Math 676 - Real Analysis I

Spring 2019

 

 
Your Instructor: Peter Perry
  755 Patterson Office Tower, 7-6791
Class Meetings: MWF 2:00-2:50, CB 343 (Déjà vu?)
Office Hours: M 3:00-5:00, F 3:30-4:30

I will be out of the office on the following dates:

January 30-February 1 (National Science Foundation)
April 17-19 (IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena)
April 26-29 (Personal)

All classes will be covered by teaching faculty or senior graduate students.

I should have e-mail access for questions and concerns on all days except April 26-29. I will announce exam week office hours at the beginning of the last week of classes.

Text and Resources

The primary text for this course is Stein and Shakarchi's book Analysis which will also be the primary text for Math 677, Analysis II. Students are strongly recommended to read the first chapter of Terence Tao's book Measure Theory (the link will take you to a free, preliminary version; serious students of analysis might want to consider buying the book, which does an excellent job of motivating the subject and giving historical insight into how it evolved.

A classic text about the history of Lebesgue integration is the book Lebesgue's theory of integration: its origins and development by Thomas Hawkins (available at the AMS bookstore).

tems of Interest

Syllabus

Your course grade will be based on:

Homework 100 points
1 Hour Exam 100 points
Final Exam 100 points
Total 300 points

Letter grades for undergraduate students will be assigned as follows:

270-300 A
240-269 B
210-239 C
180-219 D
0-218< E

The "D" grade is not allowed for graduate students. Letter grades for graduate students will be assigned as follows.

270-300 A
240-269 B
180-239 C
0-180 E

 

Lecture Notes and Resources

Lecture 1 (1/9/2019): Riemann meets Lebesgue
See also David Bressoud's lecture Wrestling with the Fundamental Theorem of Calculus

Lecture 2 (1/11/2019): Here is an overview of measure theory and integration

Lecture 4 (1/16/2019): Here's a guide to observations (about outer measure) and properties(of Lebesgue measure)

Lecture 6 (1/23/2019): Here's a guide to further properties of Lebesgue measure (countable additivity, monotonocity, regularity)

Lecture 10 (2/4/2019): Here's a guide to properties of measurable functions

Lecture 14 (2/13/2019): Here is an overview of Lebesgue integration

Lecture X (3/18/2019): Steps in Stein-Shakarchi's proof of Fubini's Theorem

Lecture X+2 (3/22/2019): Summary of Tonelli's Theorem and its consequences, Stein-Shakarchi section 3.2

Lecture Y (the end of the semester is near!) Summary of Differentiation and Integration

Homework Assignments

Homework Solutions

Exam Reviews

  • To be posted

Exam Solutions