Course Descriptions

Graduate Course Descriptions

Operator Theory I, II (3.00)

MATH 8320

Topics in the theory of operators on a Hilbert space and related areas of function theory.

Stochastic Calculus and Differential Equations (3.00)

MATH 8360

This course presents the basic theory of stochastic differential equations and provides examples of its applications. It is an essential topic for students preparing to do research in probability. Topics covered include a review of the relevant stochastic process and martingale theory; stochastic calculus including Ito's formula; existence and uniqueness for stochastic differential equations, strong Markov property; and applications. Prerequisite: MATH 7360 and 7370, or instructor permission.

Topics in Probability Theory (3.00)

MATH 8370

Selected topics in probability. Prerequisite: MATH 7360 or instructor permission.

Harmonic Analysis (3.00)

MATH 8400

Studies Banach and C* algebras, topological vector spaces, locally compact groups, Fourier analysis.

Topics in Mathematical Physics (3.00)

MATH 8450

Applies functional analysis to physical problems; scattering theory, statistical mechanics, and quantum field theory.

New Course in Mathematics (1.00 - 4.00)

MATH 8559

This course provides the opportunity to offer a new topic in the subject of mathematics.

Commutative Algebra (3.00)

MATH 8600

The foundations of commutative algebra, algebraic number theory, or algebraic geometry.

Algebraic Geometry (3.00)

MATH 8620

Studies the foundations of algebraic geometry.

Algebraic K-Theory (3.00)

MATH 8650

Includes projective class groups and Whitehead groups; Milnor's K2 and symbols; higher K-theory and finite fields.

Lie Groups (3.00)

MATH 8700

Studies basic results concerning Lie groups, Lie algebras, and the correspondence between them.

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