Introduction to

Real Analysis

Math 663-601

First Day Handout:


Professor: Thomas Schlumprecht
Office: Blocker 625 Tel: 845-8840
Hours: Mon 1:00 - 2:00, Wed 3:00 - 4:00, and by appointment
E-mail: schlump@math.tamu.edu
Homepage: http://www.math.tamu.edu/~thomas.schlumprecht

General Description

This course is designed to be a "bridging course" between undergraduate analysis and graduate real analysis. The course will cover some topological notions on the real line, continuous functions, the Riemann integral, measure theory and the Lebesgue integral. If time permits, topics in Fourier series will also be discussed. This course is suitable for students who are not quite ready for Math 607 (Real Variables) or who would rather see a concrete construction of measure and integration (as opposed to the more abstract approach taken in Math 607).

Textbook

The required textbook is The Way of Analysis by Robert Strichartz , published by Jones and Bartlett, 1995. We will cover chapters 2 (quickly), 3, 4, 5(quickly), 6, 14.

Prerequisite

The prerequisite for this course is Math 409 (Advanced Calculus I) or its equivalent. The essential background you need is familiarity with the kind of analytic reasoning used in "epsilon-delta proofs".

Grading

Course grades will be determined by homework (30%); a midterm exam (30%) and an in-class final exam (40%). You may collaborate with other students on the homework.

Copyright Statement
: All handouts and web-documents associated with this course are protected by US Copyright law. One personal copy (or download) of any of these documents is allowed by each student. Multiple copies or sale of any of these materials is strictly forbidden.

Homeworks (Due on Tuesdays)

Read Chapters 1 and 2

Homework 1 Due: 09/10

Homework 2 Due: 09/17

Homework 3 Due: 09/25

Homework 4 Due: 10/01

Homework 5 Due: 10/08

Homework 6 Due: 10/22

Midterm: October 17, 2002 Things you need to know

Homework 7 Due: 10/29

Homework 8 Due: 11/05

During the time I am out of town:

Office hours Wednesdays 1:00 - 2:00, in Milner 123 (Dr.Pop)

You can still reach me under my usual e-mail address (but expect 24 hours for an answer)

Homework 9: Exercises 1 through 6: Due 11/14

Homework 10: Exercises 7 through 12: Due 11/21


Homework 11: Exercises 13 through 20: Due 12/05

Lebesgue measure and Lebesgue integration (contains the exercises)