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Graduate Courses

MSCS 500-Level Graduate Courses

Below is a list of courses we expect to be offering in the semesters ahead.

Spring 2023 Planned Graduate Courses Heading link

Math 504:
Set Theory
Naive and axiomatic set theory. Independence of the continuum hypothesis and the axiom of choice. Course Information: Same as PHIL 565. Prerequisite(s): MATH 430 or MATH 502 or PHIL 562.Tom Benhamou
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.James Freitag
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.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.Lawrence Ein
Math 525:
Advanced Topics in Number Theory
Function Field Arithmetic: We will focus on function field arithmetic, with a particular emphasis placed on the theory of Drinfeld modules as the function field counterpart to the theory of elliptic curves. The ring of polynomials in one indeterminate over a finite field exhibits strong similarities with the ring of integers. This similarity is an illustration of the broader analogy between function fields and number fields, whose exploration has had profound consequences on major branches of mathematics such as number theory, geometry, and topology. Alina Carmen Cojocaru
Math 535:
Complex Analysis I
Analytic functions as mappings. Cauchy theory. Power Series. Partial fractions. Infinite products. Course Information: Prerequisite(s): MATH 411.Jerry Bona
Math 547:
Algebraic Topology I
The fundamental group and its applications, covering spaces, classification of compact surfaces, introduction to homology, development of singular homology theory, applications of homology. Course Information: Prerequisite(s): MATH 330 and MATH 445.Daniel Groves
Math 550:
Differentiable Manifolds II
Vector bundles and classifying spaces, lie groups and lie algbras, tensors, Hodge theory, Poincare duality. Topics from elliptic operators, Morse theory, cobordism theory, deRahm theory, characteristic classes. Course Information: Prerequisite(s): MATH 549.Kevin Whyte
Math 553: Algebraic Geometry IIDivisors and linear systems, differentials, Riemann-Roch theorem for curves, elliptic curves, geometry of curves and surfaces. Course Information: Prerequisite(s): MATH 552.Kevin Tucker
Math 555: Complex Manifolds IIDolbeault Cohomology, Serre duality, Hodge theory, Kadaira vanishing and embedding theorem, Lefschitz theorem, Complex Tori, Kahler manifolds. Course Information: Prerequisite(s): MATH 517 and MATH 535.Julius Ross
Math 569: Advanced Topics in Geometric and Differential TopologyTopics 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.Alexander Furman
Math 571:
Advanced Topics in Algebraic Geometry
Rational, Unirational and Rationally Connected Varieties. In this course, we will discuss classical and modern examples of rational and non-rational varieties. We will study spaces of rational curves on varieties with applications to unirationality and rational connectedness in mind. We will end the course by introducing recent developments due to Voisin, Colliot-Thélène, Pirutka, Schreieder and others. Prerequisites: Math 552 and Math 553.Izzet Coskun
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.Ian Tobasco
Math 590: Advanced Topics in Applied Mathematics One of the major problems in the theory of swarming is to understand formation of collective outcomes in large systems governed by local laws of interactions. This phenomenon, called emergence, occurs in a variety of applications -- flock of birds, school of fish, synchronization of UAVs, clustering in social networks, consensus of opinions. This course provides an introduction into mathematics of collective behavior and focuses on systems with alignment and other forces that model laws of self-organization. Prerequisite: Basic familiarity with ODEs and PDEs will be assumed and some functional analysis will be useful.Roman Shvydkoy
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.Gyorgy Turan
MCS 541:
Computational Complexity
Time and space complexity of computations, classification of mathproblems according to their computational complexity, P not equal NP problem. Course Information: Prerequisite(s): Consent of the instructor.Lev Reyzin
MCS 548:
Mathematical Theory of Artificial Intelligence
Valiant's learning model, positive and negative results in learnability, automation inference, perceptrons, Rosenblatt's theorem, convergence theorem, threshold circuits, inductive inference of programs, grammars and automata. Course Information: Prerequisite(s): MCS 541.Gyorgy Turan
MCS 571:
Numerical Analysis of 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.David Nicholls
MCS 572:
Introduction to Supercomputing
Introduction to supercomputing on vector and parallel processors; architectural comparisons, parallel algorithms, vectorization techniques, parallelization techniques, actual implementation on real machines. Course Information: Prerequisite(s): MCS 471 or MCS 571 or consent of the instructor.Jan Verschelde
MCS 584:
Enumerative Combinatorics
Enumerative methods in combinatorics, including inclusion/exclusion, recursion, partitions, Latin squares and other combinatorial structures. Prerequisite(s): MCS 421 and MCS 423, or consent of the instructor.Marcus Michelen
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.Kyunghee Han
Stat 522:
Multivariate Statistical Analysis
Multivariate normal distribution, estimation of mean vector and covariance matrix, T-square statistic, discriminant analysis, general linear hypothesis, principal components, canonical correlations, factor analysis. Course Information: Prerequisite(s): STAT 521.Jie Yang
Stat 536: Optimal Design Theory IIConstruction of optimal designs: BIB , Latin square and generalized Youden , repeated measurements , treatment-control studies; construction of factorial designs including orthogonal arrays Course Information: Prerequisite(s): STAT 535 or consent of the instructor.Min Yang