Introduces fundamental ideas of probability, the theory of randomness. Focuses on problem solving and understanding key theoretical ideas. Topics include sample spaces, counting, random variables, classical distributions, expectation, Chebyshev's inequality, independence, central limit theorem, conditional probability, generating functions, joint distributions. Prerequisite: MATH 1320 or equivalent. Strongly recommended: MATH 2310

Introduces the methods, theory, and applications of differential equations. Includes first-order, second and higher-order linear equations, series solutions, linear systems of first-order differential equations, and the associated matrix theory. May include numerical methods, non-linear systems, boundary value problems, and additional applications. Prerequisite: MATH 1320 or its equivalent.

Topics in probability selected from Random walks, Markov processes, Brownian motion, Poisson processes, branching processes, stationary time series, linear filtering and prediction, queuing processes, and renewal theory. Prerequisites: MATH 3100 and MATH 3351.

This course covers linear algebra/complex analysis/vector differential & integral calculus. Thus it is a compressed version of MATH 3351 & MATH 3340 and a review of some of the material in MATH 2310. Emphasis is on the physical interpretation. [This course does not count as a Mathematics elective for Mathematics majors if both MATH 3351 and MATH 3340 are to be counted.] Prerequisite: MATH 2310 or MATH 2315 or APMA 2120

A second course in ordinary differential equations, from the dynamical systems point of view. Topics include: existence and uniqueness theorems; linear systems; qualitative study of equilibria and attractors; bifurcation theory; introduction to chaotic systems. Further topics as chosen by the instructor. Applications drawn from physics, biology, and engineering. Prerequisites: MATH 3351 or APMA 3080 and MATH 3310 or MATH 4310.

Studies the basic principles of linear analysis, including spectral theory of compact and selfadjoint operators. Prerequisite: MATH 7340 and 7310, or equivalent.

This course provides the opportunity to offer a new topic in the subject of mathematics.

Harmonic Analysis and PDEs seminar

The Mathematics Colloquium is held weekly, the sessions being devoted to research activities of students and faculty members, and to reports by visiting mathematicians on current work of interest. For doctoral dissertation, taken under the supervision of a dissertation director.