Real Analysis II.
    Fall 2018

    Professor Francis Su
    Office Hours: Shan 3416, Tuesdays 1:30 - 3:30pm or by appointment.
    e-mail: [insert my last name] @ math.hmc.edu

    Graders: Shyan Akmal
    e-mail: firstinitial lastname @ g.hmc.edu

This course is a continuation of Math 131. Glad you could join us! There's a lot of interesting and deep ideas in this course that you will 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.

Text: Rudin's Principles of Mathematical Analysis.

Course webpage: http://www.math.hmc.edu/~su/math132/.

Lectures: Lecture notes are posted here (for the semester only): bit.ly/math132-fall2018.

Coursework: Homeworks will be assigned and collected weekly. Lowest homework score will be dropped. 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%.

Honor Code: Cooperation on HW assignments is fine (and in fact encouraged), but appropriate acknowledgements should be given, and you are expected to write up your solutions INDIVIDUALLY, i.e., it should be the case that after said cooperation you have understood the solution well enough to explain it on the homework! It is appropriate to acknowledge the assistance or cooperation of others when given.

Absences, late homework: The learning you are doing in this class takes place in a larger framework of school and life. While I am excited about teaching and I'm sure 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 accomodating 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!

Homeworks, due Wednesdays in box outside my office door by 2pm (Shan 2416).

  • HW #2. (Due Sep 19.) Read Chapter 6. Here is HW #2 and the TeX code.

  • HW #3. (Due Sep 26.) Do Chapter 6 (6, R7, 8, 10abc, 11, 15 ).
    Hint on 10a: for a concave up function, its values always lie below the secant line between two endpoints.
    Hint on 15: yes, that last inequality is strict.

  • HW #4. (Due Oct 3.) Read Chapter 7, theorems 7.1-7.15. Do Chapter 7 ( 1, 2, 3, R4, 5, 6 ).
    In Problem 5, you might notice how this compares with the statement of the M-test.

  • HW #5. (Due Oct 10.) Read the rest of Chapter 7. Do Chapter 7 ( 7, 8, 9, R11, R14, 15, 16 )
    Hints: On 7.8, thm 7.12 can still be useful. On 7.9, use eps/2 argument.

  • Prepare for the midterm, which will be handed out Mon 10/15 and due Friday 10/19 by 5pm. It will be 4 hours (with hour long break for food), closed book, but you're allowed an 8.5x11 sheet of paper (front and back) on which you can have notes of any kind. The exam will cover Chapters 6 and 7. You might want to study old homeworks,

  • HW #6. Do the problems on this handout. Here's the TeX file. Due Oct 31.

  • HW #7. Do Chapter 9 ( 3, 5, 6, 8, 9 ). Due Nov 7.

  • HW #8. Do Chapter 9 ( 11, 13, 16, 17 (worth 2 problems) ). I will be out of town Mon/Tue so we will not have class Monday Nov 12 and no office hours on Tuesday. On Wednesday, I will be available immediately after class to answer questions, and the HW is due Thursday Nov 15.
    For these problems, you can assume knowledge of calculus for taking derivatives of things like sin(x), etc.

  • HW #9. Do Chapter 9 ( 18 (worth two problems), 19 (worth 2 problems), 20 ). Due Nov 28.

  • HW #10. Due Wednesday December 5. Do Chapter 10 ( 15, 20, R21 ) and
    Problem A. Prove Theorem 10.20a in your own words.
    Problem B. Prove Theorem 10.20b in your own words.
    Problem C. Find a differential 2-form (omega) in R^4 such that (omega)^(omega) is not zero.

    -------------- HW #10 is last HW set, Final will be handed out Dec 5, due the following Wednesday morning at 11am. -------------------

 

 


[Recall "R" means read, but do not do the problem.]
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