Each semester, faculty propose some 600-level courses to possibly be offered to graduate students, primarily doctoral students. Some of these courses follow up on 500-level courses, and some are primarily focused on current research. Depending on several variables, including student interest, these courses may be offered as regular courses, or they may be offered by faculty as independent study courses, or the course may be withdrawn (i.e., cancelled).
| The following 600-level courses are proposed for the Spring 2001 semester: | Reference numbers (use these to enroll) |
6403 |
|
6365 |
|
5790 |
|
6366 |
Instructor: John Beachy
Prerequisite: Math 521, Algebraic Structures II
The purpose of this one-semester course is to provide the general ring-theoretic background necessary to begin studying noncommutative Noetherian rings in earnest, from a text such as Noncommutative Noetherian Rings by McConnell and Robson.
The theory of noncommutative Noetherian rings arises from a variety of classes of rings: group rings, matrix rings, rings of differential operators, Lie algebras, and others. The techniques and theorems are initially motivated by corresponding results on commutative Noetherian rings and noncommutative Artinian rings. Many crucial ideas involve Goldie's Theorem, which characterizes orders in semisimple Artinian rings. The role of fields in the commutative theory seems to be played by simple Artinian rings, rather than by skew fields. In that sense, the role of integral domains is then played by the orders in simple Artinian rings (i.e. rings of n x n matrices over skew fields), usually referred to as prime Goldie rings.
Text: Lecture notes
References:
Sylabus:
| 1. Brief review of modules and homological techniques (6 weeks) | References: Beachy, Lam |
| 2. Injective modules, the maximal ring of quotients, and Goldie's theorem (5 weeks) | References: Lam, Goodearl and Warfield, Passman |
| 3. Artinian rings (3 weeks) | Reference: Anderson and Fuller |
| 4. Quotient categories (if there is time) | Reference: Stenstrom |
Instructor: Harvey Blau
Prerequisite: Math 620 Fall 2000
A continuation of Math 620, Fall 2000 (Algebraic Combinatorics). The algebraic structure of the adjacency algebras of association schemes and distance-regular graphs will be developed and generalized. Applications will be made to combinatorial structures. The course may become a seminar on open problems by the end of the term.
Text: Notes by the instructor
References:
Instructor: Jindrich Necas
Prerequisites: Math 530
A presentation of Marcinkiewicz's multiplier theorem for Fourier series, of Lizorkin's theorem for Fourier transforms and their application to singular kernels.
Topics to include:
Text: Elias M. Stein, Singular Integrels and Differentiability Properties of Functions, Princeton, 1970.
Instructor: Jindrich Necas
Prerequisites: Math 530
A presentation of Marcinkiewicz's multiplier theorem for Fourier series, of Lizorkin's theorem for Fourier transforms and their application to singular kernels.
Topics to include:
Text: Elias M. Stein, Singular Integrels and Differentiability Properties of Functions, Princeton, 1970.
Instructor: Biswa Datta
Prerequisites: Math 562 or Math 434
The course will deal with several important topics of linear algebra arising in practical applications areas such as control theory, signal and image processing, vibration analysis, statistical and economic modeling, etc.
Three distinct aspects of each topic (problem) will be discussed thoroughly:
Any student or faculty member who desires to learn how important linear algebra problems arise in practical applications, and how to solve them effectively, is encouraged to take this course.
Topics to include: Nonnegative matrices (Finite Markov Chains, Input-output Analysis in Economics, Generalized Inverses), Inverse Eigenvalue Problems, Matrix Equations (Lyapunov, Sylvester, and Riccati), Inertia and Stability, Least-squares, Generalized Eigenvalue Problems, Singular Value Decomposition, Toeplitz Matrices, Time-Series Analysis.
Text: Detailed Lecture Notes will be provided. NO TEXT BOOK.
References: