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Mathematics Courses

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MATH 522 - Mathematics of Deep Learning

Mathematics necessary to understand how deep neural networks are formulated and designed.??Analyzing the stability, generalizability, and potential extension of neural networks to new datasets.??
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MATH 521 - Classical Applied Mathematics

Classical techniques in applied mathematics and their application to specific problems. The primary focus is on dimensional analysis and asymptotic methods for differential equations as well as asymptotic evaluation of integrals.
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MATH 799 R - Doctoral Dissertation

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MATH 751 R - Adv Special Topics in Topology

Current topics in topology of research interest.
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MATH 699 R - Master's Thesis

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MATH 698 R - Master's Project

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MATH 695 R - Readings in Math

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MATH 691 R - Graduate Math Colloquium

A diverse set of talks at the graduate level. Students will broaden their knowledge of recent and current research in mathematics. Speakers will be faculty, visitors, and students reporting on thesis work.
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MATH 687 R - Topics Analytic Number Theory

Current topics of research interest.
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MATH 686 R - Topics Algebraic Number Theory

Current topics of research interest.
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MATH 682 - Modular Forms

An introduction to modular forms including Fourier expansions, dimension formulas, Hecke operators, generalizations, and applications.
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MATH 677 - Homological Algebra

Chain complexes, derived functors, cohomology of groups, ext and tor, spectral sequences, etc. Application to algebraic geometry and algebraic number theory.
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MATH 676 - Commutative Algebra

Commutative rings, modules, tensor products, localization, primary decomposition, Noetherian and Artinian rings, application to algebraic geometry and algebraic number theory.
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MATH 675 R - Spec Tpcs-Algebra

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MATH 674 - Lie Groups and Algebras

Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.
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MATH 673 - Algebra 3

Topics from representation theory of finite groups and associative algebras. Groebner bases, homological algebra, tensor algebras, commutative rings, advanced finite group theory.
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MATH 664 - Algebraic Geometry 2

Cohomology of schemes. Classification problems. Applications.
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MATH 663 - Algebraic Geometry 1

Basic definitions and theorems on varieties, sheaves, and schemes.
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MATH 656 - Algebraic Topology

A rigorous treatment of the fundamentals of homology and cohomology of spaces: simplicial, singular, and cellular homology; excision; Mayer-Vietoris sequence; homology with coefficients; homology and the fundamental group; universal coefficient theory; cup product; and Poincare Duality.
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MATH 655 - Differential Topology

An introduction to smooth manifolds and their topology: smooth manifolds; tangent, vector, and cotangent bundles; immersions, submersions, and embeddings; tubular neighborhoods; transversality; differential forms, integration, and Stoke's Theorem; deRham cohomology; and degree theory.
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MATH 648 - Theory of PDEs 2

A study of time-dependent partial differential equations. Also, a study of calculus of variations and non-variational techniques.
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MATH 647 - Theory of PDEs 1

Classical theory of canonical linear PDEs. Introduction to Sobolev spaces and their used in second order elliptic equations.
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MATH 644 - Harmonic Analysis

Harmonic analysis on the torus and in Euclidean space; pointwise and norm convergence of Fourier series and functional-analytic aspects of Fourier transforms emphasized.
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MATH 643 R - Special Topics in Analysis

Advanced topics in analysis drawn from pure and applied mathematics.
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MATH 641 - Measure and Integration Theory

Abstract measure and integration theory; L(p) spaces; measures on topological and Euclidean spaces.
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MATH 640 - Nonlinear Analysis

Differential calculus in normed spaces, fixed point theory, and abstract critical point theory.
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MATH 637 - Advanced Probability 2

Measure-theoretic stochastic processes. Martingales, Markov processes, Brownian motion, stochastic integration.
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MATH 636 - Advanced Probability 1

Measure-theoretic probability. Axioms for and construction of probability spaces. Random variables, expectation, uniform integrability, independence, convergence of sequences of random variables, conditioning.
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MATH 635 - Dynamical Systems

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MATH 634 - Theory Ordinary Differentl Eqs

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