Senior and Graduate Math Course Offerings Spring 2003 |
MATH 4397: Selected Topics in Mathematics - NONLINEAR DYNAMICS II (Section 11854) | |
Time: | 11:00-12:00 am, MWF, Room 134 SR. |
Instructor: | K. Josic |
Prerequisites: | MATH 4340 |
Text(s): | Nonlinear Dynamics and Chaos by Steven H. Strogatz, Perseus Books (2000). |
Description: | Nonlinear terms enter into equations for many systems. The dynamics of such systems varies from relatively trivial, to extremely complex. Still many - often surprisingly general - principles can be used to describe nonlinear dynamics and chaos. This course will cover the theoretical foundations, numerical techniques, and some current applications of nonlinear dynamics. |
MATH 6395: PDES AND APPLICATIONS (Section 13313) | |
Time: | 2:30-4:00 pm, MW, Room 106 AH |
Instructor: | C. Suncica |
Prerequisites: | Multivariable Calculus, Real and Complex Analysis. |
Text(s): | Textbook: None required. (Texbooks that will be partially used are: Strauss's PDEs, R. LeVeques's "Conservation Laws", Renardy and Rogers' "PDEs", Research Papers) |
Description: | Review of basic linear PDEs. Introduction to fundamentals of fluid mechanics (basic equations of motion: continuity, momentum, energy, vorticity). Incompressible/compressible flow examples. Analysis of quasilinear PDEs with the focus on hyperbolic conservation laws. Basic numerical methods. Special topics in modeling, analysis and numerical simulation arising in the study of blood flow through compliant blood vessels. |
Math 6397: NUMBER THEORY (OnLine course) (Section 13423) | |
Time: | ?, Rm. ? |
Instructor: | M. Ru |
Prerequisites: | None |
Text(s): | Discovering Number Theory, by Jeffrey J. Holt and John W. Jones, W.H. Freeman and Company, New York, 2001. |
Description: | Number theory is a subject that has interested people for thousand of years. This course is a one-semester long graduate course on number theory. Topics to be covered include divisibility and factorization, linear Diophantine equations, congruences, applications of congruences, solving linear congruences, primes of special forms, the Chinese Remainder Theorem, multiplicative orders, the Euler function, primitive roots, quadratic congruences, representation problems and continued fractions. There are no specific prerequisites beyond basic algebra and some ability in reading and writing mathematical proofs. The method of presentation in this course is quite different. Rather than simply presenting the material, students first work to discover many of the important concepts and theorems themselves. After reading a brief introductory material on a particular subject, students work through electronic materials that contain additional background, exercises, and Research Questions, using either mathematica, maple, or HTML with Java applets. The research questions are typically more open ended and require students to respond with a conjecture and proof. We then present the theory of the material which the students have worked on, along with the proofs. The homework problems contain both computational problems and questions requiring proofs. It is hoped that students, through this course, not only learn the material, learn how to write the proofs, but also gain valuable insight into some of the realities of mathematical research by developing the subject matter on their own. |
MATH 7394: REACTION DIFFUSION SYSTEMS II (Section 11820) | |
Time: | 10:00-11:30 am, TTH, Room 350 PGH |
Instructor: | W. Fitzgibbon |
Prerequisites: | The Preceding course, Reaction Diffusion Equations or consent of instructor. |
Text(s): | Notes. |
Description: | This will be a seminar with a lecture format. The focus will be systems as opposed to scalar reaction diffused advection equations. Applications as well as theory will be discussed. |
MATH 7396: MULTIGRID METHODS (Section 11710) | |
Time: | 1:00-2:30 pm, MW, Room 345 PGH |
Instructor: | R. Hoppe |
Prerequisites: | Graduate Standing |
Text(s): | 1. J. K. Brainble, Multigrid Methods, Longman, Harlow, 1993. 2.Wolfgang Hackbusch; Iterative Solution of Large Sparse Systems of Equations. Appl. Math. Sciences, Vol. 95, Springer, New York, 1993 ISBN 0-387-94064-2. |
Description: | Multigrid methods and related multilevel approaches are the most efficient solution techniques for the numerical solution of PDEs, integral equations, and other kind of operator equations. The course starts from an introduction to the basic principles and then proceeds to a detailed analysis of the convergence behavior of various multigrid schemes. Both linear and nonlinear problems will be addressed. |
*NOTE: Teaching fellows are required to register for three regularly scheduled math courses for a total of 9 hours. Ph.D
students who have passed their prelim exam are required to register for one regularly scheduled math course and 6 hours of
dissertation.