Graduate Courses
MSCS 500-Level Graduate Courses
Below is a list of courses we expect to be offering in the semesters ahead. For complete course information including location, please consult the UIC Schedule of Classes.
Fall 2025 Planned Graduate Courses
| Course | Description | Instructor | Time on MWF | CRN | |
| Math 506: Model Theory I | Elementary embeddings, quantifier elimination, types, saturated and prime models, indiscernibles, Morley's Categoricity Theorem. Course Information: Same as PHIL 567. Prerequisite(s): MATH 502 or PHIL 562. | Gabriel Conant | 10:00 - 10:50 | 39212 | |
| Math 514 Number Theory I | Introduction to classical, algebraic, and analytic, number theory. Euclid's algorithm, unique factorization, quadratic reciprocity, and Gauss sums, quadratic forms, real approximations, arithmetic functions, Diophantine equations. | Nathan Jones | 11:00 - 11:50 | 42674 | |
| Math 516: Second Course in Abstract Algebra I | Structure of groups, Sylow theorems, solvable groups; structure of rings, polynomial rings, projective and injective modules, finitely generated modules over a PID. Course Information: Prerequisite(s): Math 330 and Math 425. | Wenliang Zhang | 9:00 - 9:50 | 13724 | |
| Math 520: Commutative and Homological Algebra | Commutative rings; primary decomposition; integral closure; valuations; dimension theory; regular sequences; projective and injective dimension; chain complexes and homology; Ext and Tor; Koszul complex; homological study of regular rings. Course Information: Prerequisite(s): MATH 516 and MATH 517; or consent of the instructor. | Maya Banks | 10:00 - 10:50 | 39213 | |
| MATH 533: Real Analysis I | Introduction to real analysis. Lebesgue measure and integration, differ entiation, L-p classes, abstract integration. Course Information: Prerequisite(s): MATH 411 or 414 or the equivalent. | Alexander Furma | 12:00 - 12:50 | 42669 | |
| MATH 539: Functional Analysis I | Topological vector spaces, Hilbert spaces, Hahn-Banach theorem, open mapping, uniform boundedness principle, linear operators in a Banach space, compact operators. Course Information: Prerequisite(s): MATH 533. | Osama Khalil | 11:00 - 11:50 | 37062 | |
| 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 | 10:00 - 10:50 | 39216 | |
| 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. | Wouter Van Limb | 11:00 - 11:50 | 38307 | |
| MATH 552: Algebraic Geometry I | Basic commutative algebra, affine and projective varieties, regular and rational maps, function fields, dimension and smoothness, projective curves, schemes, sheaves, and cohomology, posiive characteristic. | Izzet Coskun | 12:00 - 12:50 | 31610 | |
| MATH 571: Advanced Topics in Algebraic Geometry | Various topics such as algebraic curves, surfaces, higher dimensional geometry, singularities theory, moduli problems, vector bundles, intersection theory, arithematical algebraic geometry, and topologies of algebraic varieties. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. | Philip Engel | 2:00 - 2:50 | 38742 | |
| 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. | TBD | 2:00 - 2:50 | 38309 | |
| MATH 585: Ordinary Differential Equations | Introduction to ordinary differential equations, existence, uniqueness of solutions, dependence on parameters, autonomous and non-autonomous systems, linear systems, nonlinear systems, periodic solutions, bifurcations, conservative systems. Course Information: Prerequisite(s): Math 313 or Math 480 or approval of the department. | Rafail Abramov | 11:00 - 11:50 | 37428 | |
| MATH 589: Teaching and Presentation of Mathematics | Strategies and techniques for effective teaching in college and for mathematical consulting. Observation and evaluation, classroom management, presenting mathematics in multidisciplinary research teams. Required for teaching assistants in MSCS. Course Information: No graduation credit awarded for students enrolled in the Master of Science in the Teaching of Mathematics degree program. | Brooke Shipley | 3:00 - 4:15 (MW) | 32552 | |
| 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. | TBD | 9:30 - 10:45 (TR) | 34849 | |
| 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. | Lev Reyzin | 1:00 - 1:50 | 39221 | |
| 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. | Dhruv Mubayi | 11:00 - 11:50 | 43425 | |
| STAT 501: Probability Theory I | Abstract measure theory, probability measures, Kolmogorov extension theorem, sums of independent random variables, the strong and weak laws of large numbers, the central limit theorem, characteristic functions, law of iterated logarithm, infinitely divisible laws. Course Information: Prerequisite(s): MATH 414 or consent of the instructor. | Cheng Ouyang | 10:00 - 10:50 | 22762 | |
| STAT 512: Advanced Statistical Theory | Basic concepts in decision theory, prior and posterior distributions, Bayesian decision theory, hierarchical models, robustness, minimax analysis, invariance principle, sequential analysis, completeness. Course Information: Prerequisite(s): STAT 511. | Kyunghee Han | 2:00 - 2:50 | 42771 | |
| STAT 521: Linear Statistical Inference | Estimation and testing in linear models, generalized inverses of matrices, n-dimensional normal distribution, quadratic forms, likelihood ratio tests, best invariant tests, analysis of variance. Course Information: Prerequisite(s):Â STATÂ 411. | Jing Wang | 9:00 - 9:50 | 37071 | |
| Stat 585: Advanced Statistical Techniques for Machine Learning and Big Data | Cutting-edge data analysis techniques including regularization methods; ensemble learning; dimension reduction; network and graphics; recommender system; text mining; deep learning; imaging analysis; object-oriented data analysis. Course Information: Extensive computer use required. Prerequisite(s): Grade of C or better in STAT 485 or consent of the instructor. | Yichao Wu | 11:00 - 11:50 | 49956 |
Spring 2026 Planned Graduate Courses
| Course | Description | Instructor |
|---|---|---|
| Math 511: Descriptive Set Theory | Polish spaces and Baire category; Borel, analytic and coanalytic sets; infinite games and determinacy; coanalytic ranks and scales; dichotomy theorems. Course Information: Recommended background: MATH 445 or MATH 504 or MATH 533 or MATH 539. | Matthew Harrison-Trainor |
| 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. | TBD |
| 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 | 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. | TBA |
| Math 535: Complex Analysis I | Analytic functions as mappings. Cauchy theory. Power Series. Partial fractions. Infinite products. Course Information: Prerequisite(s): MATH 411. | Alexander Furman |
| 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. | Michael Greenblatt |
| 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. | TBD |
| 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. | Shiji Lyu |
| 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. | Daniel Groves |
| Math 571: Advanced Topics in Algebraic Geometry | Various topics such as algebraic curves, surfaces, higher dimensional geometry, singularities theory, moduli problems, vector bundles, intersection theory, arithematical algebraic geometry, and topologies of algebraic varieties. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. | Kevin Tucker |
| 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. | Irina Nenciu |
| Math 584: Applied Stochastic Models | Applications of stochastic models in chemistry, physics, biology, queueing, filtering, and stochastic control, diffusion approximations, Brownian motion, stochastic calculus, stochastically perturbed dynamical systems, first passage times. Course Information: Prerequisite(s): MATH 417 and MATH 481 and STAT 401, or consent of the instructor. | Cheng Ouyang |
| 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 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. | Gerard Awanou |
| MCS 591: Advanced Topics in Combinatorial Theory | Some of the following topics: combinatorial enumeration, designs, graph theory, matroid theory, combinatorial matrix theory, Ramsey theory. Contents vary from year to year. Course Information: May be repeated. Prerequisite(s): MCS 423. | Caroline Terry |
| 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. | 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. | 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. | 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. | Jing Wang |