Spring 2016 http://www.math.hmc.edu/~su/math131/ Professor Francis Su
Grader/Tutors:
Patrick Tierney, Jared Tramontano, Sam Miller, Hope Yu, Kat Dover


This course is a rigorous analysis of the real numbers, as well as an introduction to writing and communicating mathematics well. Topics will include: construction of the real numbers, fields, complex numbers, topology of the reals, metric spaces, careful treatment of sequences and series, functions of real numbers, continuity, compactness, connectedness, differentiation, and the mean value theorem, with an introduction to sequences of functions. It is the first course in the analysis sequence, which continues in Real Analysis II. 
Goals of the course:
Required Text: Walter Rudin, Principles of Mathematical Analysis, McGrawHill. We will cover Chapters 1 through 5, and part of Chapter 7. There are also many other books on analysis that you may wish to consult in the library, around the QA300 area.
Homeworks, and ReWrites: Due at my office (Shan 3416) by 1:15 pm on Thursdays. Please follow the HMC Mathematics Department format for homework, online at http://www.math.hmc.edu/teaching/homework/. Because I want you to learn from the feedback you get on your homework, as well as improve your writing skills, I will use a system of (optional) rewrites for the first few assignments, which will work as follows:
LaTeX: some of you may find LaTeX helpful in typesetting your homework. If you'd like to learn LaTeX, or have questions about it, you can visit the CCMS Software Lab.
Midterms and Grading: There will be three exams:
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, and 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 previous 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!
Taped YouTube Lectures:
These lectures were taped in 2010, and although the lectures I give this year may not be identical, they will be close enough that you may find it valuable to use them for review. Or, better yet, watch them before the class lecture, and then during class you can ask questions! I do not encourage using these lectures as a substitute for class, however, since we will be doing slightly different things and interactions with me and other students will be critical for your learning. 
Homeworks
All HW's refer Rudin's Principles of Mathematical Analysis. 


There will be no rewrites for HW#0.
Your homework should be handed in three parts.

Your homework should be handed in three parts.
Rewrites for HW#1 are also due. If you want to do rewrites, see this guide. Rewrites should be handed in in parts. 
Rewrites for HW#2 are also due. If you want to do rewrites, see this guide. Save a copy since you probably won't get the homework back in time to study for the exam. 
Rewrites for HW#3 are due. Rewrites should be handed in in parts. No more rewrites after this date. 
No further rewrites accepted. 







Possible upcoming homeworksBelow this line, all homeworks are TENTATIVE. This means they are likely to be assigned, but there is no guarantee that they will until you see them moved to the box ABOVE. I am putting them here in case you want to work ahead! 