Mathematics Courses [245-550]

[204-224] [229-244] [245-550]

MATH 245. Methods of Applied Mathematics I. Principles and techniques of modern applied mathematics with case studies involving deterministic problems, random problems, and Fourier analysis. Prereq.: Graduate status.

MATH 246. Methods of Applied Mathematics II. 3 crs. Asymptotic sequences and series, special functions, asymptotic expansions of integrals and solutions of ordinary differential equations, and singular perturbations. Prereq.: MATH 245.

MATH 247. Numerical Analysis I. 3 crs. Numerical solutions of ordinary and partial differential equations including convergence stability, and consistence of schemes. Prereq.: Graduate status.

MATH 248. Numerical Analysis II. 3 crs. Continuation of MATH 247 including numerical methods for partial differential equations using functional analysis techniques; the Lax equivalence theorem; Courant-Friedrich Levy condition; Kreiss matrix theorem; and finite element methods. Prereq.: MATH 247.

MATH 250. Topology I. 3 crs. Topological basis, continuous, open closed topological maps, product spaces, connectedness, compactness, local connectedness, local compactness; identification and weak topologies, separation axioms, metrizable spaces, covering spaces, homotopy, fundamental groups.

MATH 251. Topology II. 3 crs. Compactifications, Baire spaces, function spaces, topological vector spaces.

MATH 252. Algebraic Topology I. 3 crs. Homotopy, covering spaces, fibrations, polyhedra, simplicial complexes, simplicial and singular homology, and Eilenberg-Steenrod axioms. Prereq.: MATH 251.

MATH 253. Algebraic Topology II. 3 crs. Continuation of MATH 252 including products; cohomology; homotopy, CW spaces, obstructions; sheaf theory; and spectral sequences. Prereq.: MATH 252.

MATH 259. Differential Geometry I. 3 crs. Differential manifolds, tensors, affine connections, and Riemannian manifolds. Prereq.: Graduate status.

MATH 260. Differential Geometry II. 3 crs. Continuation of MATH 259 including Riemannian geometry; submanifolds; variations of the length integral; the Morse index theorem; complex manifolds; Hermitian vector bundles; and characteristic classes. Prereq.: MATH 259.

MATH 270. Several Complex Variables. 3 crs. Basic facts about holomorphic functions; zero sets of holomorphic functions, analytic sets; domains of holomorphy, curves; plurisubharmonic functions, pseudoconvexity Levi problem; holomorphic convexity, Stein domains; complex manifolds, complex structure on TpM, almost complex structures, Dolbeault Cohomology, cohomology. Prereq.: MATH 229, MATH 230.

MATH 280. Topics in History of Mathematics. 3 crs. Topic to be selected by the instructor. Prereq.: Graduate status.

MATH 290,-299. Reading in Mathematics. 3 crs. Topic to be selected by the instructor. Prereq.: Graduate status.

MATH 300. Graduate Seminar. 3 crs. Topic to be selected by the instructor. Prereq.: Graduate status.

MATH 350. M.S. Thesis. 6 crs. Topic to be selected by mutual consent of the student and the instructor. Prereq.: Consent of graduate chairperson.

MATH 410,- 419. Topics in Algebra. 3 crs. ea. Further topics in algebra to be selected by the instructor. Prereq.: Consent of instructor.

MATH 430,- 439. Topics in Analysis. 3 crs. ea. Further topics in real and complex analysis to be selected by the instructor. Prereq.: Consent of instructor.

MATH 450, 459. Topics in Applied Mathematics. 3 crs. ea. Further topics in applied mathematics to be selected by the instructor. Prereq.: Consent of instructor.

MATH 470,- 479. Topics in Topology and Geometry. 3 crs. ea. Further topics in geometry and topology to be selected by the instructor. Prereq.: Consent of instructor.

MATH 500, 501. Graduate Seminar. 3 crs. ea. Topics to be selected by the instructor. Prereq.: Consent of instructor.

MATH 550. Ph.D. Dissertation. 12 crs. Prereq.: Consent of Ph.D. adviser.