Math 579  Singular Perturbations

Instructor: C. Tier 
Offered: Spring Semester, 2001 
Timetable: 08384 LECD 01000150 M W F 0305 TH 
Office: 720 SEO ; Phone: 3129962442 ; Email: tier@uic.edu 
Course Description: (Bulletin) Algebraic and transcendental equations, regular perturbation expansions of differential equations, matched asymptotic expansions, boundary layer theory, PoincareLindstedt, multiple scales, bifurcation theory, homogenization. 
Detailed Description: The course deals with perturbation methods (regular and singular) which are used to systematically construct approximations to problems (e.g. ODE and PDE) that are otherwise intractable. The approximations are analytic and often provide important insight into the behavior of the solution. This is in contrast to numerical solutions which can provide extremely accurate results yet not provide sufficient information about the solution. The purpose of the course is to survey important perturbation methods. These methods will be contrasted with numerical methods and it will be illustrated how the perturbation and numerical methods often complement one another. 
Course Web Page: www.math.uic.edu/~tier/Math579 
Text: M. H. Holmes, Introduction to Perturbation Methods, SpringerVerlag, 1995. 
Reference: E. Bender and D. Orszag, Advanced Mathematical Methods for Scientists and Engineers, Wiley. 
Tentative Topics:

Prerequisites: Background in differential equations (ODE and PDE) or consent of instructor. 
Math 590 Advanced Topics in Applied Mathematics: Computational Finance 
Instructor: C. Tier 
Office: 720 SEO ; Phone: 3129962442 ; Email: tier@uic.edu 
Offered: Spring Semester, 2001 
Timetable: 62915 LECD 03000415 M W 0208 TH 
Description:
Financial derivatives are a multitrillion dollar component of today's financial markets and often play a key role in complicated financial transactions. Because of their importance, the study of financial derivatives has grown dramatically in the financial industry. The course will present current topics in computational finance including pricing of derivative instruments such as options, interest rates and other contracts. The emphasis will be on the computation of fair market prices and other quantities of interest. This will involve the solution of partial differential equations that arise from stochastic models. Analytic methods will be used if possible. Numerical methods applicable to intractable models will be stressed. Computation tools such as Maple will be used along with programming in higher level languagues. 
Comments: This course is part of the Computational Finance track in the MISI program in MSCS. 
Prequisites/background: Students should be familiar with basic probability, differential equations and elementary numerical methods. 
Topics:

Math 590 Advanced Topics in Applied Mathematics: Mathematical Finance 
Instructor: S. Yau 
Offered: Spring Semester, 2001 
Timetable: 62907 LECD 11001150 M W F 0303 AH 
MCS 504  Mathematics and Information Science for Industry Workshop.

Instructor: R. Grossman 
Text: None; selected articles will be used. 
Offered: Spring Semester, 2001 
Timetable: 63931 LECD 02000500 F 0700 SEO 
Course 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 and information sciences 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, techniques for effectively working in groups, software engineering, and effectively communicating technical material. 
Comments: The course may be repeated for credit. 
Prerequisites: Prior course work in data structures and algorithms and C/C++ programming 
MCS 507  Mathematical, Statistical & Scientific Software

Instructor: F. Hanson 
Text: (Background Reference to Prof. Hanson's Lectures): William H. Press et al., Numerical Recipes in C: The Art of Scientific Computing, Cambridge U. Press, ISBN: 0521431085 (www.amazon.com price: $57.95; also available for F77 and/or F90; Disk of programs available in Fortran and nonstandard fortran translated C). (NRC) 
Offered: Spring Semester, 2001 
Timetable: 63945 LECD 04300545 M W 0202 LH 
Course Description: (Bulletin) The design, analysis and use and of mathematical, statistical, and scientific software. 
Comments: This is a new course that is a core course in the Master of Science Degree program in Mathematics and Information Sciences for Industry, which became official Fall 2K. 
Prerequisites: Grade of B or better in MCS 471, an equivalent course, or consent of instructor. 
The MCS 507 , web page has further information for this course. 
Email Comments or Questions to Professor Hanson