To complete this research-methods topic, a student is required to take 2 of the following 4 courses. Note that MATH 51900/STAT 51900 (Intro to Probability) is a prerequisite for MATH 53200
MATH 50400 Real Analysis
Completeness of the real number system, basic topological properties, compactness, sequences and series, absolute convergence of series, rearrangement of series, properties of continuous functions, the Riemann-Stieltjes integral, sequences and series of functions, uniform convergence, the Stone-Weierstrass Theorem, equicontinuity, the Arzela-Ascoli Theorem.
MATH 51100 Linear Algebra With Applications
Real and complex vector spaces; linear transformations; Gram-Schmidt process and projections; unitary and orthogonal diagonalization; Jordan canonical form; quadratic forms.
MATH 53200 Elements of Stochastic Processes (STAT 53200 is the same course)
A basic course in stochastic models, including discrete and continuous time Markov chains and Brownian motion, as well as an introduction to topics such as Gaussian processes, queues, epidemic models, branching processes, renewal processes, replacement, and reliability problems.
MATH 54400 Real Analysis and Measure Theory
Metric space topology; continuity, convergence; equicontinuity; compactness; bounded variation, Helly selection theorem; Riemann-Stieltjes integral; Lebesgue measure; abstract measure spaces; Lp-spaces; Hölder and Minkowski inequalities; Riesz-Fischer theorem.