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 2026 500-Level Courses
| Course | Description | Instructor | Time on MWF | CRN |
|---|---|---|---|---|
| Math 502: Mathematical Logic | First order logic, completeness and incompleteness theorems, introduction to model theory and computability theory. Course Information: Same as PHIL 562. Prerequisite(s): MATH 430 or consent of the instructor. | Gabriel Conant | 1:00 - 1:50 | 38305 |
| 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 | 10:00 - 10:50 | 34413 |
| 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. | Ramin Takloo-Bighash | 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. | Wenliang Zhang | 1:00 - 1:50 | 39213 |
| Math 535: Complex Analysis I | Analytic functions as mappings. Cauchy theory. Power Series. Partial fractions. Infinite products. Course Information: Prerequisite(s): MATH 411. | Izzet Coskun | 10:00 - 10:50 | 50762 |
| 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. | Gerard Awanou | 11:00 - 11:50 | 37062 |
| Math 546: Advanced Topics in Analysis | Subject may vary from semester to semester. Topics include partial differential equations, several complex variables, harmonic analysis and ergodic theory. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. | Christof Sparber | 2:00 - 2:50 | 42128 |
| 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 218 or MATH 320 or the equivalent; and graduate standing. | Emily Dumas | 2:00 - 2:50 | 40616 |
| 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, positive characteristic. Course Information: Prerequisite(s): Grade of C or better in MATH 516 and Grade of C or better in MATH 517; and graduate standing; or consent of the instructor. | Kevin Tucker | 12:00 - 12:50 | 31610 |
| 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. | Wouter Van Limbeek | 12:00 - 12:50 | 38308 |
| 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. | Izzet Coskun | 12:00 - 12:50 | 38742 |
| 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. | Roman Shvydkoy | 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 | MW 3:00 - 4:15 | 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. | Lev Reyzin | 11:00 - 11:50 | 34849 |
| MCS 549: Mathematical Foundations of Data Science | Topics will include random graphs, small world phenomena, random walks, Markov chains, streaming algorithms, clustering, graphical models, singular value decomposition, and random projections. Course Information: Prerequisite(s): MCS 401 and MCS 441; or consent of the instructor. | Lev Reyzin | 9:00 - 9:50 | 43424 |
| 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 | 9:00 - 9:50 | 39222 |
| MCS 582: The Probabilistic Method | Introduction to the probabilistic method, which includes a range of applications to address various problems that arise in combinatorics. Prerequisite(s): MCS 421 and 423, or consent of the instructor. | Dhruv Mubayi | 12:00 - 12:50 | 45127 |
| Stat 501: Probability Theory I | Abstract measure theory, probability measure, random variables, Lebesgue integration and expectation, and convergence of random variables. Course Information: Prerequisite(s): MATH 414 or consent of the instructor. | Cheng Ouyang | 10:00 - 10:50 | 22762 |
| 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): STAT 411. | Jing Wang | 9:00 - 9:50 | 37071 |
| Stat 585: | 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 2027 Planned 500 - Level Classes
| Course | Description | Instructor | Time on MWF |
|---|---|---|---|
| Math 507: Model Theory II | Stability theory: forking and indpendence, stable groups, geometric stability. Course Information: Same as PHIL 568. Prerequisite(s): MATH 506 or PHIL 567. | Gabriel Conant | TBD |
| 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 | 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 | TBD |
| 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 MATH 414 or the equivalent. | Osama Khalil | TBD |
| 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 | TBD |
| 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 | 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. | Kevin Tucker | TBD |
| Math 555: Complex Manifolds II | Dolbeault 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. | Ben Bakker | TBD |
| 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. | Christof Sparber | TBD |
| Math 581: Special Topics in Fluid Mechanics | Geophysical fluids with applications to oceanography and meteorology, astrophysical fluids, magnetohydrodynamics and plasmas. Course Information: Prerequisite(s): Grade of C or better in MATH 580. | Roman Shvydkoy | TBD |
| 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 | TBD |
| 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 | TBD |
| MCS 590: Advanced Topics in Computer Science | Topics in areas such as: mathematical aspects of artificial intelligence, symbolic methods in mathematics, mathematical cryptography, automated reasoning. Topics may vary from term to term. Course Information: May be repeated. Students may register in more than one section per term. Prerequisite(s): Approval of the department. | Matthew Harrison-Trainor | TBD |
| 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. | Vishesh Jain | TBD |
| 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 | TBD |
| 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 | TBD |
| Stat 536: Optimal Design Theory II | Construction 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 | TBD |
| 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. | Cheng Ouyang + Kyunghee Han | TBD |