REAL ANALYSIS

MATH 524/525/526
ACADEMIC YEAR 2009-2010

INSTRUCTOR INFORMATION:
Instructor: Tatiana Toro.
Office: Padelford C-343, Phone: 543-1173.
E-mail: toro@math.washington.edu
Office hours: Monday 1-2, Wednesday 10-11 or by appointment.

TA INFORMATION:
TA: Mauricio Duarte
Office: Padelford C-20.
E-mail: maduarte@math.washington.edu
Office hours: Tuesday 12-1, Friday 2-3 or by appointment.

TEXTS:
Real Analysis, Measure Theory, Integration, & Hilbert Spaces, Stein & Shakarchi (required)
Real Analysis, Folland, 2nd Edition (recommended)

RESERVE LIST:
Real Analysis, Measure Theory, Integration, & Hilbert Spaces, Stein & Shakarchi
Real Analysis, Folland, 2nd Edition.
Real Analysis, Royden, 3rd Edition.
Real and Abstract Analysis, Hewitt & Stromberg.
Real and Complex Analysis, Rudin.
Functional Analysis, Rudin.

Sequence Topics:

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).

Fall Topics:

The following syllabus should give you a reasonable idea of what lies ahead this quarter

0. Introduction

1. Lebesgue measure: Chapter 1

2. Lebesgue integral: Chapter 2

3. Differentiation and Integration: Chapter 3

4. Hilbert Spaces: An Introduction: Chapter 4

5. Abstract Measure and Integration Theory: Chapter 6

Important Dates:
Midterm, Math 524: Friday, November 13, 2009.
Final Exam, Math 524: Wednesday, December 16, 2009, 2:30-5:30pm.

Grading policy: The grades will be determined on the basis of the following percentages.

• Homework 40%.
There will 9 weekly homeworks due on Wednesday at the beginning of class.
No homework due on Wednesday November 11.

• Midterm 20%.

• Final exam 40%.

Remarks: