**Professor Francis Su**

**Fall 2022**

**Course Webpage**: https://math.hmc.edu/su/math132/

**My Office:** Shanahan 3416**Drop-In Hours**:

Fridays 1:30-2:30pm (on Zoom)

Mondays 4-5pm (on Zoom, or in-person with notice).

The Zoom sessions require a passcode, which is on the course Sakai page.

Also available by appointment.**My Email:** (my last name) at math.hmc.edu

**Grader: **Maxwell Thum (mthum at g.hmc.edu)

This course is a continuation of the ideas in Analysis (Math 131). There’s a lot of interesting and deep ideas that you’ll enjoy learning about. Topics include: Riemann-Stieltjes integration, function spaces, equicontinuity, uniform convergence, the inverse and implicit function theorems, differential forms, and an introduction to Lebesgue integration and measure theory.

## Required Text

Walter Rudin, *Principles of Mathematical Analysis*, McGraw-Hill, 3rd edition. We will cover Chapter 6 onward. There are also many other books on analysis that you may wish to consult in the library, around the QA300 area.

## Coursework

Homeworks will be assigned and collected weekly. There will be one midterm and one final exam. Each component (homework, midterm, final) is worth at least 30% of your final grade, with the “best” component worth 40%.

It is helpful to remember that course grades are just intended to assess what you have learned. But they are a not a reflection of your potential ability in mathematics, nor your worth as a human being. I believe everyone in the class is fully capable of mastering this material. Questions are valued, even simple ones because they can lead to profound ideas. Exploration is encouraged, especially risk-taking in trying out things that may not work, because this is how we learn.

The learning you are doing in this class takes place in a larger framework of school and life. Even if I am excited about teaching and you are excited about learning, work is not the most important thing, and sometimes life outside the classroom can take precedence. I can be somewhat flexible in accommodating requests for homework extensions and absences for other important events. Please make these requests 24 hours in advance, if possible.

Similarly, ‘success’ by whatever measure is not the most important thing in this course either. Every assessment of your work in this class is a measure of progress, not a measure of promise. Joy, wonder, productive struggle, having your mind expanded—these are more important!

## Honor Code

The HMC Honor Code applies in all matters of conduct concerning this course. Though **cooperation on homework assignments is encouraged**, you are expected to **write up all your solutions individually**. Thus copying is prohibited. You should understand your solutions well enough to write them up yourself. It is appropriate to acknowledge the assistance of others; if you work with others on a homework question, please write their names in the margin. Part of the fun of this course is the struggle, as well as the joy of discovering a solution for yourself. **Please note: using solutions found online or solutions of prior students will be regarded as a violation of the HMC Honor Code and will be handled accordingly. **I encourage you instead to talk to me or the tutors or each other!

## Lecture Notes and Zoom

Lecture Notes are available here. **If you cannot come to class, but would like to join via Zoom**, go to the Sakai page for the course. Keep your camera off and you won’t appear on the Zoom recording. (Also, on Zoom, I will not be able to hear or see the chat.)

## Reviewing Analysis I

These lectures were taped in 2010 and you may find them valuable for review:

Real Analysis Lectures, Spring 2010.

## Homeworks

Due on Gradescope on** Tuesdays at 10pm**.

Some of you may find LaTeX helpful in typesetting your homework. If so, there is a LaTeX class for homework here.

All HW’s refer Rudin’s *Principles of Mathematical Analysis.*