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Courses - Spring 2019
MATH
Mathematics Department Site
MATH601
Abstract Algebra II
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: MATH600.
Field theory, Galois theory, multilinear algebra. Further topics from: Dedekind domains, Noetherian domains, rings with minimum condition, homological algebra.
Offered Spring only.
MATH603
Commutative Algebra
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: MATH600.
Ideal theory of Noetherian rings, valuations, localizations, complete local rings, Dedekind domains.
MATH607
Algebraic Geometry II
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: MATH606.
Topics in contemporary algebraic geometry chosen from among: theory of algebraic curves and surfaces, elliptic curves, Abelian varieties, theory of schemes, theory of zeta functions, formal cohomology, algebraic groups, reduction theory.
MATH631
Real Analysis II
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: MATH630.
Abstract measure and integration theory, metric spaces, Baire category theorem and uniform boundedness principle, Radon-Nikodym theorem, Riesz Representation theorem, Lebesgue decomposition, Banach and Hilbert Spaces, Banach-Steinhaus theorem, topological spaces, Arzela-Ascoli and Stone-Weierstrass theorems, compact sets and Tychonoff's theorem.
Offered Spring only.
MATH660
Complex Analysis I
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: MATH410; or students who have taken courses with comparable content may contact the department.
Linear transformations, analytic functions, conformal mappings, Cauchy's theorem and applications, power series, partial fractions and factorization, elementary Riemann surfaces, Riemann's mapping theorem.
MATH674
Partial Differential Equations II
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: MATH673 or AMSC673; or permission of instructor.
Also offered as: AMSC674.
Credit only granted for: AMSC674 or MATH674.
Boundary value problems for elliptic partial differential equations via operator-theoretic methods. Hilbert spaces of functions. Duality, weak convergence. Sobolev spaces. Spectral theory of compact operators. Eigenfunction expansions.
Offered Spring only.
MATH713
Mathematical Logic II
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: MATH712.
Incompleteness and undecidability results of Godel, Church, Tarski and others. Recursive function. Basic proof theory and axiomatic set theory.
MATH734
Algebraic Topology
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: MATH403; or students who have taken courses with comparable content may contact the department.
Recommended: MATH730.
Singular homology and cohomology, cup products, Poincare duality, Eilenberg-Steenrod axioms, Whitehead and Hurewicz theorems, universal coefficient theorem, cellular homology.
MATH740
Fundamental Concepts of Differential Geometry
Credits: 3
Grad Meth: Reg, Aud
Prerequisite: MATH405, MATH411, and MATH730; or students who have taken courses with comparable content may contact the department.
Manifolds, tangent vectors and differential forms, Riemannian metrics, connections, curvature, structure equations, geodesics, calculus of variations.
MATH808M
Selected Topics in Algebra; Arithmetic of Modular Curves
Credits: 1 - 3
Grad Meth: Reg, Aud
MATH848G
Selected Topics in Geometry and Topology; Dynamics on Moduli Spaces
Credits: 1 - 3
Grad Meth: Reg, Aud
MATH858D
Selected Topics in Analysis; Stochastic Methods with Applications
Credits: 1 - 3
Grad Meth: Reg, Aud
MATH858T
Selected Topics in Analysis; Minimal Cantor Systems
Credits: 1 - 3
Grad Meth: Reg, Aud