Rigorous introduction to probability, using techniques of measure theory. Includes limit theorems, martingales, and stochastic processes. Prerequisite: 7310 or equivalent.
Course Descriptions
Graduate Course Descriptions
Probability Theory II (3.00)
MATH 7370
Continuation of Probability Theory I. Elements of stochastic processes, including Brownian motion, continuous time martingales, and Markov processes.
Functional Analysis I (3.00)
MATH 7410
Studies the basic principles of linear analysis, including spectral theory of compact and selfadjoint operators. Prerequisite: MATH 7340 and 7310, or equivalent.
Functional Analysis II (3.00)
MATH 7420
Studies the spectral theory of unbounded operators, semigroups, and distribution theory. Prerequisite: MATH 7410 or equivalent.
Introduction to Mathematical Physics (3.00)
MATH 7450
An introduction to classical mechanics, with topics in statistical and quantum mechanics, as time permits. Prerequisite: MATH 5310.
New Course in Mathematics (1.00 - 4.00)
MATH 7559
This course provides the opportunity to offer a new topic in the subject of mathematics.
Problems In Topology (3.00)
MATH 7705
A continuation of the theory presented in MATH 5770 and 7800 intensively training students to apply the theory to proving theorems and solving problems in topology, especially in preparation for the General Examination in Topology. Problems are based on those from past General Exams. This course is offered in the summer and restricted to Mathematics and Graduate Arts and Science students.
Algebra I (3.00)
MATH 7751
Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent.
Algebra II (3.00)
MATH 7752
Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent.
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