{"id":887,"date":"2022-08-29T15:13:01","date_gmt":"2022-08-29T15:13:01","guid":{"rendered":"https:\/\/math.hmc.edu\/su\/?page_id=887"},"modified":"2026-09-02T01:28:20","modified_gmt":"2026-09-02T01:28:20","slug":"math132","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/su\/math132\/","title":{"rendered":"Math 132: Real Analysis II"},"content":{"rendered":"
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Professor Francis Su<\/strong><\/p>\n\n\n\n

Fall 2026<\/strong><\/p>\n\n\n\n

Course Webpage<\/strong>: https:\/\/math.hmc.edu\/su\/math132\/<\/a><\/p>\n\n\n\n

My Office:<\/strong> Shanahan 3416

Drop-In Hours<\/strong>:
– Tuesday 11am – noon (Charlie Lyall)
– Tuesday 3pm – 4:30pm (Francis Su)
Also available by appointment.

My Email:<\/strong> (my last name) at math.hmc.edu<\/p>\n\n\n\n

Grutor: <\/strong>Charles Lyall<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Required Text<\/h2>\n\n\n\n

Walter Rudin, Principles of Mathematical Analysis<\/em>, 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.<\/p>\n\n\n\n

Coursework<\/h2>\n\n\n\n

Homeworks will be assigned and collected weekly. There will be one oral midterm and one in-person final exam, worth 30% and 40% respectively. Homeworks are worth 20%.<\/p>\n\n\n\n

It is helpful to remember that course grades may 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.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

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!<\/p>\n\n\n\n

Honor Code<\/h2>\n\n\n\n

The HMC Honor Code applies in all matters of conduct concerning this course. Though cooperation on homework assignments is encouraged<\/strong>, you are expected to write up all your solutions individually<\/strong>. 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.<\/p>\n\n\n\n

Please note: using solutions obtained from online sources, from an AI, or from prior students will be regarded as a violation of the HMC Honor Code and will be handled accordingly. <\/strong><\/em><\/p>\n\n\n\n

AI Policy<\/h2>\n\n\n\n

You are welcome to use AI tools to review concepts and help you learn.
You may *not* use it to solve homework or exam problems.<\/p>\n\n\n\n

I encourage you to not let an AI replace your interaction with humans discussing the ideas of this course.
A good rule of thumb: If you are talking to an AI about Math 132 more than you are talking to humans, you are using it too much.
Another good rule: AI should be used to increase your friction with the material, not decrease it. That is, prompting an AI to quiz you, or to provide review problems, or to help you figure out what’s correct by asking you questions is far better than prompting it to simply explain stuff.<\/p>\n\n\n\n

Lecture Notes and Zoom<\/h2>\n\n\n\n

Lecture Notes will be available through a link here.<\/p>\n\n\n\n

Reviewing Analysis I<\/h2>\n\n\n\n

These lectures were taped in 2010 and you may find them valuable for review:<\/p>\n\n\n\n

Real Analysis Lectures, Spring 2010<\/a>.<\/p>\n\n\n\n

Homeworks<\/h2>\n\n\n\n

Due on Gradescope<\/a> on Wednesdays by 4pm<\/strong>.<\/p>\n\n\n\n

Some of you may find LaTeX helpful in typesetting your homework. If so, there is a LaTeX class for homework here<\/a>. <\/p>\n\n\n\n

All HW’s refer Rudin’s Principles of Mathematical Analysis.<\/em><\/p>\n\n\n