Real Analysis

Math 524/525/526
Academic year 2000-2001

Instructor information:
Instructor: Tatiana Toro.
Office: Padelford C-332, Phone: 543-1173.
E-mail: toro@math.washington.edu
Office hours: Monday 2-3, Friday 2-3.

TA information:
TA: Dan Fox.
Office: Padelford C8F.
E-mail: fox@math.washington.edu
Office hours: Tuesday 12-1, Wednesday 2-3.

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.

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).

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.

Important Dates:
Midterm, Math 524: Friday, November 3rd, 2000.
Final Exam, Math 524: Tuesday, December 12th, 2000.

Grading policy: The grades will be determined on the basis of the following percentages. Homework 40%. Midterm 20% each. Final exam 40%. There will be weekly homework due on Wednesdays at the beginning of class.