Home page for Math 508, Advanced Analysis

Fall 2018

Instructor: Charles L. Epstein

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The Course

In this course we study the foundations of analysis. The goal of this course is to develop your skills and instincts as mathematical analysts. This entails understanding the basic concepts and techniques of analysis, as well as developing intuition and proficiency in the construction of rigorous proofs. I like to use   The Way of Analysis, by Robert Strichartz as a text, but I noticed that the price is now $263.  A free pdf is readily available online.  Other good books include Terry Tao's Analysis I  (it can be purchased from the AMS), Principles of Mathematical Analysis by Walter Rudin, A Consise Introduction to Analysis by Daniel Stroockand  Mathematical Thinking by John P. D'Angelo and Douglas B. West. Another good text is Real Analysis and Foundations, 4th ed. by Steven Krantz.

A problem set will be assigned every week, on Tuesdays. We may have one or more midterms and a final.

Syllabus for the course

Lecture Notes et al.


Problem Sets

  1. Problem set 1 due September 11, 2018.
  2. Problem set 2 due September 18, 2018.
  3. Problem set 3 due September 25, 2018.
  4. Problem set 4 due October 2, 2018.
  5. Problem set 5 due October 11, 2018.
  6. Problem set 6 due October 23, 2018.
  7. Problem set 7 due October 30, 2018.
  8. Problem set 8 due November 6, 2018.
  9. Problem set 9 due November 13, 2018.
  10. Problem set 10 due November 27, 2018.
  11. Problem set 11 due December 6, 2018.