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 class introduces students to the mathematics used in pricing derivative securities. Topics include a review of the relevant probability theory of conditional expectation and martingales/the elements of financial markets and derivatives/pricing contingent claims in the binomial & the finite market model/(time permitting) the Black-Scholes model. Prerequisites: MATH 3100, MATH 3351 and a proof-based course (MATH 3000, MATH 3310 or MATH 3354).

The study of the integers and related number systems. Includes polynomial congruences, rings of congruence classes and their groups of units, quadratic reciprocity, diophantine equations, and number-theoretic functions. Additional topics such as the distribution of prime numbers may be included. Prerequisite: MATH 3354.

Studies the fundamental theorems of analytic function theory.

A second calculus course for natural-science majors, students planning additional work in mathematics, and students intending to pursue graduate work in the applied social sciences. Topics include applications of the integral, techniques of integration, differential equations, infinite series, parametric equations, and polar coordinates. Prerequisite: MATH 1310 or equivalent; at most one of MATH 1220 and MATH 1320 may be taken for credit.

Surveys major topics of modern algebra: groups, rings, and fields. Presents applications to areas such as geometry and number theory; explores rational, real, and complex number systems, and the algebra of polynomials. Students without prior experience constructing rigorous proofs are encouraged to take Math 3000 before or concurrently with Math 3354. Prerequisite: MATH 1320.

Review of topics from Math 3351: vector spaces, bases, dimension, matrices and linear transformations, diagonalization; however, the material is covered in greater depth and generality. The course continues with more advanced topics including Jordan canonical forms and introduction to bilinear forms. Prerequisites: a proof-based course and familiarity with computational aspects of elementary linear algebra. Math 3354 is strongly recommended

This course is a beginning course in partial differential equations/Fourier analysis/special functions (such as spherical harmonics and Bessel functions). The discussion of partial differential equations will include the Laplace and Poisson equations and the heat and wave equations. Prerequisites: MATH 3250 and either MATH 3351 or MATH 4210.

Covers the material from Math 2310 (multivariable calculus) plus topics from complex numbers, set theory, and linear algebra. Prepares students for taking advanced mathematics classes at an early stage. Credit is not given for both Math 2310 and Math 2315.

Structural properties of basic algebraic systems such as groups, rings, and fields. A special emphasis is made on polynomials in one and several variables, including irreducible polynomials, unique factorization, and symmetric polynomials. Time permitting such topics as group representations or algebras over a field may be included. Prerequisites: MATH 3351 or 4651 and MATH 3354 or permission of the instructor.