Topics to be chosen from graduate mathematics and related fields. This course can be repeated at most 2 times for a maximum of 12 credits total.
Department consent.
4 hr./wk.
Cauchy-Riemann equations, conformal mapping, elementary, entire, meromorphic, multiple-valued functions, Cauchy integral theorems, series expansion.
A grade of C or higher in
MATH 32404 or placement by the Department.
4 hr./wk.
Lebesgue measure and integration on the real line, differentiation of real functions and the relation with integration, classical Lp spaces.
A grade of C or higher in
MATH 32300 or permission of the instructor.
4 hr./wk.
First order equations, shock waves; classification and canonical forms of higher order equations, characteristics, the Cauchy problem for the wave equation: Huygens' principle; the heat equation; Laplace's equation; the Dirichlet and Neuman problems; harmonic functions; eigenvalue expansions; Green's functions.
4 hr./wk.
Axioms of Zermelo-Fraenkel set theory; relations, functions, equivalences and orderings; cardinal numbers and cardinal arithmetic; well-ordered sets; ordinal numbers, transfinite induction and recursion; the Axiom of Choice and the Continuum Hypothesis.
A grade of C or higher in
MATH 32300 or permission of the instructor.
4 hr./wk.
The propositional calculus, the sentential calculus, normal forms, first order theories, consistency, categoricity, decidability, Godel's incompleteness theorem, the Loewenheim-Skolem theorem.
A grade of C or higher in
MATH 32300 or permission of the instructor.
4 hr./wk.
Dynamical systems in one and more dimensions, symbolic dynamics, chaos theory, hyperbolicity, stable manifolds, complex dynamics.
C or better om
MATH 32404 or permission of the instructor.
4 hr./wk.
Linear systems, matrix decompositions, inner product spaces, self-adjoint transformations, spectral theory, discrete Fourier Transforms.
C or better in
MATH 34600 or permission of the instructor.
4 hr./wk.
Fall only
4 hr./wk.
The theory of curves and surfaces in three-dimensional space: frames, fundamental forms, geodesics; curvature of surfaces; surface area; surfaces with boundary, the Gauss-Bonnet Theorem; introduction to Riemannian metrics.
4 hr./wk.
A course in general topology. Sets of points on the real line and in general abstract spaces, relations between sets of points and between a set and the space containing it, operations with sets, open sets, countability, compactness, connectedness, maps, continuity, metric spaces, general topological spaces.
A grade of C or higher in
MATH 32404 or placement by the Department.
4 hr./wk.
A first course in algebraic number theory which assumes some abstract algebra. Topics include: unique factorization in the integers and Euclidean domains, structure of the groups Z/mZ and their multiplicative units, quadratic residues and quadratic reciprocity, algebraic number fields, finite fields.
Grade of C or better in
MATH 34700 or departmental permission.
4 hr./wk.
Problems from industry, mathematical models, process of mathematical abstraction, problem-solving techniques, application of solutions.
3 hr./wk.
Permutations, combinations, generating functions and recurrence relations, inclusion and exclusion, applications to matching theory, linear and dynamic programming, Polya's theory of counting, introduction to graph theory and coloring theory.
4 hr./wk.
Special topics in probability such as stochastic processes, Markov chains.
4 hr./wk.
The multivariate normal distribution, multiple and partial correlation, regression and least squares, the analysis of variance.
Fall only
4 hr./wk.