and excellent background for graduate study in any science. Prerequisite: MAT 320. (Spring)

Topology and Geometry

MAT 360 (Geometric Structures) -- develops and contrasts Euclidean geometry with more exotic geometries, emphasizing topics relevant to the high school curriculum. Involves some computer workshops using software available in high schools. An accessible class. (Spring)

MAT 364 (Topology and Geometry) -- a broadly based introduction to mathematical theories of space, shape and form. Topics are selected from 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. Though there are no formal 300 level prerequisites for this class, it is advisable for students to have taken some analysis or differential equations class beyond Calculus IV. (Fall)

MAT 362 (Differential Geometry of Surfaces) -- studies the shapes of low-dimensional spaces and how they curve. This is the most sophisticated of the topology/geometry classes, and students are advised to take either MAT 320 or MAT 364 first. (Spring)

Various

MAT 331 (Problem solving with computers) -- a highly recommended course because of the ever-increasing role of computers in today's mathematics. The emphasis in this course is on the \lq\lq problem solving" portion of the title. The discussion of the problems and development of the necessary mathematics will be done in the classroom, and then students 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). This is NOT a programming course and no previous experience with computers is required. (Fall and Spring)

MAT 316 (Invitation to Modern Mathematics) -- aims to give students an idea what research in mathematics is about. Students first study the proofs of some basic results to get a feel for the kinds of ideas and arguments which lead to interesting conclusions, and then start asking their own questions and trying to come up with some answers. The grade is based on homework and an extended project. The formal prerequisites for this class are few, and students at all stages have enjoyed taking it. The main qualification is an interest in mathematics. (Spring)

MAT 401/2 (Seminar in Mathematics) -- a bridge between undergraduate and graduate level mathematics, and may be repeated. Topics vary from semester to semester. The Fall 99 topic is Dynamical Systems and the Spring 2000 topic may be Measure Theory and Probability. Recent topics have included: Manifolds and Tensors, Differential Geometry, Distribution Theory, and Foundations of Mathematical Logic. Required for the Honors program and highly recommended for those thinking of graduate school. (Fall and Spring)

The Honors Program is open to junior and senior mathematics majors who have completed at least two upper-division MAT courses with grades of B or higher and who have maintained a 3.0 overall grade point average. The program consists of a set of six MAT courses, at least three of which are not used to fulfil the major requirements, and should include MAT 316, MAT 322, MAT 401, MAT 311 or 313, and MAT 495 Honors Thesis. (Substitutions may be permitted.) Students interested in this program should consult with a faculty advisor before the beginning of their senior year.

Stony Brook, April 1999