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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

CourseDescriptionTime and LocationInstructorCRN
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 - 9:50James Freitag39212
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 Looper42674
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 - 10:50Kevin Tucker13724
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 - 1:50Wenliang Zhang39213
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 - 2:50Nathan Jones43414
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 - 1:50Irina Nenciu42669
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 - 11:50Roman Shvydkoy48533
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 Furman37062
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 - 2:50David Dumas39216
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 - 11:50Kevin Whyte38307
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 - 12:50Izzet Coskun31610
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 - 2:50Izzet Coskun38742
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 - 10:50Alexey Cheskidov40613
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 - 2:50Jerry Bona37428
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 Shipley32552
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 - 9:50Osama Khalil46089
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 - 11:50Jan Verschelde43423
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 - 1:50Vishesh Jain38317
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 - 12:50Lev Reyzin43424
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 - 10:50David Nicholls40622
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 - 11:50Cheng Ouyang22762
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 - 2:50Kyunghee Han42771
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 - 10:50Jing Wang37071
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 - 1:50Yichao Wu37945