Constructive Analysis, Spring 2003, M894

OUTLINE: This two-credit reading course will meet Tuesdays from 1.00-2.30k in CoLab (the first meeting is 1.30-3.30 on Tuesday 21. We will discuss Selected Applications from among the following:

  1. Fourier Analysis: Physics and Approximation Theory
  2. Ordinary Differential Equations
  3. Discrete Dynamical Systems
  4. Classical Approximation Theory and Wavelets
  5. Convex Analysis and Optimization
  6. Special Functions

FIRST TEXT: Real Analysis with Real Applications, by Davidson and Donsig, Prentice Hall, 2001.

"More than half the book consists of independent chapters on topics ranging from Fourier series and polynomial approximation to discrete dynamical systems and convex optimization. Each application presents a number of results and shows how these results depend on fundamental ideas of real analysis."

but will focus on:

SECOND TEXT (TWO VOLUMES): Mathematics by Experiment: Plausible Reasoning in the 21st Century and Mathematics: Computational Paths to Discovery by Jonathan Borwein, and David Bailey, with the assistance of Roland Girgensohn, AK Peters, In press. (To appear in September 2003).

"This new approach to mathematics --- the utilization of advanced computing technology in mathematical research --- is often called experimental mathematics. The computer provides the mathematician with a ``laboratory'' in which she can perform experiments --- analyzing examples, testing out new ideas, or searching for patterns."

APPROACH: I will to add a symbolic/numeric computational component to each topic and problem set. The texts allow for quite ambitious and various additional topic projects. In addition, the opportunities afforded by working in the SFU CoLab will be exploited.

PREREQUISITES: Math 831 or permission of the instructor.

GRADING: 65% on Problem Sets and Classroom Participation and 35% for a Project.

J. M. Borwein, January 02 2003