# 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 2024 Planned Graduate Courses Heading link

Course | Description | Time and Location | Instructor | 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. | MWF 1:00 - 1:50 | Matthew Harrison-Trainor | 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 Instructor. | MWF 10:00 - 10:50 | Joel (Ronnie) Nagloo | 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. | MWF 11:00 - 11:50 | Nathan Jones | 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. | MWF 9:00 - 9:50 | Wenliang Zhang | 13724 |

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 2:00 - 2:50 | Ramin Takloo-Bighash | 43414 |

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. | MWF 1:00 - 1:50 in TH 215 | Mimi Dai | 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. | MWF 11:00 - 11:50 | Osama Khalil | 37062 |

MATH 549: Differentiable Manifolds | 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 10:00 - 10:50 | Daniel Groves | 38306 |

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. | MWF 12:00 - 12:50 | 31610 | |

MATH 555: Complex Manifolds | 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. | MWF 2:00 - 2:50 | Ben Bakker | 39215 |

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 12:00 - 12:50 | David Dumas | 38308 |

MATH 577: Advanced Partial Differential Equations | Linear elliptic theory, maximum principles, fixed point methods, semigroups and nonlinear dynamics, systems of conservation laws, shocks and waves, parabolic equations, bifurcation, nonlinear elliptic theory. Course Information: Prerequisite(s): MATH 533 and MATH 576 or consent of the instructor. | MWF 12:00 - 12:50 | Christof Sparber | 40006 |

MATH 580: Mathematics of Fluid Mechanics | Development of concepts and techniques used in mathematical models of fluid motions. Euler and Navier Stokes equations. Vorticity and vortex motion. Waves and instabilities. Viscous fluids and boundary layers. Asymptotic methods. Course Information: Prerequisite(s): Grade of C or better in MATH 410 and grade of C or better in MATH 417 and grade of C or better in MATH 481. | MWF 2:00 - 2:50 | Roman Shvydkoy | 40613 |

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. | MWF 10:00 - 10:50 | Rafail Abramov | 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. | MW 3:00 - 3:50 | Brooke Shipley | 32552 |

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 534 or consent of the instructor. | MWF 10:00 - 10:50 | Cheng Ouyang | 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. | MWF 9:00 - 9:50 | Jing Wang | 37071 |

STAT 591: Advanced Topics in Statistics, Probability and Operations Research | High dimensional and big data analysis is one of the most active research areas in statistics today given the unprecedented size and complexity of high-throughput data. We will study cutting-edge developments in the methods and theory of statistical inference including data from genetic, microarrays, proteomics, fMRI, cancer clinical trials and high frequency financial data. | MWF 1:00 - 1:50 | Yichao Wu | 37945 |

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. | TR 5:00 - 6:15 | Xiaorui Sun | 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. | MWF 11:00 - 11:50 | Gyorgy Turan | 39221 |

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. | MWF 9:00 - 9:50 | Lev Reyzin | 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. | MWF 12:00 - 12:50 | Jan Verschelde | 39222 |

MCS 583: Extremal Combinatorics | Extremal combinatorics, including extremal graph and set theory, Ramsey theory, the linear algebra method, and applications to computer science. Prerequisite(s): MCS 421 and MCS 423, or consent of the instructor. | MWF 10:00 - 10:50 | Dhruv Mubayi | 44948 |