# Graduate Courses

MSCS 500-Level Graduate Courses

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

## Fall 2023 Planned Graduate Courses Heading link

## Fall 2023 Planned Graduate Courses

Course | Description | Time and Location | Instructor | 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. | MWF 9:00 - 9:50 | James Freitag | 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. | MWF 11:00 - 11:50 | Nicole Looper | 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 10:00 - 10:50 | Kevin Tucker | 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. | MWF 1:00 - 1:50 | Wenliang Zhang | 39213 |

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 | Nathan Jones | 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 | Irina Nenciu | 42669 |

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. | MWF 11:00 - 11:50 | Roman Shvydkoy | 48533 |

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 12:00 - 12:50 | Alexander Furman | 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. | MWF 2:00 - 2:50 | David Dumas | 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. | MWF 11:00 - 11:50 | Kevin Whyte | 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. | MWF 12:00 - 12:50 | Izzet Coskun | 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. | MWF 2:00 - 2:50 | Izzet Coskun | 38742 |

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 10:00 - 10:50 | Alexey Cheskidov | 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 2:00 - 2:50 | Jerry Bona | 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 |

Math 590: Advanced Topics in Applied Mathematics | Topics from areas such as: elastic scattering, nonlinear problems in chemistry and physics, mathematical biology, stochastic optimal control, geophysical fluid dynamics, stability theory, queueing theory. Course Information: Prerequisite(s): Approval of the department. | MWF 9:00 - 9:50 | Osama Khalil | 46089 |

MCS 507: Mathematical, Statistical and Scientific Software | The design, analysis, and use of mathematical, statistical, and scientific software. Course Information: Prerequisite(s): Grade of B or better in MCS 360 or the equivalent or consent of instructor. | MWF 11:00 - 11:50 | Jan Verschelde | 43423 |

MCS 521: Combinatorial Optimization | Combinatorial optimization: network flows, bipartite matching, Edmonds algorithm for non-bipartite matching, the matching polytope, matroids, greedy algorithm, matroid union and intersection algorithms, matroid polyhedra, polymatroids. Course Information: Prerequisite(s): MCS 423 and STAT 471. | MWF 1:00 - 1:50 | Vishesh Jain | 38317 |

MCS 549: Mathematical Foundations of Data Science | This course covers the mathematical foundations of modern data science from a theoretical computer science perspective. Topics will include random graphs, small world phenomena, random walks, Markov chains, streaming algorithms, clustering, graphical models, singular value decomposition, and random projections. | MWF 12:00 - 12:50 | Lev Reyzin | 43424 |

MCS 573: Topics in Numerical Analysis of Partial Differential Equations | Topics in numerical analysis of partial differential equations which may include: High-order Finite Element methods, Discontinuous Glerkin methods, Spectral methods, or Integral Equation methods. Course Information: May be repeated if topics vary. Prerequisite(s): MATH 481 and MCS 471; and consent of the instructor. | MWF 10:00 - 10:50 | David Nicholls | 40622 |

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 11:00 - 11:50 | Cheng Ouyang | 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. | MWF 2:00 - 2:50 | Kyunghee Han | 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): STAT 411. | MWF 10:00 - 10:50 | Jing Wang | 37071 |

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. | MWF 1:00 - 1:50 | Yichao Wu | 37945 |