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What is a mathematical derivative

Sprague Library, 1st floor

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:
  • Learn the content of real analysis.
  • Learn to read and write rigorous proofs.
  • Learn good mathematical writing skills and style.

Required Text: Walter Rudin, Principles of Mathematical Analysis. McGraw-Hill. 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 Re-Writes: Due at my office (Shan 3416) by 1:15 pm on Thursdays. 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) re-writes for the first few assignments, which will work as follows:
  • Turn in the homework on the due date.
  • The homework will be graded and returned to you within one week.
  • If you are not satisfied with the grade you received on the homework, you have the option of re-doing any question(s) you wish, and submitting the re-written version together with the previously graded version. (You may only re-write a question if you made a serious attempt at it on the first version.)
  • If you choose to do a re-write, it is due at my office two weeks after the original due date of the assignment. Your re-write will be graded, with particular attention to whether you adopted the graders' suggestions, and new grades will be assigned for rewritten questions. Your grade for a rewritten question will always go up or stay the same; it will never go

    down. Rewrites will only be accepted for Homeworks 1 through 4.

See also this guide . Late homeworks can only be accepted by special permission. Please ask at least 24 hours in advance. The lowest homework assignment will be dropped. Please follow the HMC Mathematics Department format for homework, online at

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:
  1. Midterm 1: Part in-class, part take-home. In class portion: Oct 6. Take-home due Oct 9.
  2. Midterm 2: Take-home Mon Nov 10, due Thu Nov 13.
  3. Final: during the regularly schedule final period.
Each of these and your homework average will count 25% of your course grade. It is helpful to remember that course grades are just intended to assess your learning. But they do not determine your worth as a human being.

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.

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!

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