# Graduate Courses

Below is a list of courses being offered in the upcoming semester.

## Fall 2021

Course | Description | Time and Location | Instructor |
---|---|---|---|

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 10:00 - 10:50 in BH 304 | Ronnie (Joel) Najloo |

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. | MWF 2:00 - 2:50 in TH 300 | Filippo Calderoni |

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 in TH 300 | Alina Cojocaru |

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 in AH 307 | Benjamin Bakker |

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 9:00 - 9:50 in TH 215 | Alexander Furman |

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 in AH 310 | Jerry Bona |

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 in LH 107 | Daniel Groves |

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 in AH 303 | Izzet Coskun |

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 1:00 - 1:50 in TH 300 | Kevin Whyte |

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 in LH 101 | Benjamin Bakker |

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 1:00 - 1:50 in LH 320 | Roman Shvydkoy |

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. | MWF 12:00 - 12:50 in TH 300 | Cheng Ouyang |

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 in TH 300 | Roman Shvydkoy |

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 in GH 205 | Brooke Shipley |

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 11:00 - 11:50 in TH 301 | Ian Tobasco |

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 1:00 - 1:50 in AH 303 | Cheng Ouyang |

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 in AH 303 | Jing Wang |

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. | MWF 1:00 - 1:50 in LH 300 | Yichao Wu |

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 1:00 - 1:50 in LH 215 | Aditya Potukuchi |

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 12:00 - 12:50 in LH 215 | Lev Reyzin |

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 in LH 300 | Gerard Awanou |

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 TBD in LH 300 | Dhruv Mubayi |