Graduate Courses
Spring 2022 Graduate Courses: *TENTATIVE*
Below is a tentative list of courses being offered in the upcoming Spring, 2022 semester.
Graduate Courses
| Course | Description | Time and Location | Instructor | CRN |
|---|---|---|---|---|
| MATH 512: Advanced Topics in Logic | Advanced topics in modern logic; e.g. large cardinals, infinitary logic, model theory of fields, o-minimality, Borel equivalence relations. Course Information: Same as PHIL 569. May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. | MWF 2:00-2:50 | Dima Sinapova | |
| MATH 515: Number Theory II | Introduction to classical, algebraic, and analytic number theory. Algebraic number fields, units, ideals, and P-adic theory. Riemann Zeta-function, Dirichlet's theorem, prime number theorem. Course Information: Prerequisite(s): MATH 514. | MWF 10:00 - 10:50 | Nathan Jones | |
| MATH 517: Second Course in Abstract Algebra II | Rings and algebras, polynomials in several variables, power series rings, tensor products, field extensions, Galois theory, Wedderburn theorems. Course Information: Prerequisite(s): MATH 516. | MWF 1:00 - 1:50 | Izzet Coskun | |
| MATH 525: Advanced Topics in Number Theory | Introduction to topics at the forefront of research in number theory. Topics will vary and may include elliptic curves, automorphic forms, diophantine geometry or sieve methods. Course Information: May be repeated. Prerequisite(s): MATH 515; or consent of the instructor. | MWF 11:00 - 11:50 | Ramin Takloo-Bighash | |
| MATH 535: Complex Analysis | Analytic functions as mappings. Cauchy theory. Power Series. Partial fractions. Infinite products. Course Information: Prerequisite(s): MATH 411. | MWF 2:00 - 2:50 | ||
| MATH 537: Introduction to Harmonic Analysis | Fourier transform on L(p) spaces, Wiener's Tauberian theorem, Hilbert transform, Paley Wiener theory. Course Information: Prerequisite(s): MATH 533; and MATH 417 or MATH 535. | MWF 1:00 - 1:50 | Michael Greenblatt | |
| MATH 548: Algebraic Topology II | Cohomology theory, universal coefficient theorems, cohomology products and their applications, orientation and duality for manifolds, homotopy groups and fibrations, the Hurewicz theorem, selected topics. Course Information: Prerequisite(s): MATH 547. | MWF 9:00 - 9:50 | ||
| MATH 549: Differentiable Manifolds I | Smooth manifolds and maps, tangent and normal bundles, Sard's theorem and transversality, embedding, differential forms, Stokes's theorem, degree theory, vector fields. Course Information: Prerequisite(s): MATH 445; and MATH 310 or MATH 320 or the equivalent. | MWF 11:00 - 11:50 | Wouter Van LImbeek | |
| MATH 551: Riemannian Geometry | Riemannian metrics and Levi-Civita connections, geodesics and completeness, curvature, first and second variation of arc length, comparison theorems. Course Information: Prerequisite(s): MATH 442 and MATH 549. | MWF 12:00 - 12:50 in TH 300 | Julius Ross | |
| MATH 553: Algebraic Geometry II | Divisors and linear systems, differentials, Riemann-Roch theorem for curves, elliptic curves, geometry of curves and surfaces. Course Information: Prerequisite(s): MATH 552. | MWF 12:00 - 12:50 | Lawrence Ein | |
| MATH 569: Advanced Topics in Geometric and Differential Topology | Topics from areas such as index theory, Lefschetz theory, cyclic theory, KK theory, non-commutative geometry, 3-manifold topology, hyperbolic manifolds, geometric group theory, and knot theory. Course Information: Prerequisite(s): Approval of the department. | MWF | Alex Furman | |
| MATH 576: Classical Methods of Partial Differential Equations | First and second order equations, method of characteristics, weak solutions, distributions, wave, Laplace, Poisson, heat equations, energy methods, regularity problems, Green functions, maximum principles, Sobolev spaces, imbedding theorems. Course Information: Prerequisite(s): MATH 410 and MATH 481 and MATH 533; or consent of instructor. | MWF 12:00 - 12:50 | Irina Nenciu | |
| MATH 582: Linear and Nonlinear Waves | Analysis of partial differential equations describing (non-) linear wave phenomena. In particular, dispersive and hyperbolic equations. Analytical techniques include Fourier transformation and fixed point theorems. Course Information: Prerequisite(s): Graduate standing and MATH 533 and MATH 576 OR MATH 539 or consent of the instructor. | MWF 3:00 - 3:50 | Christof Sparber | |
| MATH 586: Computational Finance | Introduction to the mathematics of financial derivatives; options, asset price random walks, Black-Scholes model; partial differential techniques for option valuation, binomial models, numerical methods; exotic options, interest-rate derivatives. Course Information: Prerequisite(s): Grade of C or better in MATH 220 and grade of C or better in STAT 381; or consent of the instructor. | MW 9:00 - 9:50 | David Nicholls | |
| MCS 501: Computer Algorithms II | Continuation of MCS 401 (same as CS 401). Advanced topics in algorithms. Lower bounds. Union-find problems. Fast Fourier transform. Complexity of arithmetic, polynomial, and matrix calculations. Approximation algorithms. Parallel algorithms. Course Information: Same as CS 501. Prerequisite(s): MCS 401 or CS 401. | MWF 9:00 - 9:50 in TH 301 | Gyorgy Turan | |
| MCS 507: Mathematical, Statistical and Scientific Software | Statistical models, criteria of optimum estimation, large sample theory, optimum tests and confidence intervals, best unbiased tests in exponential families, invariance principle, likelihood ratio tests. Course Information: Prerequisite(s): STAT 411. | MWF 11:00 - 11:50 in AH 303 | Jan Verschelde | |
| MCS 521: Combinatorial Optimization | Combinatorial optimization: network flows, bipartite matching, Edmonds algorithm for non-bipartite matching, the matching polytope, matroids, greedy algorithm, matroid union and intersection algorithms, matroid polyhedra, polymatroids. Course Information: Prerequisite(s): MCS 423 and STAT 471. | MWF | ||
| MCS 571: Numerical analysis Partial Differential Equations | Numerical analysis of Finite Difference methods for PDE of mathematical physics: Wave, heat, and Laplace equations. Introduction to numerical analysis of the Finite Element method. Course Information: Prerequisite(s): MATH 481 and MCS 471 or consent of the instructor. | MWF 9:00 - 9:50 in LH 300 | Awanou | |
| STAT 502: Probability Theory II | Radon-Nikodym theorem, conditional expectations, martingales, stationary processes, ergodic theorem, stationary Gaussian processes, Markov chains, introduction to stochastic processes, Brownian motions. Course Information: Prerequisite(s): STAT 501. | MWF 2:00 - 2:50 | Cheng Ouyang | |
| STAT 511: Advanced Statistical Theory I | Statistical models, criteria of optimum estimation, large sample theory, optimum tests and confidence intervals, best unbiased tests in exponential families, invariance principle, likelihood ratio tests. Course Information: Prerequisite(s): STAT 411. | MWF 11:00 - 11:50 in LH 215 | Kyunghee Han | |
| STAT 535: Optimal Design Theory I | Gauss-Markov theorem,optimality criteria, optimal designs for 1-way, 2-way elimination of heterogeneity models,repeated measurements, treatment-control ; Equivalence theorem,approximate designs for polynomial regression. Course Information: Prerequisite(s): STAT 521. | MWF 9:00 - 9:50 in LH 300 | Min Yang | |
| STAT 591: Advanced Topics in Statistics, Probability and Operations Research | Special topics. Topics drawn from areas such as: Data analysis; Bayesion inference; Nonlinear models; Time series; Computer aided design; reliability models; game theory. Course Information: May be repeated. Prerequisite(s): Approval of the department. | MWF 1:00-1:50 in LH 300 | Jing Wang |