I will be out of the office on the following dates:
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 ResourcesThe 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
SyllabusYour course grade will be based on:
Letter grades for undergraduate students will be assigned as follows:
The "D" grade is not allowed for graduate students. Letter grades for graduate students will be assigned as follows.
Lecture Notes and ResourcesLecture 1 (1/9/2019): Riemann meets Lebesgue 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 SolutionsExam Reviews
Exam Solutions |