Math 347     Advanced Real Analysis     Summer 2011

Instructor: Sunil Chebolu


Announcements:


Course links:


Projects and presentations: Each group will work on an assigned project and will present it in the last week of classes. Here are some interesting and exciting topics from which you can pick. You can borrow the relevant references from me.




Homework Problems

Section

3rd Edition

4th Edition

Section 5 1, 2, 4, 15, 18 1,2, 4, 5, 26
Section 6 1, 4, 6, 11 1, 10, 12, 19
Section 7 1, 8, 13, 16, 18 1, 10, 19, 26, 30
Section 8 1, 3, 9 13 1, 3, 9, 13
Section 9 skip skip
Section 10 3, 4, 6, 10, 12 3, 4, 6, 14, 16
Section 11 3, 7, 6, 8 3, 7, 6, 8
Section 12 1, 3, 6, 10, 11 1, 3, 6, 10, 11
Section 13 1, 3, 5, 7, 11, 13, 15, 17 1, 3, 5, 11, 15, 17, 19, 21
Section 14 1, 3, 4, 6, 8, 11 1, 3, 4, 6, 8, 11
Section 15 1, 3, 8, 9, 10, 15, 17 1, 3, 10, 11, 12, 17, 19
Section 16 1,5, 7, 8, 13 1, 7, 9, 10, 15
Section 17 1, 6, 7, 9, 15 1, 6, 9, 9, 15
Section 18 1, 2, 4, 6 1, 2, 4, 10
Section 19 1, 3, 5, 6 1, 3, 5, 8
Section 20 1, 3, 7, 11, 13, 15 1, 3, 9, 13, 15, 17
Section 21 1, 3, 5, 9, 12, 17 1, 3, 5, 9, 12, 17
Section 22 1, 3, 4, 6, 7, 9 1, 3, 4, 6, 7, 9
Section 23 1, 3, 5, 6, 11, 14 1, 3, 5, 6, 11, 15
Section 24 skip skip
Section 25 3, 5, 7, 10, 17 4, 5, 7, 11, 18
Section 26 1, 5, 6, 10, 12, 14, 15 1, 5, 8, 12, 14, 16, 17
Section 27 3, 4, 6, 7, 8 3, 4, 6, 7, 8
Section 28 1, 3, 4, 6, 13 1, 3, 4, 6, 13



Presentations:

Here is the schedule of the presentations for the final week. It is important that you attend ALL talks and not just your own talk. There is a lot that you (and I) can learn from these talks. So please don't skip any talks. In fact, you may not get any credit if you don't attend all presentations.

Your goal: A student who walks out of the classroom after your presentation should think: "wow! That's pretty cool stuff. I really understood it." That is your goal -- make every student in the class feel that way. To this end, you may want to keep the following things in mind.

Things to keep in mind about your presentation
  1. Explain very clearly at the beginning what you are going to present.
  2. Try to convey the big picture of the topic/proof before getting into technicalities which might obscure the beautiful underlying ideas. If time is short, you don't have to present all the proofs. Mention the key steps and explain how you can link them to get the result.
  3. Your board work should be tidy and your handwriting should be legible.
  4. Go slow and pause for questions.
  5. Use pictures whenever appropriate to illustrate ideas.
  6. Use of technology in the classroom is encouraged but certainly not necessary. A traditional chalk and board discussion is good enough.
  7. Finally make sure you follow the c^5 rule: Be Clear, Concise, Coherent, Creative, and Cool. That is the key to learning the art of writing or presenting beautiful mathematics. As the famous English Mathematician G. H. Hardy said, "There is no permanent place for ugly mathematics in the world."


PRESENTATIONS SCHEDULE

Date

Project Title

Speakers

Abstract

Monday, July 18, 1:00 - 2:00 On the sum of the kth powers of the first n natural numbers Amber Anderson
Lindsey Gaworski
Jill Horne
TBA
Monday, July 18, 2:15 - 3:15 The fundamental Theorem of Algebra Chris Pedersen
Sam Stalter
and Beth Waller
TBA
Tuesday, July 19, 1:00 - 2:00 The Cantor set and the space filling curve Christy Engel
Kate Lawrence
Xiheng Tong
Lisa Schuckman
TBA
Tuesday, July 19, 2:15 - 3:15 Continuous but nowhere differentiable curves Will Cragoe
Sara Poland
Michael Sanchez
TBA.
Wednesday July 20, 1:00 - 2:00 How can a man escape from a lion in a circular arena? Eric Larson
Mike Mayers
Jason Robart
David Rogers
TBA




Sunil's Homepage