MA301 - Functions of Real Variables, Fall 2017

• Here is the final exam.

• Midterm 2 is due Wednesday, Dec. 13.

• In the proof of Theorem 10.42 Browder used the singular-value decomposition. More details can be found here.

• Assignment 9 due Tuesday, Dec. 5: Ch. 10 #21, 24, 25, 26, 28

• Assignment 8 due Tuesday, Nov. 28: Ch. 10 #16, 17, 18, 19, 20

• Assignment 7 due Tuesday, Nov. 21: Ch. 10 #7, 8, 11, 12, 13, 14, 15

• Assignment 6 due Tuesday, Nov. 14: Ch. 10 #1, 3, 4, 5, 6, 9, 10

• Assignment 5 due Tuesday, Nov. 7: Ch. 9 #7, 9, 10, 13, 15, 17, 18

• Midterm 1 is due Wednesday, Nov. 1.

• Assignment 4 due Tuesday, Oct. 24: Ch. 6 #22; Ch. 10 #2; Ch. 9 #2, 3, 4, 5

• Assignment 3 due Tuesday, Oct. 17: Ch. 7 #1, 5, 6; Ch. 6 #19, 20, 23, 24

• Assignment 2 due Tuesday, Oct. 10: Ch. 6 #13, 14, 15, 16, 17, 18

• Assignment 1 due Tuesday, Sept. 19: Ch. 6 #1, 2, 5 (give a counterexample if you can't prove it as stated), 7, 9, 11, 12

Instructor

Yifei Zhu

Huiyuan 3-419

8801 5911

zhuyf@sustc.edu.cn

Office Hours: Monday & Tuesday 12:00-1:30 pm

Objectives

This is an advanced undergraduate course on modern foundations of analysis. The official course syllabus asks that we cover the general theory of integration, based on the concept of measure. We will begin with an introduction to general topology, focusing on Euclidean space and spaces of functions. We will work toward integration over manifolds, in particular, the important generalized Stokes' theorem and its applications.

Prerequisites

101a, 102a, 203a (or 101b, 102b, 213).

Textbooks

We will be working from Andrew Browder's Mathematical analysis : an introduction. Hard copies have been available for in-library 2-hour loan since the end of October (sorry for the delay).

A useful reference in Chinese is 《实变函数论》， 周民强编著.

For further reading and other perspectives, Measure and integral by Wheeden and Zygmund is recommended.

Exams

There will be two midterm exams and one final, each in a take-home format. Each of these exams is worth 20% of your final grade.

• Midterm 1 will be the week of October 23.

• Midterm 2 will be the week of December 4.

• The final will be the week of January 15.

Homework

The assigned problems for each week are due each Tuesday in-class at 2pm, listed on this page. Homework is worth 40% of your final grade. Students must make arrangements in advance if they will not be handing in homework on time.

We encourage you to discuss homework problems with your classmates, including strategies for solving different kinds of problems. However, when you actually write up your solutions, you must do this on your own.