# Complete Course List

## MATH 8001 - Preparation for College Teaching

1.0 [max 3.0 cr] cr; Prereq: ! math grad student in good standing or #;
S-N or Aud
Fall, Spring, Every Year
New approaches to teaching/learning, issues in mathematics education, components/expectations of a college mathematics professor.

## MATH 8141 - Applied Logic

A-F or Aud
Fall, Spring
Applying techniques of mathematical logic to other areas of mathematics and computer science. Sample topics: complexity of computation, computable analysis, unsolvability of diophantine problems, program verification, database theory.

## MATH 8142 - Applied Logic

A-F or Aud
Spring
Applying techniques of mathematical logic to other areas of mathematics, computer science. Complexity of computation, computable analysis, unsolvability of diophantine problems, program verification, database theory.

## MATH 8151 - Axiomatic Set Theory

3.0 cr; Prereq: 5166 or #;
A-F or Aud
Periodically
Axiomatic development of basic properties of ordinal/cardinal numbers, infinitary combinatorics, well founded sets, consistency of axiom of foundation, constructible sets, consistency of axiom of choice and of generalized continuum hypothesis.

## MATH 8152 - Axiomatic Set Theory

3.0 cr; Prereq: 8151 or #;
A-F or Aud
Periodically
Notion of forcing, generic extensions, forcing with finite partial functions, independence of continuum hypothesis, forcing with partial functions of infinite cardinalities, relationship between partial orderings and Boolean algebras, Boolean-valued models, independence of axiom of choice.

## MATH 8166 - Recursion Theory

3.0 cr; Prereq: Math grad student or #;
A-F or Aud
Periodically

## MATH 8167 - Recursion Theory

3.0 cr; Prereq: 8166;
A-F or Aud
Spring
Sample topics: complexity theory, recursive analysis, generalized recursion theory, analytical hierarchy, constructive ordinals.

## MATH 8172 - Model Theory

3.0 cr; Prereq: Math grad student or #;
A-F or Aud
Periodically
Interplay of formal theories, their models. Elementary equivalence, elementary extensions, partial isomorphisms. Lowenheim-Skolem theorems, compactness theorems, preservation theorems. Ultraproducts.

## MATH 8173 - Model Theory

3.0 cr; Prereq: 8172 or #;
A-F or Aud
Periodically
Types of elements. Prime models, homogeneity, saturation, categoricity in power. Forking.

## MATH 8190 - Topics in Logic

A-F or Aud
Fall, Spring, Periodically

## MATH 8201 - General Algebra

3.0 cr; Prereq: 4xxx algebra or equiv or #;
A-F or Aud
Fall, Every Year
Groups through Sylow, Jordan-H[o]lder theorems, structure of finitely generated Abelian groups. Rings and algebras, including Gauss theory of factorization. Modules, including projective and injective modules, chain conditions, Hilbert basis theorem, and structure of modules over principal ideal domains.

## MATH 8202 - General Algebra

3.0 cr; Prereq: 8201 or #;
A-F or Aud
Spring, Every Year
Classical field theory through Galois theory, including solvable equations. Symmetric, Hermitian, orthogonal, and unitary form. Tensor and exterior algebras. Basic Wedderburn theory of rings; basic representation theory of groups.
Course Number and Name Section Location Term Instructor
8202 General Algebra 1 Spring 2021 Christine Berkesch

## MATH 8207 - Theory of Modular Forms and L-Functions

3.0 cr; Prereq: 8202 or #;
A-F or Aud
Fall, Spring, Periodically
Zeta and L-functions, prime number theorem, Dirichlet's theorem on primes in arithmetic progressions, class number formulas; Riemann hypothesis; modular forms and associated L-function; Eisenstein series; Hecke operators, Poincar[e] series, Euler products; Ramanujan conjectures; Theta series and quadratic forms; waveforms and L-functions.

## MATH 8208 - Theory of Modular Forms and L-Functions

3.0 cr; Prereq: 8207 or #;
A-F or Aud
Periodically
Applications of Eisenstein series: special values and analytic continuation and functional equations of L-functions. Trace formulas. Applications of representation theory. Computations.

## MATH 8211 - Commutative and Homological Algebra

3.0 cr; Prereq: 8202 or #;
A-F or Aud
Fall
Selected topics.

## MATH 8212 - Commutative and Homological Algebra

3.0 cr; Prereq: 8211 or #;
A-F or Aud
Periodically
Selected topics.

## MATH 8245 - Group Theory

3.0 cr; Prereq: 8202 or #;
A-F or Aud
Fall, Every Year
Permutations, Sylow's theorems, representations of groups on groups, semi-direct products, solvable and nilpotent groups, generalized Fitting subgroups, p-groups, co-prime action on p-groups.

## MATH 8246 - Group Theory

3.0 cr; Prereq: 8245 or #;
A-F or Aud
Fall, Spring
Representation and character theory, simple groups, free groups and products, presentations, extensions, Schur multipliers.

## MATH 8251 - Algebraic Number Theory

3.0 cr; Prereq: 8202 or #;
A-F or Aud
Periodically
Algebraic number fields and algebraic curves. Basic commutative algebra. Completions: p-adic fields, formal power series, Puiseux series. Ramification, discriminant, different. Finiteness of class number and units theorem.

## MATH 8252 - Algebraic Number Theory

3.0 cr; Prereq: 8251 or #;
A-F or Aud
Periodically
Zeta and L-functions of global fields. Artin L-functions. Hasse-Weil L-functions. Tchebotarev density. Local and global class field theory. Reciprocity laws. Finer theory of cyclotomic fields.
Course Number and Name Section Location Term Instructor
8252 Algebraic Number Theory 1 Spring 2021 Kai-Wen Lan

## MATH 8253 - Algebraic Geometry

3.0 cr; Prereq: 8202 or #;
A-F or Aud
Fall
Curves, surfaces, projective space, affine and projective varieties. Rational maps. Blowing-up points. Zariski topology. Irreducible varieties, divisors.

## MATH 8254 - Algebraic Geometry

3.0 cr; Prereq: 8253 or #;
A-F or Aud
Spring
Sheaves, ringed spaces, and schemes. Morphisms. Derived functors and cohomology, Serre duality. Riemann-Roch theorem for curves, Hurwitz's theorem. Surfaces: monoidal transformations, birational transformations.
Course Number and Name Section Location Term Instructor
8254 Algebraic Geometry 1 Spring 2021 Tian-Jun Li

## MATH 8270 - Topics in Algebraic Geometry

1.0 - 3.0 [max 12.0 cr] cr; Prereq: Math 8201, Math 8202;
A-F or Aud
Fall, Spring, Every Year, Periodically

## MATH 8271 - Lie Groups and Lie Algebras

3.0 cr; Prereq: 8302 or #;
A-F or Aud
Fall
Definitions and basic properties of Lie groups and Lie algebras; classical matrix Lie groups; Lie subgroups and their corresponding Lie subalgebras; covering groups; Maurer-Cartan forms; exponential map; correspondence between Lie algebras and simply connected Lie groups; Baker-Campbell-Hausdorff formula; homogeneous spaces.

## MATH 8272 - Lie Groups and Lie Algebras

3.0 cr; Prereq: 8271 or #;
A-F or Aud
Spring
Solvable and nilpotent Lie algebras and Lie groups; Lie's and Engels's theorems; semisimple Lie algebras; cohomology of Lie algebras; Whitehead's lemmas and Levi's theorem; classification of complex semisimple Lie algebras and compact Lie groups; representation theory.

## MATH 8280 - Topics in Number Theory

1.0 - 3.0 [max 12.0 cr] cr; Prereq: #;
A-F or Aud
Periodically
Course Number and Name Section Location Term Instructor
8280 Topics in Number Theory 1 Spring 2021 Dihua Jiang

## MATH 8300 - Topics in Algebra

1.0 - 3.0 [max 12.0 cr] cr; Prereq: Grad math major or #;
A-F or Aud
Fall, Every Year, Periodically
Selected topics.
Course Number and Name Section Location Term Instructor
8300 Topics in Algebra 1 Spring 2021 Gennady Lyubeznik

## MATH 8301 - Manifolds and Topology

3.0 cr; Prereq: [Some point-set topology, algebra] or #;
A-F or Aud
Fall, Every Year
Classification of compact surfaces, fundamental group/covering spaces. Homology group, basic cohomology. Application to degree of a map, invariance of domain/dimension.

## MATH 8302 - Manifolds and Topology

3.0 cr; Prereq: 8301 or #;
A-F or Aud
Spring, Every Year
Smooth manifolds, tangent spaces, embedding/immersion, Sard's theorem, Frobenius theorem. Differential forms, integration. Curvature, Gauss-Bonnet theorem. Time permitting: de Rham, duality in manifolds.
Course Number and Name Section Location Term Instructor
8302 Manifolds and Topology 1 Spring 2021 Anar Akhmedov

## MATH 8306 - Algebraic Topology

3.0 cr; Prereq: 8301 or #;
A-F or Aud
Periodically
Singular homology, cohomology theory with coefficients. Eilenberg-Stenrod axioms, Mayer-Vietoris theorem.

## MATH 8307 - Algebraic Topology

3.0 cr; Prereq: 8306 or #;
A-F or Aud
Periodically
Basic homotopy theory, cohomology rings with applications. Time permitting: fibre spaces, cohomology operations, extra-ordinary cohomology theories.
Course Number and Name Section Location Term Instructor
8307 Algebraic Topology 1 Spring 2021 Craig Westerland

Periodically
No description

## MATH 8360 - Topics in Topology

1.0 - 3.0 [max 12.0 cr] cr; Prereq: 8301 or #;
A-F or Aud
Fall, Spring, Periodically
Selected topics.

## MATH 8365 - Riemannian Geometry

3.0 cr; Prereq: 8301 or basic point-set topology or #;
A-F or Aud
Fall, Every Year
Riemannian metrics, curvature. Bianchi identities, Gauss-Bonnet theorem, Meyers's theorem, Cartan-Hadamard theorem.

## MATH 8366 - Riemannian Geometry

3.0 cr; Prereq: 8365 or #;
A-F or Aud
Spring, Every Year
Gauss, Codazzi equations. Tensor calculus, Hodge theory, spinors, global differential geometry, applications.

## MATH 8370 - Topics in Differential Geometry

1.0 - 3.0 [max 12.0 cr] cr; Prereq: 8301 or 8365;
A-F or Aud
Fall, Spring, Every Year, Periodically
Current research in Differential Geometry.

## MATH 8380 - Topics in Advanced Geometry

1.0 - 3.0 [max 12.0 cr] cr; Prereq: 8301, 8365;
A-F or Aud
Fall, Spring
Current research.

## MATH 8385 - Calculus of Variations and Minimal Surfaces

3.0 cr; Prereq: 4xxx partial differential equations or #;
A-F or Aud
Periodically
Comprehensive exposition of calculus of variations and its applications. Theory for one-dimensional problems. Survey of typical problems. Necessary conditions. Sufficient conditions. Second variation, accessory eigenvalue problem. Variational problems with subsidiary conditions. Direct methods.

## MATH 8386 - Calculus of Variations and Minimal Surfaces

3.0 cr; Prereq: 8595 or #;
A-F or Aud
Periodically
Theory of multiple integrals. Geometrical differential equations, i.e., theory of minimal surfaces and related structures (surfaces of constant or prescribed mean curvature, solutions to variational integrals involving surface curvatures), all extremals for variational problems of current interest as models for interfaces in real materials.

## MATH 8387 - Mathematical Modeling of Industrial Problems

3.0 cr; Prereq: [5xxx numerical analysis, some computer experience] or #;
A-F or Aud
Fall, Every Year
Mathematical models from physical, biological, social systems. Emphasizes industrial applications. Modeling of deterministic/probabilistic, discrete/continuous processes; methods for analysis/computation.

## MATH 8388 - Mathematical Modeling of Industrial Problems

3.0 cr; Prereq: 8597 or #;
A-F or Aud
Periodically
Techniques for analysis of mathematical models. Asymptotic methods; design of simulation and visualization techniques. Specific computation for models arising in industrial problems.

## MATH 8390 - Topics in Mathematical Physics

1.0 - 3.0 [max 12.0 cr] cr; Prereq: 8601;
A-F or Aud
Periodically
Current research.

## MATH 8401 - Mathematical Modeling and Methods of Applied Mathematics

3.0 cr; Prereq: 4xxx numerical analysis and applied linear algebra or #;
A-F or Aud
Fall, Every Year
Dimension analysis, similarity solutions, linearization, stability theory, well-posedness, and characterization of type. Fourier series and integrals, wavelets, Green's functions, weak solutions and distributions.

## MATH 8431 - Mathematical Fluid Mechanics

3.0 cr; Prereq: 5xxx numerical analysis of partial differential equations or #;
A-F or Aud
Periodically
Equations of continuity/motion. Kinematics. Bernoulli's theorem, stream function, velocity potential. Applications of conformal mapping.

## MATH 8432 - Mathematical Fluid Mechanics

3.0 cr; Prereq: 8431 or #;
Periodically
Plane flow of gas, characteristic method, hodograph method. Singular surfaces, shock waves, shock layers. Viscous flow, Navier-Stokes equations, exact solutions. Uniqueness, stability, existence theorems.

## MATH 8441 - Numerical Analysis and Scientific Computing

3.0 cr; Prereq: [4xxx analysis, 4xxx applied linear algebra] or #;
Fall, Every Year
Approximation of functions, numerical integration. Numerical methods for elliptic partial differential equations, including finite element methods, finite difference methods, and spectral methods. Grid generation.

## MATH 8442 - Numerical Analysis and Scientific Computing

3.0 cr; Prereq: 8441 or #; 5477-5478 recommended for engineering and science grad students;
Spring, Every Year
Numerical methods for integral equations, parabolic partial differential equations, hyperbolic partial differential equations. Monte Carlo methods.
Course Number and Name Section Location Term Instructor
8442 Numerical Analysis and Scientific Computing 1 Spring 2021 Douglas Arnold

Periodically

## MATH 8445 - Numerical Analysis of Differential Equations

3.0 cr; Prereq: 4xxx numerical analysis, 4xxx partial differential equations or #;
A-F or Aud
Fall, Spring, Every Year
Finite element and finite difference methods for elliptic boundary value problems (e.g., Laplace's equation) and solution of resulting linear systems by direct and iterative methods.

## MATH 8446 - Numerical Analysis of Differential Equations

3.0 cr; Prereq: 8445 or #;
A-F or Aud
Spring, Every Year
Numerical methods for parabolic equations (e.g., heat equations). Methods for elasticity, fluid mechanics, electromagnetics. Applications to specific computations.
Course Number and Name Section Location Term Instructor
8446 Numerical Analysis of Differential Equations 1 Spring 2021 Bernardo Cockburn

## MATH 8450 - Topics in Numerical Analysis

1.0 - 3.0 [max 12.0 cr] cr; Prereq: Grad math major or #;
A-F or Aud
Fall, Spring, Every Year, Periodically
Selected topics.

## MATH 8470 - Topics in Mathematical Theory of Continuum Mechanics

A-F or Aud
Fall, Spring, Periodically

## MATH 8501 - Theory of Ordinary Differential Equations

3.0 cr; Prereq: 4xxx ODE or #;
A-F or Aud
Fall, Every Year
Existence, uniqueness, continuity, and differentiability of solutions. Linear theory and hyperbolicity. Basics of dynamical systems. Local behavior near a fixed point, a periodic orbit, and a homoclinic or heteroclinic orbit. Perturbation theory.

## MATH 8502 - Dynamical Systems and Differential Equations

3.0 cr; Prereq: 8501 or #;
A-F or Aud
Spring, Every Year
Selected topics: stable, unstable, and center manifolds. Normal hyperbolicity. Nonautonomous dynamics and skew product flows. Invariant manifolds and quasiperiodicity. Transversality and Melnikov method. Approximation dynamics. Morse-Smale systems. Coupled oscillators and network dynamics.
Course Number and Name Section Location Term Instructor
8502 Differential Equations and Dynamical Systems II 1 Spring 2021 Richard Moeckel

## MATH 8503 - Bifurcation Theory in Ordinary Differential Equations

3.0 cr; Prereq: 8501 or #;
A-F or Aud
Periodically
Basic bifurcation theory, Hopf bifurcation, and method averaging. Silnikov bifurcations. Singular perturbations. Higher order bifurcations. Applications.

## MATH 8505 - Applied Dynamical Systems and Bifurcation Theory I

3.0 cr; Prereq: 5525 or 8502 or #;
A-F or Aud
Periodically
Static/Hopf bifurcations, invariant manifold theory, normal forms, averaging, Hopf bifurcation in maps, forced oscillations, coupled oscillators, chaotic dynamics, co-dimension 2 bifurcations. Emphasizes computational aspects/applications from biology, chemistry, engineering, physics.

## MATH 8506 - Applied Dynamical Systems and Bifurcation Theory II

3.0 cr; Prereq: 5587 or #;
A-F or Aud
Fall
Background on analysis in Banach spaces, linear operator theory. Lyapunov-Schmidt reduction, static bifurcation, stability at a simple eigenvalue, Hopf bifurcation in infinite dimensions invariant manifold theory. Applications to hydrodynamic stability problems, reaction-diffusion equations, pattern formation, and elasticity.

## MATH 8520 - Topics in Dynamical Systems

1.0 - 3.0 [max 12.0 cr] cr; Prereq: 8502;
A-F or Aud
Fall, Spring
Current research.

## MATH 8530 - Topics in Ordinary Differential Equations

1.0 - 3.0 [max 3.0 cr] cr; Prereq: 8502;
A-F or Aud
Fall, Spring, Periodically

## MATH 8540 - Topics in Mathematical Biology

A-F or Aud
Fall, Spring, Every Year, Periodically
Course Number and Name Section Location Term Instructor
8540 Topics in Mathematical Biology 1 Spring 2021 Hans Othmer

## MATH 8571 - Theory of Evolutionary Equations

3.0 cr; Prereq: 8502 or #;
A-F or Aud
Fall, Every Year
Infinite dimensional dynamical systems, global attractors, existence and robustness. Linear semigroups, analytic semigroups. Linear and nonlinear reaction diffusion equations, strong and weak solutions, well-posedness of solutions.

## MATH 8572 - Theory of Evolutionary Equations

3.0 cr; Prereq: 8571 or #;
A-F or Aud
Spring
Dynamics of Navier-Stokes equations, strong/weak solutions, global attractors. Chemically reacting fluid flows. Dynamics in infinite dimensions, unstable manifolds, center manifolds perturbation theory. Inertial manifolds, finite dimensional structures. Dynamical theories of turbulence.

## MATH 8580 - Topics in Evolutionary Equations

1.0 - 3.0 [max 12.0 cr] cr; Prereq: 8572 or #;
A-F or Aud
Periodically

## MATH 8581 - Applications of Linear Operator Theory

3.0 cr; Prereq: 4xxx applied mathematics or #;
A-F or Aud
Periodically
Metric spaces, continuity, completeness, contraction mappings, compactness. Normed linear spaces, continuous linear transformations. Hilbert spaces, orthogonality, projections.

## MATH 8582 - Applications of Linear Operator Theory

3.0 cr; Prereq: 8581 or #;
A-F or Aud
Periodically
Fourier theory. Self-adjoint, compact, unbounded linear operators. Spectral analysis, eigenvalue-eigenvector problem, spectral theorem, operational calculus.

## MATH 8583 - Theory of Partial Differential Equations

3.0 cr; Prereq: [Some 5xxx PDE, 8601] or #;
A-F or Aud
Fall, Every Year
Classification of partial differential equations/characteristics. Laplace, wave, heat equations. Some mixed problems.

## MATH 8584 - Theory of Partial Differential Equations

3.0 cr; Prereq: 8583 or #;
A-F or Aud
Spring, Every Year
Fundamental solutions/distributions, Sobolev spaces, regularity. Advanced elliptic theory (Schauder estimates, Garding's inequality). Hyperbolic systems.
Course Number and Name Section Location Term Instructor
8584 Theory of Partial Differential Equations 1 Spring 2021 Hao Jia

## MATH 8590 - Topics in Partial Differential Equations

1.0 - 3.0 [max 3.0 cr] cr; Prereq: 8602;
A-F or Aud
Fall, Spring, Every Year, Periodically
Research topics.

## MATH 8600 - Topics in Advanced Applied Mathematics

Fall, Spring, Every Year
Offered for one yr or one semester as circumstances warrant. Topics vary. For details, contact instructor.

## MATH 8601 - Real Analysis

3.0 cr; Prereq: 5616 or #;
A-F or Aud
Fall, Every Year
Set theory/fundamentals. Axiom of choice, measures, measure spaces, Borel/Lebesgue measure, integration, fundamental convergence theorems, Riesz representation.

## MATH 8602 - Real Analysis

3.0 cr; Prereq: 8601 or #;
A-F or Aud
Spring, Every Year
Radon-Nikodym, Fubini theorems. C(X). Lp spaces (introduction to metric, Banach, Hilbert spaces). Stone-Weierstrass theorem. Basic Fourier analysis. Theory of differentiation.
Course Number and Name Section Location Term Instructor
8602 Real Analysis 1 Spring 2021 Max Engelstein

## MATH 8640 - Topics in Real Analysis

3.0 [max 12.0 cr] cr; Prereq: 8602 or #;
A-F or Aud
Periodically
Current research.

## MATH 8651 - Theory of Probability Including Measure Theory

3.0 cr; Prereq: 5616 or #;
Fall, Every Year
Probability spaces. Distributions/expectations of random variables. Basic theorems of Lebesque theory. Stochastic independence, sums of independent random variables, random walks, filtrations. Probability, moment generating functions, characteristic functions. Laws of large numbers.

## MATH 8652 - Theory of Probability Including Measure Theory

3.0 cr; Prereq: 8651 or #;
Spring, Every Year
Conditional distributions and expectations, convergence of sequences of distributions on real line and on Polish spaces, central limit theorem and related limit theorems, Brownian motion, martingales and introduction to other stochastic sequences.
Course Number and Name Section Location Term Instructor
8652 Theory of Probability Including Measure Theory 1 Spring 2021 Sergey Bobkov

## MATH 8654 - Fundamentals of Probability Theory and Stochastic Processes

3.0 cr; Prereq: 8651 or 8602 or #;
Spring
Review of basic theorems of probability for independent random variables; introductions to Brownian motion process, Poisson process, conditioning, Markov processes, stationary processes, martingales, super- and sub-martingales, Doob-Meyer decomposition.

## MATH 8655 - Stochastic Calculus with Applications

3.0 cr; Prereq: 8654 or 8659 or #;
Fall, Every Year
Stochastic integration with respect to martingales, Ito's formula, applications to business models, filtering, and stochastic control theory.

## MATH 8659 - Stochastic Processes

3.0 cr; Prereq: 8652 or #;
Fall, Every Year
In-depth coverage of various stochastic processes and related concepts, such as Markov sequences and processes, renewal sequences, exchangeable sequences, stationary sequences, Poisson point processes, Levy processes, interacting particle systems, diffusions, and stochastic integrals.

## MATH 8660 - Topics in Probability

Fall, Spring, Every Year, Periodically

Periodically
No description

## MATH 8668 - Combinatorial Theory

A-F or Aud
Fall
Basic enumeration, including sets and multisets, permutation statistics, inclusion-exclusion, integer/set partitions, involutions and Polya theory. Partially ordered sets, including lattices, incidence algebras, and Mobius inversion. Generating functions.

## MATH 8669 - Combinatorial Theory

3.0 cr; Prereq: 8668 or #;
A-F or Aud
Spring, Odd Years
Further topics in enumeration, including symmetric functions, Schensted correspondence, and standard tableaux; non-enumerative combinatorics, including graph theory and coloring, matching theory, connectivity, flows in networks, codes, and extremal set theory.

## MATH 8680 - Topics in Combinatorics

1.0 - 3.0 [max 12.0 cr] cr; Prereq: Grad math major or #;
A-F or Aud
Fall, Spring, Every Year, Periodically
Selected topics.
Course Number and Name Section Location Term Instructor
8680 Topics in Combinatorics 1 Spring 2021 Victor Reiner

## MATH 8701 - Complex Analysis

3.0 cr; Prereq: 5616 or #;
A-F or Aud
Fall, Every Year
Foundations of holomorphic functions of one variable; relation to potential theory, complex manifolds, algebraic geometry, number theory. Cauchy's theorems, Poisson integral. Singularities, series, product representations. Hyperbolic geometry, isometries. Covering surfaces, Riemann-Hurwitz formula. Schwarz-Christoffel polygonal functions. Residues.

## MATH 8702 - Complex Analysis

3.0 cr; Prereq: 8701 or #;
A-F or Aud
Spring, Every Year
Riemann mapping, uniformization, Dirichlet problem. Dirichlet principle, Green's functions, harmonic measures. Approximation theory. Complex analysis on tori (elliptic functions, modular functions, conformal moduli). Complex dynamical systems (Julia sets, Mandelbrot set).
Course Number and Name Section Location Term Instructor
8702 Complex Analysis 1 Spring 2021 Paul Garrett

Periodically
No description

## MATH 8790 - Topics in Complex Analysis

1.0 - 3.0 [max 12.0 cr] cr; Prereq: 8702 or #;
A-F or Aud
Periodically
Current research.

## MATH 8801 - Functional Analysis

3.0 cr; Prereq: 8602 or #;
A-F or Aud
Fall, Every Year
Motivation in terms of specific problems (e.g., Fourier series, eigenfunctions). Theory of compact operators. Basic theory of Banach spaces (Hahn-Banach, open mapping, closed graph theorems). Frechet spaces.

## MATH 8802 - Functional Analysis

3.0 cr; Prereq: 8801 or #;
A-F or Aud
Spring
Spectral theory of operators, theory of distributions (generalized functions), Fourier transformations and applications. Sobolev spaces and pseudo-differential operators. C-star algebras (Gelfand-Naimark theory) and introduction to von Neumann algebras.
Course Number and Name Section Location Term Instructor
8802 Functional Analysis 1 Spring 2021 Arnd Scheel

Periodically
No description

## MATH 8990 - Topics in Mathematics

1.0 - 6.0 [max 24.0 cr] cr; Prereq: #;
S-N or Aud
Fall, Spring, Every Year

## MATH 8991 - Independent Study

1.0 - 6.0 [max 24.0 cr] cr; Prereq: #;
S-N or Aud
Spring, Summer, Every Year
Individually directed study.

## MATH 8992 - Directed Reading

1.0 - 6.0 [max 24.0 cr] cr; Prereq: #;
S-N or Aud
Fall, Spring, Every Year