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MATH 622 - Matrix Theory 2

Research topics in combinatorial matrix theory.
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MATH 621 - Matrix Theory 1

Symmetric matrices, spectral graph theory, interlacing, the Laplacian matrix of a graph.
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MATH 611 - Finite Elements

A rigorous introduction to the numerical method of finite elements with focus on the mathematical foundations of the subject.
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MATH 587 - Intro to Analytic Number Thry

Arithmetical functions; distribution of primes; Dirichlet characters; Dirichlet's theorem; Gauss sums; primitive roots; Dirichlet L-functions; Riemann zeta-function; prime number theorem; partitions.
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MATH 586 - Intro Algebraic Number Theory

Algebraic integers; different and discriminant; decomposition of primes; class group; Dirichlet unit theorem; Dedekind zeta function; cyclotomic fields; valuations; completions.
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MATH 572 - Algebra 2

Modules, vector spaces, field theory, Galois theory.
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MATH 571 - Algebra 1

Group theory, ring theory.
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MATH 570 - Matrix Analysis

Special classes of matrices, canonical forms, matrix and vector norms, localization of eigenvalues, matrix functions, applications.
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MATH 565 - Differential Geometry

A rigorous treatment of the theory of differential geometry.
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MATH 562 - Intro to Algebraic Geometry 2

Local properties of quasi-projective varieties. Divisors and differential forms.
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MATH 561 - Intro to Algebraic Geometry 1

Basic definitions and theorems on affine, projective, and quasi-projective varieties.
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MATH 554 - Foundations of Topology 2

An introduction to the topology of manifolds with particular emphasis on low dimensions: topological and smooth manifolds; smooth maps; tangent spaces; vector fields and flows; Sard's Theorem; Morse Theory; classification of compact manifolds in dimensions 1 and 2; and theory of 3 dimensional manifolds.
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MATH 553 - Foundations of Topology 1

An introduction to the topology of the plane and algebraic topology: simplicial complexes, CW-complexes, the fundamental group, classification of covering spaces, homotopy, Seifer-van Kampen Theorem, Jordan Curve Theorem, and Invariance of Domain.
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MATH 547 - Modeling and Analysis of PDEs

Methods for modeling and analyzing partial differential equations.
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MATH 541 - Real Analysis

An introduction to abstract measure and Lebesgue integration theory.
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MATH 540 - Linear Analysis

Normed vector spaces and linear maps between them.
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MATH 536 - Applied Discrete Probability

Rigorous probability without the use of measure theory. Intensive study of finite and countable probability spaces. Applications to particle statistics, random walks, Markov decision processes, information theory, and asset pricing.
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MATH 534 - Intro to Dynamical Systems 1

Discrete dynamical systems; iterations of maps on the line and the plane; bifurcation theory; chaos, Julia sets, and fractals. Computational experimentation.
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MATH 532 - Complex Analysis

Introduction to theory of complex analysis at beginning graduate level. Topics: Cauchy integral equations, Riemann surfaces, Picard's theorem, etc.
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MATH 525 - Network Theory

Representing networks mathematically. Measures and metrics, computer algorithms, random graphs, and large-scale structures. Percolation and network resilience. Dynamical systems on networks.
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MATH 522 - Methods of Applied Math 2

Possible topics include variational, integral, and partial differential equations; spectral and transform methods; nonlinear waves; Green's functions; scaling and asymptotic analysis; perturbation theory; continuum mechanics.
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MATH 521 - Methods of Applied Math 1

Possible topics include variational, integral, and partial differential equations; spectral and transform methods; nonlinear waves; Green's functions; scaling and asymptotic analysis; perturbation theory; continuum mechanics.
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MATH 513 R - Adv Topics in Applied Math

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MATH 511 - Num Methods for Partial Diff

Finite difference and finite volume methods for partial differential equations. Stability, consistency, and convergence theory.
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MATH 510 - Num Methods for Linear Algebra

Numerical matrix algebra, orthogonalization and least squares methods, unsymmetric and symmetric eigenvalue problems, iterative methods, advanced solvers for partial differential equations.
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MATH 502 - Job Search Strategies

Course will assist graduating students in identifying and connecting to potential employers.
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MATH 500 - Business Career Essentials

Introduction for science, math, and statistics majors to careers in industry. Project planning, oral and written business presentations, business accounting, and technology readiness.
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