{"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":"2023-01-18T16:46:15","modified_gmt":"2023-01-18T16:46:15","slug":"math132","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/su\/math132\/","title":{"rendered":"Math 132: Real Analysis II"},"content":{"rendered":"\n
\"\"<\/figure><\/div>\n\n\n\n

Professor Francis Su<\/strong><\/p>\n\n\n\n

Fall 2022<\/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>:
Fridays 1:30-2:30pm (on Zoom<\/a>)
Mondays 4-5pm (on Zoom<\/a>, or in-person with notice).
The Zoom sessions require a passcode, which is on the course Sakai page.
Also available by appointment.

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

Grader: <\/strong>Maxwell Thum (mthum at g.hmc.edu)<\/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 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%.<\/p>\n\n\n\n

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.<\/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. 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. <\/strong>I encourage you instead to talk to me or the tutors or each other!<\/p>\n\n\n\n

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

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

Lecture Notes are available here<\/a>. If you cannot come to class, but would like to join via Zoom<\/strong>, go to the Sakai page for the course<\/a>. 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.)<\/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 Tuesdays at 10pm<\/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