MATHEMATICS 831-4

Real Analysis I

Lecturer: J. M. Borwein

Lectures: Tuesdays and Thursdays (backup Monday)   Time: 13:30 - 15:20   Room: Colab or AQ 4115

Office: K10526 or CoLab (CECM)             Phone: 604 291-3070

Email:  jborwein@cecm.sfu.ca          URL: http://oldweb.cecm.sfu.ca/~jborwein

 

 

Course Outline and Details

  1. Review of Basic Concepts in Real Analysis
  2. Metric spaces and Point Set Topology
  3. General Measure Theory and Integration
  4. Some Basic Tenets of Functional Analysis
  5. Selected Applications:
    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

 

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

 

“Early chapters cover basics of real analysis, using a streamlined approach that gets to the applications quickly, with some material flagged as advanced. 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. The role of normed vector spaces is emphasized, and they provide a framework for most of the applications.”


Secondary: Real Analysis by Bruckner, Bruckner and Thomson, Prentice Hall, 1997.

 

APPROACH:  I will try to add a symbolic computational component to each topic and problem set.  The text allows for quite ambitious and various additional topic projects.

 

GRADING is as follows
100% will be judged on Problem Sets and Classroom Participation

  • Problem Set 1 Sections 2.4 to 2.7, Exercises G,H,I (due Sept 19).

  • Problem Set 2 Sections 4.3, 4.4, 5.4, 5.5, Exercises I,J,K (due October 8).

  • Problem Set 3 Stromberg: pages 274-285, Exercises 1, 6, 7 ,19, 23, 27, and 33 (due November 7).

  • Problem Set 4 Stromberg: pages 306 etc., Exercises 4, 6, 9, 12, 19, 29, and 30 (due December 3).

    September 12th 2002