Complete Course List

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.
Course Number and Name Section Location Term Instructor
8001 Preparation for College Teaching 1 Vincent Hall 16 Fall 2017 Jonathan Rogness

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 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 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.
Course Number and Name Section Location Term Instructor
8201 General Algebra 1 Vincent Hall 209 Fall 2017 Peter Webb

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 Vincent Hall 301 Spring 2017 Christine Berkesch Zamaere
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.
Course Number and Name Section Location Term Instructor
8207 Theory of Modular Forms and L-Functions 1 Vincent Hall 113 Fall 2017 Paul Garrett
3.0 cr; Prereq: 8202 or #;
A-F or Aud
Fall
Selected topics.
Course Number and Name Section Location Term Instructor
8211 Commutative and Homological Algebra 1 Vincent Hall 207 Fall 2017 Christine Berkesch Zamaere
8211 Commutative and Homological Algebra 1 Vincent Hall 213 Spring 2017 William Messing

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 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.
Course Number and Name Section Location Term Instructor
8253 Algebraic Geometry 1 Vincent Hall 211 Fall 2017 Alexander Voronov

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 Vincent Hall 213 Spring 2017 Ionut Ciocan-Fontanine
1.0 - 3.0 [max 12.0 cr] cr; Prereq: Math 8201, Math 8202;
A-F or Aud
Fall, Spring, Every Year, Periodically
Course Number and Name Section Location Term Instructor
8270 Topics in Algebraic Geometry 1 Vincent Hall 301 Spring 2017 William Messing
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.
Course Number and Name Section Location Term Instructor
8271 Lie Groups and Lie Algebras 1 Vincent Hall 213 Fall 2017 Kai-Wen Lan
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.
Course Number and Name Section Location Term Instructor
8272 Lie Groups and Lie Algebras 1 Vincent Hall 206 Spring 2017 Kai-Wen Lan
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 Vincent Hall 301 Fall 2017 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 Vincent Hall 213 Fall 2017 Ionut Ciocan-Fontanine
8300 Topics in Algebra 1 Vincent Hall 213 Spring 2017 Peter Webb
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.
Course Number and Name Section Location Term Instructor
8301 Manifolds and Topology 1 Vincent Hall 113 Fall 2017 Craig Westerland
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 Vincent Hall 209 Spring 2017 Anar Akhmedov

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.
Course Number and Name Section Location Term Instructor
8366 Riemannian Geometry 1 Vincent Hall 364 Spring 2017 Jiaping Wang
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.
1.0 - 3.0 [max 12.0 cr] cr; Prereq: 8301, 8365;
A-F or Aud
Fall, Spring
Current research.
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.
1.0 - 3.0 [max 12.0 cr] cr; Prereq: 8601;
A-F or Aud
Periodically
Current research.
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.
Course Number and Name Section Location Term Instructor
8401 Mathematical Modeling and Methods of Applied Mathematics 1 Vincent Hall 209 Fall 2017 Yoichiro Mori
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.
Course Number and Name Section Location Term Instructor
8441 Numerical Analysis and Scientific Computing 1 Vincent Hall 207 Fall 2017 Bernardo Cockburn
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 Vincent Hall 206 Spring 2017 Matthias Maier
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.
Course Number and Name Section Location Term Instructor
8445 Numerical Analysis of Differential Equations 1 Vincent Hall 209 Fall 2017 Douglas Arnold
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 Vincent Hall 364 Spring 2017 Bernardo Cockburn
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
8450 Topics in Numerical Analysis 1 Vincent Hall 207 Spring 2017 Bryan Mosher
A-F or Aud
Fall, Spring, Periodically
Course Number and Name Section Location Term Instructor
8470 Topics in Mathematical Theory of Continuum Mechanics 1 Vincent Hall 364 Spring 2017 Bryan Mosher
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.
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 Vincent Hall 213 Spring 2017 Richard Moeckel
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.
1.0 - 3.0 [max 12.0 cr] cr; Prereq: 8502;
A-F or Aud
Fall, Spring
Current research.
1.0 - 3.0 [max 3.0 cr] cr; Prereq: 8502;
A-F or Aud
Fall, Spring, Periodically
A-F or Aud
Fall, Spring, Every Year, Periodically
Course Number and Name Section Location Term Instructor
8540 Topics in Mathematical Biology 1 Vincent Hall 113 Fall 2017 Jasmine Foo
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.
Course Number and Name Section Location Term Instructor
8571 Theory of Evolutionary Equations 1 Vincent Hall 213 Fall 2017 Arnd Scheel
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.
1.0 - 3.0 [max 12.0 cr] cr; Prereq: 8572 or #;
A-F or Aud
Periodically
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.
Course Number and Name Section Location Term Instructor
8583 Theory of Partial Differential Equations 1 Vincent Hall 2 Fall 2017 Jeffrey Calder
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 Vincent Hall 1 Spring 2017 Peter Polacik
1.0 - 3.0 [max 3.0 cr] cr; Prereq: 8602;
A-F or Aud
Fall, Spring, Every Year, Periodically
Research topics.
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.
Course Number and Name Section Location Term Instructor
8601 Real Analysis 1 Vincent Hall 311 Fall 2017 Paul Garrett

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 Vincent Hall 209 Spring 2017 Paul Garrett
3.0 [max 12.0 cr] cr; Prereq: 8602 or #;
A-F or Aud
Periodically
Current research.
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.
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 Vincent Hall 207 Spring 2017 Maury Bramson
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.
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.
Course Number and Name Section Location Term Instructor
8659 Stochastic Processes 1 Vincent Hall 20 Fall 2017 Maury Bramson

MATH 8660 - Topics in Probability

Fall, Spring, Every Year, Periodically

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.
Course Number and Name Section Location Term Instructor
8668 Combinatorial Theory 1 Vincent Hall 364 Fall 2017 Pavlo Pylyavskyy

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.
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 Civil Engineering Bldg 214 Spring 2017 Pavlo Pylyavskyy

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.
Course Number and Name Section Location Term Instructor
8701 Complex Analysis 1 Vincent Hall 20 Fall 2017 Albert Marden

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 Vincent Hall 301 Spring 2017 Adrian Diaconu
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.
Course Number and Name Section Location Term Instructor
8801 Functional Analysis 1 Vincent Hall 20 Fall 2017 Peter Polacik

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 Vincent Hall 301 Spring 2017 Paul Garrett

MATH 8990 - Topics in Mathematics

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

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
Individually directed reading.

MATH 8993 - Directed Study

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