MATHEMATICS 245A

Lectures: James Ralston, MWF 10:00-10:50 in MS 6229

Discussion: Joseph Viola, Tu 10:00-10:50 also in MS 6229

Office Hours: My office hours are Thursday 10-11 and Wednesday and Friday 4-5 in MS 5238. Of course, I will also usually respond when you catch me around the department.

Prerequisites: A good understanding of undergraduate real analysis (Math 131A at UCLA) is required. It is also essential that you are sufficiently comfortable with abstraction to know when you have proved something.

This course covers basic measure theory, integration on measure spaces, differentiation and basic analysis in Hilbert space. Our textbook is Real Analysis (Volume III of the Princeton Lectures in Analysis) by E.M. Stein and R. Shakarchi. We will start with Chapter 1 of that text, and I hope that by the end of the quarter we will be somewhere in Chapter 4. Up to now no one has been able to learn this subject without doing a lot of problems. There will be weekly assignments with varying numbers of problems. Ordinarily these will be assigned on Fridays, and they will be due the following Friday when solutions will be handed out. However, the first assignment will be due Wednesday, October 8. The standard schedule will begin with the second assignment which will be due Friday, October 17.

Grading: The course will be graded with a weight of 50% on the homework and 50% on the final examination.

Assignment 1: All of these are from exercises and problems on pages 37-48. Letters, as in "4abc", refer to parts of problems when the whole problem is not assigned. Exercises: 4abc, 5, 11, 14b, 17, 28. Problems: 5.

Assignment 2 due Friday, October 17.

Assignment 3 due Friday, October 24.

Assignment 4 due Friday, October 31.

Assignment 5 due Friday, November 7.

The November 5 Quiz (slightly improved)

Assignment 6 due Friday, November 14.

The Vitali Covering Lemma and an Application.

Assignment 7 due Friday, November 21.

Assignment 8 due Friday, December 5.