# Courses

## MATH-6240 (3) Introduction to Differential Geometry 2

Continuation of MATH 6230. Undergraduates must have instructor consent.

## MATH-6250 (3) Theory of Rings

Studies semi-simple Artinian rings, the Jacobson radical, group rings, representations of finite groups, central simple algebras, division rings and the Brauer group. Prereq., MATH 6130, 6140. Undergraduates must have approval of the instructor.

## MATH-6260 (3) Geometry of Quantum Fields and Strings

Focuses on differential geometric techniques in quantum field and string theories. Topics include spinors, Dirac operators, index theorem, anomalies, geometry of superspace, supersymmetric quantum mechanics and field theory, and nonperturbative aspects in field and string theories. Prereq., MATH 6230, PHYS 5250, or instructor consent. Recommended prereqs., MATH 6240 and PHYS 7280. Undergraduates must have approval of the instructor. Same as PHYS 6260.

## MATH-6270 (3) Theory of Groups

Studies nilpotent and solvable groups, simple linear groups, multiply transitive groups, extensions and cohomology, representations and character theory, and the transfer and its applications. Prereq., MATH 6130. Recommended prereq., MATH 6140. Undergraduates must have approval of the instructor.

## MATH-6280 (3) Advanced Algebraic Topology

## MATH-6290 (3) Homological Algebra

## MATH-6310 (3) Introduction to Real Analysis 1

## MATH-6320 (3) Introduction to Real Analysis 2

Covers general metric spaces, the Baire Category Theorem, and general measure theory, including the Radon-Nikodym and Fubini theorems. Presents the general theory of differentiation on the real line and the Fundamental Theorem of Lebesgue Calculus. Prereq., MATH 6310. Instructor consent required for undergraduates.

## MATH-6350 (3) Functions of a Complex Variable 1

## MATH-6360 (3) Functions of a Complex Variable 2

Focuses on conformal mapping, analytic continuation, singularities, and elementary special functions. Prereq., MATH 6350. Instructor consent required for undergraduates.

## MATH-6534 (3) Topics in Mathematical Probability

## MATH-6550 (3) Introduction to Stochastic Processes

## MATH-6730 (3) Set Theory

## MATH-6740 (3) Forcing

Presents independence of the axiom of choice and the continuum hypothesis, Souslin's hypothesis, and other applications of the method of forcing. Introduces the theory of large cardinals. Prereq., MATH 6730. Undergraduates need instructor consent.

## MATH-6900 (1-3) Independent Study

Undergraduates must have approval of the instructor. May be repeated up to 6 total credit hours.

## MATH-6940 (1) Master's Degree Candidate

## MATH-8114 (3) Topics in Number Theory

## MATH-8174 (3) Topics in Algebra I

Prereqs., MATH 6130 and 6140. Undergraduates must have approval of the instructor.

## MATH-8250 (3) Mathematical Theory of Relativity 1

Focuses on Maxwell equations, Lorentz force, Minkowski space-time, Lorentz, Poincare, and conformal groups,metric manifolds, covariant differentiation, Einstein space-time, cosmologies, and unified field theories. Prereq., instructor consent. Undergraduates must have approval of the instructor.

## MATH-8304 (3) Topics in Analysis 1

## MATH-8330 (3) Functional Analysis 1

## MATH-8340 (3) Functional Analysis 2

Introduces such topics as Banach spaces (Hahn-Banach theorem, open mapping theorem, etc.), operator theory (compact operators and integral equations, and spectral theorem for bounded self-adjoint operators), and Banach algebras (the Gelfand theory). See also MATH 8330. Prereq., MATH 8330. Undergraduates must have approval of the instructor.

## MATH-8370 (3) Harmonic Analysis 1

Examines trigonometric series, periodic functions, diophantine approximation, and Fourier series. Also covers Bohr and Stepanoff almost periodic functions, positive definite functions, and the L1 and L2 theory of the Fourier integral. Applications to group theory and differential equations. See also MATH 8380. Prereq., MATH 5150 and 6320. Undergraduates must have approval of the instructor.