Math 524/525/526
Real Analysis

Tatiana Toro

Autumn/Winter/Spring 2002-2003, Monday/Wednesday/Friday 11:30-12:20

In these three courses students are expected to learn the fundamental tools needed to work in the general field of analysis. This sequence will cover 3 main topics:

I. Measure and Integration (includes Lebesgue measure and Lebesgue integral).

II. Topological spaces (includes metric spaces).

III. Basic Functional Analysis (includes L p spaces).


Texts:
 Real Analysis, Folland, 2nd Edition (required) [F].
 Real Analysis, Royden, 3rd Edition (required) [R].

Reserve list:
 Real Analysis, Folland, 2nd Edition.
 Real Analysis, Royden, 3rd Edition.
 Real and Abstract Analysis, Hewitt & Stromberg.
 Real and Complex Analysis, Rudin.
 Functional Analysis, Rudin.

Syllabus:

The following syllabus is tentative. Nevertheless it should give you a reasonable idea of what is ahead. The course will be divided in 9 chapters as follows:
  1. Basics: [R] Ch. 1, 2; [F] Ch. 0.
  2. Metric spaces: [R ] Ch. 7.
  3. Measures (Lebesgue measure): [R] Ch.3, 11; [F] Ch. 1.
  4. Integration (Lebesgue integral): [R] Ch. 4, 11; [F] Ch. 2.
  5. Differentiation and Integration: [R] Ch. 5, 11; [F] Ch. 3.
  6. Topological spaces: [R] Ch. 8, 9; [F] Ch. 4.
  7. Functional analysis: [R] Ch. 10; [F] Ch. 5.
  8. L p spaces: [R] Ch. 6; [F] Ch. 6.
  9. Selected topics: Radon measures ([F] Ch. 7); Elements of Fourier Analysis ([F] Ch. 8); Elements of Distribution Theory ([F] Ch. 9).
I plan to cover Chapters 1-3 and part of Chapter 4 in the Autumn quarter. In the Winter I expect to cover the rest of Chapter 4 and Chapters 5-6. In the Spring I plan to cover Chapters 7-8 and selected topics from the subjects mentioned in Chapter 9.