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.

Spring 2025 Planned Graduate Courses Heading link

 
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.Matthew Harrison-TrainorMWF2:00 - 2:50 PM
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.Ramin Takloo-BighashMWF9:00 - 9:50 AM
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 EinMWF1:00 - 1:50 PM
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. Frederick SaiaMWF11:00 - 11:50
Math 535:
Complex Analysis I		Analytic functions as mappings. Cauchy theory. Power Series. Partial fractions. Infinite products. Course Information: Prerequisite(s): MATH 411.Izzet CoskunMWF2:00 - 2:50 PM
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.Kevin WhyteMWF12:00 - 12:50 PM
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.Wouter Van LimbeekMWF1:00 - 1:50 PM
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.Gwyneth MorelandMWF10:00 - 10:50 AM
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.Ben BakkerMWF1:00 - 1:50 PM
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 SparberMWF11:00 - 11:50 AM
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 TuranMWF11:00 - 11:50 AM
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.Gyorgy TuranMWF1:00 - 1:50 PM
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 NichollsMWF9:00 - 9:50 AM
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 HanMWF11:00 - 11:50
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 YangMWF10:00 - 10:50
Stat 591:
Advanced Topics in Statistics, Probability and Operations Research		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.Ping-Shou ZhongMWF 11:00 - 11:50