Graduate Courses

This/Next semester's graduate courses

For this or next semester's course offering, click here.

You can access syllabi of the courses you have registered for here

Typical course loads

First and second year students usually take three courses per semester, sometimes supplementing them with a reading course. Third and fourth year students usually take one course and one research course with their advisor. To register for the Independent Study or research courses 9082 and 999x please fill out the form below. All graduate students are strongly encouraged to register for their courses by the beginning of July for the Fall semester and by the beginning of November for the Spring semester.

Registration for Independent Study and the various 999x level courses

For registration in Independent Study and the various 999x level courses use this form. TU password required!
Registration for these courses must be completed by August 10 for the Fall semester and by December 15 for the Spring semester.

Graduate Courses

Note: Unless otherwise noted, all prerequisite courses must be passed with a grade of C- or higher. Under normal circumstances it is assumed that a student has taken basic courses on the 8000 level before entering any of the 9000-level courses.

MATH 5032. Stochastic Calculus. 3 Credit Hours.

This course is an introduction to stochastic calculus based on Brownian motion and Gaussian processes, covering stochastic differential equations as well as applications to option pricing in finance. Concepts and results are illustrated with examples and numerical projects.

MATH 5033. Introduction to Stochastic Processes. 3 Credit Hours.

This course is an introduction to some of the basic models, concepts, results and techniques in the study of stochastic processes and touches upon applications along the way. It covers a large selection of the following topics: finite- and countable-state Markov chains, Poisson and birth-and-death processes, optimal stopping, martingales, renewal processes, Markov chain algorithms, introduction to Brownian motion.

MATH 5034. High-Dimensional Probability. 3 Credit Hours.

This course provides a self-contained introduction to the area of high-dimensional probability and statistics from a non-asymptotic perspective, aimed at students across the mathematical sciences. It will include a focus on core methodology and theory (tail bounds, concentration of measure, random matrices, random graphs and networks) as well as in-depth exploration of various applications (to statistical learning theory, sparse linear and graphical models, community detection, as examples).

MATH 5041. Concepts of Analysis I. 3 Credit Hours.

This is a first semester course in basic real analysis. Topics include the real number system and the completeness property, ordered fields, topology of metric spaces, sequences and series, limits of functions and continuity, and differentiation.

References: Rudin, Principles of Mathematical Analysis; Pugh, Real Mathematical Analysis

MATH 5042. Concepts of Analysis II. 3 Credit Hours.

This is a second semester course in real analysis, representing a continuation of MATH 5041. Topics include, the Riemann integral, infinite series and convergence tests, sequences of functions, uniform convergence, power and Taylor series and operations with them, differentiability of vector valued functions, inverse and implicit function theorems, differential forms, vector analysis, and formula of change of variables in multiple integrals.

Prerequisites: Minimum grade of B- in MATH 5041.

MATH 5043. Numerical Analysis. 3 Credit Hours.

This course provides a graduate level introduction to classical and modern methods for fundamental problems in computational science and engineering, including approximation and interpolation, numerical integration/quadrature, direct methods for systems of equations, and solution of systems of nonlinear equations. A rigorous mathematical approach to these topics is taken, including floating point arithmetic, error analysis, conditioning and stability, and convergence theorems. The course is accessible to graduate students from all areas of science and engineering interested in a mathematical foundation for the listed computational methods.

MATH 5044. Numerical Methods for Ordinary Differential Equations. 3 Credit Hours.

This course introduces numerical methods for ordinary differential equations, including explicit, implicit, and semi-implicit time stepping methods (such as Runge-Kutta, multistep, and Taylor series methods). A rigorous mathematical basis is established, including convergence, stability, and error estimators. Critical challenges commonplace in applications, like stiff problems, and specialized time stepping methods, are also presented.

MATH 5045. Ordinary Differential Equations. 3 Credit Hours.

The course covers existence and uniqueness theorems for ordinary differential equations (ODEs), along with continuous and smooth dependence on initial conditions and parameters, assuming familiarity with the material of advanced calculus. Topics include linear differential equations, their qualitative and asymptotic behavior, and the analysis of isolated singularities. The course also introduces nonlinear equations and Sturm-Liouville problems, emphasizing both theoretical aspects and applications. Basic methods for the numerical solution of ODEs are presented, including stability and convergence considerations.

MATH 5057. Applied Differential Equations and Optimization. 3 Credit Hours.

This course introduces and studies partial differential equations (PDEs) central to applied mathematics and related fields, arising from continuum mechanics and optimization. Material includes continuum mechanics, methods for linear PDEs, calculus of variations, as well as basic constrained optimization and control. Course topics have a wide applicability to the sciences and engineering. MATH 5058. Fundamentals of Mathematical Modeling. 3 Credit Hours.

This course introduces fundamental principles of mathematical modeling. Basics of constructing and analyzing models, including scaling and asymptotics, are studied in large part through dynamical systems and their applications. Examples from many areas across the sciences and engineering disciplines are central to this course.

MATH 5065. Topology. 3 Credit Hours.

This course covers the fundamentals of metric spaces and topological spaces. Core topics include continuity, compactness, connectedness, and convergence. Time permitting, the course will include the classification of compact surfaces and an introduction to algebraic topology, including fundamental groups and covering spaces.

MATH 5067. Introduction to Abstract Algebra I. 3 Credit Hours.

This is the first semester in a year-long introduction to modern algebra. It is a thorough introduction to the theory of groups and rings.

A typical textbook is Hungerford's Abstract Algebra: An Introduction

MATH 5068. Introduction to Abstract Algebra II. 3 Credit Hours.

This is the second semester in a year-long introduction to modern algebra. Topics come from the theory of rings, fields, modules, and Galois theory. Add prerequisite: Math 5067 MATH 5071. Mathematical Aspects of Cryptography. 3 Credit Hours.

This course on the mathematical aspects of cryptography proceeds in four parts. In Part 1, we go over groups, rings, and finite fields. Part 2 is devoted to symmetric key cryptosystems, including both classical cryptosystems (affine cipher, substitution cipher, Hill cipher) and modern cryptosystems, e.g., the Advanced Encryption Standard (AES, Rijndael). Part 3 is devoted to aspects of elementary number theory related to cryptography. Part 4 is devoted to public key cryptosystems. In this part, we learn the discrete logarithm problem, the Diffie-Hellman key exchange, the Pohlig-Hellman algorithm and the collision algorithm, the ElGamal public key cryptosystem, the Rivest-Shamir-Adleman (RSA) public key cryptosystem, and attacks on RSA. The course involves programming problems and a study project.

MATH 8011. Abstract Algebra I. 3 Credit Hours.

This is the first semester of a year-long sequence in Abstract Algebra. Topics in group theory include group actions, the Sylow theorems, nilpotent and solvable groups, and free groups. Topics in ring theory include structure results on factorization and polynomial rings. The structure theorem for finitely generated modules over principal ideal domains is proved. Throughout, the theme of universal properties and basic category theory is developed.

The textbook is usually either Hungerford's Algebra or Dummit and Foote's Abstract Algebra.

MATH 8012. Abstract Algebra II. 3 Credit Hours.

This is the second semester of a year-long sequence in Abstract Algebra. The course covers fields and Galois theory, module theory including canonical forms for matrices, and Noetherian rings and modules.

Prerequisites: Minimum grade of B- in MATH 8011.

MATH 8013. Numerical Linear Algebra. 3 Credit Hours.

This course presents the fundamental numerical techniques for Linear Algebra, aimed at graduate students in mathematics and related areas who seek a mathematical introduction. Topics include orthogonalization and QR factorization in theory and practice, iterative methods for solving linear systems, Krylov subspace methods, variational formulations for symmetric and nonsymmetric problems, convergence estimates, relations to orthogonal polynomials, preconditioning techniques, incomplete factorizations, multigrid methods, domain decomposition, and basic methods for eigenvalue problems.

MATH 8023. Numerical Methods for Partial Differential Equations. 3 Credit Hours.

This course is designed for graduate students of all disciplines and areas who are interested in numerical methods for partial differential equations, focusing on a rigorous mathematical derivation and analysis. Topics include finite difference, finite element, Fourier, and spectral methods for boundary value problems, elliptic equations, transport, diffusion/heat equation, and wave propagation problems. Fundamental concepts like stability, convergence, and error analysis are a key focus.

MATH 8024. Numerical Methods for Nonlinear Partial Differential Equations. 3 Credit Hours.

This course covers classical and modern numerical methods, including finite volume methods, ENO/WENO, discontinuous Galerkin, staggered grids, semi-spectral, and level set methods, for important nonlinear partial differential equations, including hyperbolic conservation laws, Hamilton-Jacobi equations, interface problems, Stokes and NavierStokes equations. Knowledge of numerical methods for linear partial differential equations is advisable when taking this course.

MATH 8031. Probability Theory. 3 Credit Hours.

This course provides a rigorous treatment of probability theory, covering the following: the axioms of probability, random variables and their distributions, expectation and variance, conditional probability and independence, Markov chains, random walks, laws of large numbers, weak convergence of measures, characteristic functions, the central limit theorem, and additional topics if time permits.

MATH 8032. Stochastic Processes. 3 Credit Hours.

This course provides a rigorous treatment of stochastic processes, focusing on the following: existence of stochastic processes, Poisson process, conditional expectation and martingales, continuous-time Markov processes, stationary processes, ergodicity and mixing, Brownian motion and its properties.

Prerequisites: Math 8031

MATH 8041. Real Analysis I. 3 Credit Hours.

This course focuses on the development of the Lebesgue measure and integration theory. It covers core areas in analysis, including functions of bounded variation, Lebesgue measure and outer measure, measurable functions, Lebesgue integral, modes of convergence, and repeated integration. This course presumes knowledge of undergraduate Real Analysis.

References: Folland, Real Analysis: Modern Techniques and Their Applications Rudin, Real and Complex Analysis

Wheeden-Zygmund, Measure and Integral, An Introduction to Real Analysis Stein and Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces]

MATH 8042. Real Analysis II. 3 Credit Hours.

This course is a continuation of Math 8041. It covers core areas in analysis including Lebesgue differentiation theory, maximal functions, absolute continuity, approximation of identity, L\^{}p spaces, Hilbert spaces, abstract measures and integration.

Prerequisites: Math 8041

MATH 8051. Functions of a Complex Variable. 3 Credit Hours.

This course is an introduction to the theory of functions of one complex variable. Topics include holomorphic functions, derivatives and path integrals, power series, exponential and trigonometric functions, the Cauchy integral theorem and consequences (the maximum principle, Liouville's theorem, Morera's theorem, Schwarz' reflection principle, and Goursat's theorem), residue calculus, convergence in the space of holomorphic functions, Hurwitz' theorem, Montel's theorem, conformal maps and the Riemann mapping theorem. This course presumes knowledge of undergraduate Real Analysis.

Example references: Taylor, Introduction to Complex Analysis; Stein & Shakarchi, Complex Analysis; Conway, Functions of One Complex Variable.

MATH 8052. Intermediate Complex Variable. 3 Credit Hours.

The topics and the textbook choice are at the instructor's discretion. Topics of focus include: Phragmen-Lindelöf method, Runge's theorem, Weierstrass factorization theorem, Mittag-Leffler theorem, theory of entire functions, elements of theory of elliptic functions, several complex variables, theory of Riemann surfaces.

MATH 8061. Smooth Manifolds. 3 Credit Hours.

This is a standard introductory graduate course in differential topology. Topics include: smooth structures on manifolds; smooth functions and maps between manifolds; tangent and cotangent bundles; vector bundles; differential forms; tensors; integration and Stokes' theorem.

MATH 8062. Algebraic Topology. 3 Credit Hours.

This is a standard introductory graduate course in algebraic topology. Topics include: the fundamental group; van Kampen's theorem; covering space theory; singular homology and cohomology; exact sequences; de Rham cohomology and de Rham's theorem; Poincare duality.

MATH 8107. Mathematical Modeling for Science, Engineering, and Industry. 3 Credit Hours.

In this course, students form research groups for projects provided by partners in industry, engineering, or in other disciplines of science. Throughout the semester, the teams are advised by the course instructors and the external partners. The problems themselves are formulated in non-mathematical language, so the students are required to translate these into mathematical language and develop solutions using methods of mathematical modeling. This means that the mathematical and computational methods must be selected or created by the students themselves. At the end, research findings and final results need to be formulated in a language accessible to the external partner. Students disseminate their progress and achievements in weekly presentations, a mid-term and a final project report, as well as a final presentation. Group work with and without the instructors' involvement is a crucial component in this course. Graduate students from disciplines other than mathematics, interested in collaborating in teams on mathematical modeling, and with a background in principles of modeling and computational methods, are welcome to this course.

MATH 8141. Partial Differential Equations. 3 Credit Hours.

This course introduces fundamental concepts and results in the theory of elliptic, parabolic, and hyperbolic differential equations, preparing students for problem-solving in PDEs and their applications. Topics covered: Laplace's equation (maximum principles, Dirichlet problem, Green's function and Poisson kernel), Heat equation (initial boundary value problems, fundamental solution, mean value formula, maximum principle, uniqueness theorems, examples of non-uniqueness, backward heat equation, and energy methods), Wave equation (D'Alembert's formula, plane waves, solution by spherical means, Huygens' Principle, Energy methods: uniqueness, domain of dependence). Solution of the Cauchy problem for nonlinear first order PDEs. This course presupposes knowledge of undergraduate Real Analysis.

Example References: Evans, Partial Differential Equations; Folland, Introduction to Partial Differential Equations; Taylor, Partial Differential Equations I.

MATH 8142. Intermediate Partial Differential Equations. 3 Credit Hours.

This course builds on the foundations of graduate-level PDE theory. The choice of content is at the instructor's discretion. Topics to be covered include nonlinear PDEs, Fourier transform methods, dispersive equations, Sobolev spaces, energy methods, and the Fredholm alternative.

References: Taylor, Partial Differential Equations II-III; Evans, Partial Differential Equations.

MATH 8981. Graduate Development Seminar. 1 Credit Hour.

This course aims to familiarize first-year PhD students with the structure of a PhD in Mathematics. A significant focus of the course is professional development, wherein students learn about important milestones in the program and are trained in the related responsibilities. Students enrolled in this course must attend at least one seminar or colloquium per week, in order to be exposed to research-level mathematics and best practices for communicating mathematics. The seminar itself features a weekly discussion on a topic of interest, led by the Director of Graduate Studies and/or a senior TA. Topics covered in the seminar should include: Basics of departmental structure; effective study techniques for graduate courses and qualifying exams; best practices for professional conduct; creating a professional webpage; written and oral communication of research-level mathematics; research topics studied by faculty in the department; the process of finding a PhD advisor, e.g. through independent study courses; organizing PhD studies with perspective of post-PhD career goals; finding and applying for summer internships in industry and education; and applying for post-PhD employment, in and out of academia.

Level Registration Restrictions: Must be enrolled in one of the following Levels: Graduate.

Repeatability: This course may not be repeated for additional credits.

MATH 8985. Teaching in Higher Education. 1 to 3 Credit Hours.

This course is required for any student seeking Temple's Teaching in Higher Education Certificate. The course focuses on the research on learning theory and the best teaching practices, with the aim of preparing students for effective higher education teaching. All educational topics will be considered through the lens of teaching mathematics and quantitative thinking.

Level Registration Restrictions: Must be enrolled in one of the following Levels: Graduate.

Repeatability: This course may not be repeated for additional credits.

MATH 9000. Algebraic Number Theory. 3 Credit Hours.

This course introduces students to the basic objects, tools, and questions of algebraic number theory. The focus is on number fields and their rings of integers, though some topics related to local fields or global function fields may be introduced. After covering the basics of Dedekind domains and the behavior of prime ideals in extension fields, the two major finiteness theorems --- Dirichlet's unit theorem and the finiteness of class groups --are proved. Additional possible topics include the analytic class number formula, Dirichlet's Theorem for primes in arithmetic progressions, Chebotarev's Density Theorem, the Kronecker-Weber Theorem, and an introduction to class field theory. Corequisite: MATH 8012

MATH 9003. Modular Forms. 3 credit Hours.

This course introduces students to modular forms. Topics include Eisenstein series, finiteness of spaces of modular forms, Hecke operators, modular curves, L-functions of modular forms, and moduli descriptions of modular curves and modular forms. Additional possible topics include congruences between modular forms and an introduction to modularity.

Prerequisite: MATH 8051

Possible textbooks include Zagier's The 1-2-3 of Modular Forms; Serre's A Course in Arithmetic; and Diamond and Shurman's A First Course in Modular Forms.

MATH 9011. Homological Algebra. 3 Credit Hours.

The course is devoted to fundamental notions of homological algebra: chain complexes, abelian categories, derived functors, and spectral sequences. A portion of this course is also devoted to rudiments of category theory. Students will learn how to apply constructions of homological algebra and category theory to questions from abstract algebra, topology and deformation theory.

Possible books include Weibel's An Introduction to Homological Algebra, and Gelfand and Manin's Methods of Homological Algebra.

Prerequisites: Minimum grade of B- in MATH 8012.

MATH 9012. Representation Theory. 3 Credit Hours.

This course primarily focuses on representations of finite groups over a field of characteristic zero. The bulk of the course covers the basics of subrepresentations, irreducibility, semisimplicity, character theory and orthogonality relations, induced representations, and Mackey theory. Additional possible topics include Schur indices, pseudorepresentations, representations of Lie algebras, and modular representation theory.

Possible textbooks include Lorenz's A Tour of Representation Theory; Serre's Linear Representations of Finite Groups; and Curtis and Reiner's Representation Theory of Finite Groups and Associative Algebras.

Prerequisite: MATH 8012

MATH 9014. Commutative Algebra. 3 Credit Hours.

This course focuses on the fundamental concepts of commutative algebra. Topics of the course include ideals of commutative rings, modules, Noetherian and Artinian rings, Noether normalization, Hilbert's Nullstellensatz, rings of fractions, primary decomposition, discrete valuation rings and the rudiments of dimension theory.

Prerequisite: MATH 8012

Possible textbooks include Atiyah and MacDonald's Introduction to Commutative Algebra; Eisenbud's Commutative Algebra with a View Toward Algebraic Geometry; and Matsumura's Commutative Ring Theory.

MATH 9015. Algebraic Geometry. 3 Credit Hours.

This course introduces students to the vast subject of algebraic geometry. Topics of the course include affine and projective varieties, morphisms of algebraic varieties, birational equivalence, and basic intersection theory. Students will also learn about schemes, morphisms of schemes, coherent sheaves, and divisors.

Prerequisite: MATH 8012

Possible textbooks include R. Hartshorne's Algebraic Geometry; R. Vakil's The Rising Sea: Foundations of Algebraic Geometry; and W. Fulton's Algebraic Curves. An Introduction to Algebraic Geometry.

MATH 9021. Riemannian Geometry. 3 Credit Hours.

The goal of this course is to provide a solid introduction to the two central concepts of Riemannian geometry, namely, geodesics and curvature. Topics include Riemannian metrics, Riemannian connections, geodesics, curvature (sectional, Ricci, and scalar), the Jacobi equation, the second fundamental form, and global results such as the GaussBonnet theorem, Hopf-Rinow theorem, and Hadamard's theorem.

Prerequisites: MATH 8062 (may be taken concurrently)

MATH 9023. Knot Theory. 3 Credit Hours.

This course covers the theory of knots and links, with a focus on different flavors of invariants. The course covers a large selection of the following topics: polynomial invariants, connections to braid groups, Dehn surgery, geometric invariants, quantum invariants of 3-manifolds.

Prerequisites: Minimum grade of B- in MATH 8062.

MATH 9024. Low-Dimensional Topology. 3 Credit Hours.

This course is a broad introduction to low-dimensional topology with an emphasis on 3manifolds, especially their construction, classification results, and invariants. Potential topics include: gluing constructions, Dehn surgery, foliations and flows, geometric structures, and connections to group theory.

Prerequisites: Minimum grade of B- in MATH 8062.

MATH 9041. Functional Analysis. 3 Credit Hours.

Functional Analysis provides the foundation for high-dimensional geometry, analysis, and probability. This course introduces the fundamental concepts and methods of functional analysis, with an emphasis on concrete examples. Topics include the Baire Category Theorem and its applications, particularly to Banach space theory principles such as the Uniform Boundedness Principle, the Open Mapping Theorem, and the Closed Graph Theorem. The course also explores different notions of convergence, weak topology, duality, and convexity. In addition, it introduces linear operator theory, including spectral theory for compact operators, self-adjoint operators, Fredholm theory, and their applications.

Prerequisites: MATH 5042 or MATH 8042

References: Reed and Simon, Functional Analysis; Conway, A Course in Functional Analysis; Brezis, Functional Analysis, Sobolev Spaces and PDEs; Stein & Shakarchi, Functional Analysis.

MATH 9042. Fourier Analysis and Distribution Theory. 3 Credit Hours.

This course is a basic introduction to Fourier Analysis and Distribution Theory. Topics include Fourier series, the Fourier transform, Schwartz functions, tempered distributions, convolutions, and applications to partial differential equations. Knowledge of Math 9041, Functional Analysis, is recommended but not required.

Prerequisites: MATH 8042

Example References: Stein and Weiss, Introduction to Fourier analysis on Euclidean spaces; Korner, Fourier analysis; Hormander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis; Gelfand and Shilov, Generalized functions.

MATH 9043. Calculus of Variations. 3 Credit Hours.

The course covers the first variation and Euler-Lagrange equations, including null Lagrangians and Carathéodory's "Royal Road". It introduces geodesic coverings, the eikonal equation, and the Hamilton-Jacobi equation. The second variation is explored through Jacobi's theory of conjugate points and Weierstrass's E-function. The Hamiltonian formalism, convex duality, and Hilbert's invariant integral are also discussed, highlighting connections between variational principles, geometry, and physics.

Example References: Caratheodory: Calculus of Variations and Partial Differential Equations of First Order; Giaquinta and Hildebrand: Calculus of Variations, Vols. I and II.

MATH 9044. Harmonic Analysis. 3 Credit Hours.

This course presents a rapid introduction to modern tools of Harmonic Analysis. These tools are relevant to problems in a very dynamic area of mathematics at the interface of several branches such as Fourier Analysis, Functional Analysis, Partial Differential Equations, Index Theory, and Geometric Measure Theory. Topics of focus include Hardy spaces, singular integrals, maximal operators, functions of bounded and vanishing mean oscillation, square functions, applications to elliptic partial differential equations in the upper half space.

Prerequisites: MATH 8042

Example References: Grafakos, Classical and Modern Fourier Analysis; Stein, Harmonic Analysis, Real-Variable Methods, Orthogonality, and Oscillatory Integrals; Garcia-Cuerva & De Francia, Weighted Norm Inequalities.

MATH 9061. Lie Groups. 3 Credit Hours.

This course develops Lie theory from the ground up. Starting with basic definitions of Lie groups and Lie algebras, the course develops structure theory, analytic and algebraic aspects, structure of nilpotent and solvable Lie groups, and the classification of semisimple Lie groups.

Prerequisites: Minimum grade of B- in MATH 8062.

MATH 9063. Riemann Surfaces. 3 Credit Hours.

This course covers the analytic and geometric theory of Riemann surfaces. Topics include: uniformization, algebraic perspectives, calculus on Riemann surfaces, moduli space. Moduli and Teichmueller spaces for compact Riemann surfaces; introduction to modular forms; embedding of compact Riemann surfaces in complex projective spaces. Branched coverings and maps onto the Riemann sphere.

Prerequisites: Math 8051, Complex Analysis

MATH 9071. Hyperbolic geometry. 3 Credit Hours.

This is an introduction to hyperbolic manifolds, their structure, and their deformations. Potential topics include: thick-thin decomposition, rigidity results, hyperbolic Dehn filling, arithmetic manifolds, and the general theory of Kleinian groups.

MATH 9073. Geometric Group Theory. 3 Credit Hours.

This course surveys the rapidly expanding field of geometric group theory, focusing on the role played by negative curvature. The course begins with classical combinatorial techniques used to construct and study infinite discrete groups. After introducing basic concepts in coarse geometry, it turns attention to Gromov's notion of hyperbolic groups. In addition to studying geometric, algebraic, and algorithmic properties of these groups, the course keeps an eye towards several generalizations of hyperbolicity that have recently played a large role in understanding many geometrically significant groups. As examples, it also touches on the study of mapping class groups, outer automorphism groups of free groups, and cubical groups.

Prerequisites: Minimum grade of B- in MATH 8062.

MATH 9100. Topics in Algebra. 3 Credit Hours.

This course covers variable topics in theory of commutative and non-commutative rings, groups, algebraic number theory, and algebraic geometry.

MATH 9200. Topics in Numerical Analysis. 3 Credit Hours.

This course covers a variable set of timely topics in Numerical Analysis, including, but not limited to, numerical optimization, computational fluid dynamics, numerical methods for general flow problems, or advanced finite element methods.

MATH 9210. Topics in Applied Mathematics. 3 Credit Hours.

This course covers a variable set of timely topics in Applied Mathematics, including, but not limited to, mathematical biology, multiscale modeling and methods, material science, or control theory.

MATH 9300. Topics in Probability. 3 Credit Hours.

This course presents research topics related to probability theory, depending on the interests of the students and the instructor. Potential topics include interacting particle systems, random matrix theory, probability models in mathematical physics, statistical mechanics, homogenization, stochastic optimal control, differential and mean-field games.

MATH 9400. Topics in Analysis. 3 Credit Hours.

This course focuses on advanced topics in Analysis and the theory of Partial Differential Equations with the goal of introducing students to open problems in the field. The focus changes with the instructor. Potential topics covered include non-linear PDEs, MongeAmpère equations, elliptic PDE in irregular domains, spectral theory, singular integrals, optimal transport, regularity theory of solutions to elliptic PDEs, mathematical analysis of fluid equations, and analysis on quasi-metric spaces.

MATH 9500. Topics in Geometry and Topology. 3 Credit Hours.

Variable topics in geometric topology and related areas. Possibilities include: Morse theory, surfaces and their diffeomorphisms, mapping class groups, Teichmuller theory, braids, dynamics of group actions, and homogeneous dynamics.

Pre-requisites: MATH 8062.

MATH 9991. Master's Research Projects. 1 to 6 Credit Hour.

Short-term, limited research project or laboratory project in the field. This course is not the capstone project course, nor can it be used for thesis based research. The course is for master's students only, including PSM, MA or MS. This class will not confer full-time program status unless nine credits are taken.

Level Registration Restrictions: Must be enrolled in one of the following Levels: Graduate.
Degree Restrictions: Must be enrolled in one of the following Degrees: Master of Arts, Master of Science, Prof Science Masters.