Upper Division Mathematics Courses
Here are the 300-level courses offered by the Stony Brook Mathematics
department. The courses are grouped by subject, and within each
subject, are listed roughly in increasing order of difficulty; note
that higher numbered courses are not necessarily more difficult than
lower numbered ones.
We recommend that students start with MAT318, MAT312, MAT303/5, and MAT360. The most advanced classes are MAT313, MAT311, MAT322, MAT362, and MAT401/2. We also recommend those students thinking of graduate school take beginning graduate courses like Topology I (MAT530) and Algebra I (MAT534).
There are three "entry level" algebra classes with 200 level prerequisites: MAT318, MAT312, and MAT310. Two more advanced classes -- MAT313 and MAT311 -- require 300 level prerequisites, and are offered in the Fall and Spring respectively. MAT318 includes a written project, while MAT312 requires work with computers. The other three classes are more theoretical, with a considerable emphasis on proofs.
MAT318: Classical algebra
This course provides an examination of algebra from an historical perspective. Topics include the Euclidean algorithm, congruences and the unsolvability of the three "great problems": trisecting the angle, squaring the circle, and solving quintics. All students are required to write an extended project on topics ranging from the quaternions to Pascal's triangle. This course is offered in the Fall and the Spring. Its prerequisites are MAT211 or AMS210.
MAT312: Applied algebra
This course covers applications of congruence arithmetic to cryptography and applications of group theory to the theory of error-correction codes. Students participate in computer workshops in order to illustrate these applications. This course is crosslisted with AMS351. It is offered in the Fall and the Spring, and has MAT203 or MAT205 or AMS261, and MAT211 or AMS210 as prerequisites.
MAT310: Linear algebra
This course develops the basic theory of vector spaces and linear transformations. Together with MAT320, it forms the core of the mathematics major, teaching students how to write proofs. It is given in the Fall and the Spring, and has as prerequisites: MAT203 or MAT205 or AMS261, and MAT211 or AMS210.
MAT313: Abstract algebra
This course describes the basic properties of groups, rings, and fields. Students are expected to have taken either MAT312 or MAT318, which provide relevant examples of the general theory, or MAT310 which gives students experience with the theoretical development of algebraic structures. The course is only offered in the Fall. Students without any of the above prerequisites may take the class if they receive special permission from the instructor.
MAT311: Number theory
The fascinating properties of numbers are one of the main driving forces behind much of mathematics. This course discusses some accessible parts of number theory, such as continued fractions, quadratic residues, and properties of prime numbers. Students are required to have a knowledge of congruence arithmetic. The course is only offered in the Spring, and has as prerequisites MAT312 or MAT318 or MAT313, or permission of the instructor.
MAT303/5: Calculus IV
This course provides a basic introduction to differential equations. It is a prerequisite for all subsequent courses in this area.
MAT341: Applied Real Analysis
This course studies the classical equations governing the flow of heat, the motion of waves, and the distribution of electric charge. It is offered in the Fall.
MAT351: Differential equations: dynamics and chaos
This course studies systems which evolve with time, especially those with a chaotic nature. It involves short computer projects and is offered in the Spring.
MAT342: Applied complex analysis
This course studies complex-valued functions of a single complex
variable. These functions have many beautiful and unexpected
properties, as well as many applications to physics, engineering, and
other subjects. It is offered in the Spring and has
MAT303/5 as a prerequisite.
MAT320: Introduction to analysis
This introductory course in analysis is required of all
mathematics majors. It provides a rigorous, close look at
material which most students encounter, at least on an informal level,
during their first two semesters of calculus. The course teaches
students how to write proofs. All students, especially those who are
thinking of going to graduate school, should take this course as soon
as possible, although students who find abstract reasoning difficult
should first take
MAT322: Analysis in several dimensions
This course is a continuation of MAT320. It revisits and develops the basic ideas of multi-variable calculus. Since most applications of calculus involve more than one dimension, this course provides essential preparation for graduate level mathematics, and in fact, gives a good background for graduate study in any of the sciences. The course is offered in the Spring and has MAT320 as a prerequisite.
Topology and geometry
MAT360: Geometric structures
This course develops and contrasts Euclidean geometry with more exotic geometries, emphasizing topics relevant to high school curricula. The course involves some computer workshops, using software available in high schools. It is an accessible class, and is offered in the Spring.
MAT364: Topology and geometry
This course provides 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, and higher dimensional spaces. Although there are no formal 300-level prerequisites for this class, students should have taken some analysis or differential equations course beyond the level of MAT303/5. This course is offered in the Fall.
MAT362: Differential geometry of surfaces
This course studies the shape and curvature of low-dimensional spaces. It is the most sophisticated of the topology/geometry classes, and students are advised to take either MAT320 or MAT364 first. This course is offered in the Spring.
MAT331: Problem solving with computers
This course is highly recommended because of the ever-increasing role of computers in today's mathematics. The course's emphasis is on the "problem solving" portion of the title, and any development of the necessary mathematics will be done in the classroom. Students will be expected to calculate solutions using both computer experimentation and mathematical analysis (plus some help from the instructor!) This is not a programming course and no previous experience with computers is required. The course is offered in the Fall and the Spring.
MAT316: Invitation to modern mathematics
This course aims to give students an idea of what research mathematics is all about. Students first study the proofs of some basic results so as to acquire a feel for the kinds of ideas and arguments that lead to interesting conclusions. They then start asking their own questions -- and trying to come up with answers. The course grade is based on homework and an extended project. There are few formal prerequisites for this class, and students at all stages have enjoyed taking it. The main qualification is an interest in mathematics. The course is offered in the Spring.
MAT401/2: Seminar in mathematics
This course is intended as a bridge between undergraduate and graduate level mathematics and may be repeated. Topics vary from semester to semester. Recent topics have included: dynamical systems, measure theory and probability, manifolds and tensors, differential geometry, distribution theory, and foundations of mathematical logic. This course is required for the honors program and is highly recommended for all students thinking of graduate school. It is offered in the Fall and the Spring.