Courses for Fall 1996

**Math 480 Applied Differential Equations***Time=2MWF Room=305TH Call=61447 Instructor=Friedlander**Catalog description:*Linear first-order systems. Numerical methods. Nonlinear differential equations and stability. Introduction to Partial differential equations. Sturm-Liouville theory. Boundary value problems and Green's functions.*Prerequisites:*Grade of C or better in Math 220 Elementary Differential Equations.

**Math 484 Tensor Analysis***Time=11MWF Room=216TH Call=61454 Instructor=Barston**Catalog description:*Cartesian tensors, orthogonal transformations. General tensor calculus, Riemannian space, covariant differentiation, Christoffel symbols, curvature tensor, differential geometry. Emphasis on aspects of interest in science and engineering.*Prerequisites:*Grade of C or better in Math 410 Advanced Calculus I, Math 310 Applied Linear Algebra I or Math 320 Linear Algebra I.

**Math 572 Advanced Topics in Geometric Analysis: Introduction to Mathematical Control Theory***Time=2MWF Room=321TH Call=61692 Instructor=Yau**Catalog description:*Mathematics of dynamic processes, characterization of systems, stability analysis, controllability, observability, canonical forms, realization, estimation, and design. See Professor Yau.*Prerequisites:*Graduate standing and Math 325, Linear Algebra II, and ordinary differential equation, or consent of instructor. See Professor Yau.*Track course:*Industrial Mathematics Track in Control, Information, and Optimization (CIO).

**Math 590: Financial Engineering or Mathematics of Stock Markets. (Special Topics in Applied Math)***Time=11MWF Room=316TH Call=61738 Instructor=Lipton**Description:*This is an introduction into a rapidly developing area of mathematics known as financial engineering. Recent advances in understanding the behavior of the bond and stock markets will be described from a mathematical viewpoint. Modern financial instruments and mathematical methods of their valuation will be discussed in detail. Hands on experience in numerical methods will be provided.*Prerequisites:*Consent of instructor.*Text:*P.W. Wilmott, S. Howison and J. Dewynne, "The mathematics of financial derivatives: a student introduction", Cambridge Univ Press 1995.

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**MCS 565 Mathematical Theory Of Databases: Image Database***Time=12MWF Room=???TH Call=????? Instructor=Yau**Catalog description:*See Professor Yau.*Prerequisites:*See Professor Yau.*Track course:*Industrial Mathematics Track in Control, Information, and Optimization (CIO).

**MCS 572 Introduction to Supercomputing**-
Time=2MWF Room=320TH Call=62503 Instructor=Hanson

*Catalog description:*Introduction to supercomputing on vector, parallel and massively parallel processors; architectural comparisons, parallel algorithms, vectorization techniques, parallelization techniques, actual implementation on real machines (Crays, Connection Machines and others).*Prerequisites:*MCS 471 Numerical Analysis or MCS 571 Numerical Methods for Partial Differential Equations or consent of the instructor. Graduate standing.*Core course:*High Performance Computing Preliminary Examination.

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**MCS 575 Computer Performance Evaluation***Time=10MWF Room=313TH Call=98938 Instructor=Tier**Catalog description:*Modeling of computer systems, basic queues, central server models, Little's Law, operational analysis, Markovian networks, Jackson and BCMP networks, product form solutions, computational algorithms, mean value analysis, approximation methods.*Prerequisites:*Graduate standing and Math 450 Introduction to Probability and MCS 412 Computer Operating Systems; or consent of the instructor.*Core course:*High Performance Computing Preliminary Examination.

**MCS 590 Industrial Mathematics Problem Solving (Special Topics in Computer Science)***Time=1MWF Room=208TH Call=62512 Instructor=Grossman**Description:*This course is centered around one or more "industrial" problems. The goal of the course is to provide an opportunity for students to use mathematics to work on problems arising from industrial applications. The course will cover: mathematical modeling, problem formulation, problem analysis, problem solution, developing software to implement the solution, validating the software, analyzing the results, documenting the problem and its solution, and communicating the results.*Prerequisites:*Prior coursework in algorithms, applied mathematics, and C programming, or consent of instructor.*Core course:*Proposed Industrial Mathematics Program.

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