Graduate Courses

Spring 2022 Graduate Courses: *TENTATIVE*

Below is a tentative list of courses being offered in the upcoming Spring, 2022 semester.

CourseDescriptionTime and LocationInstructorCRN
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
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