640:411

MATHEMATICAL ANALYSIS I

FALL 2012

Basic information for Fall 2012

• Instructor: Professor Eugene Speer
  • Hill Center 520
  • 848–445–7974
  • speer at math.rutgers.edu
• Office hours:
  • Monday, 1:40–3:00 PM, Hill 520
  • Wednesday, 2:45–4:15 PM, Hill 520
  • Thursday, 9:00–10:00 AM, Hill 520
  • Or by appointment or chance in Hill 520
• Detailed course information and policies: As web page and as a PDF file.
• Homework assignments.
• Hints on writing proofs:
  • From your instructor: As web page and as a PDF file.
  • From Professor James Munkres (the author of the text used in Math 441, Introductory Topology; I can now find these notes only on a Swarthmore website, given here.)
• Other texts:
• Here is a link to a discussion of supplementary reading, prepared by Prof. Stephen Greenfield for a previous year's 411 class.
• I am having several books placed on reserve in the reading room in SERC (it will take a while for all of these to get there):
  • Apostol, Tom: Mathematical Analysis. One of the classic texts.
  • Buck, R. Creighton: Advanced Calculus. Another classic; discussed in Professor Greenfield's posting.
  • Bartle, Robert Gardner: The elements of real analysis. A former 311 text.
  • Gelbaum, Bernard R.: Counterexamples in analysis. Discussed in Professor Greenfield's posting and in the next item.
• The book Counterexamples in analysis listed immediately aobve is not a text, but rather a collection of examples showing that various plausible-sounding statements in analysis are in fact not true. It is available as an inexpensive paperback from Amazon. I recommend that you buy a copy.

Final exam

• The exam is cumulative, covering everything in the course with one exception: there will be no questions on the construction of the real numbers, Dedekind cuts, etc. Summation by parts, or any other topic in Rudin which we did not cover either in class or via the notes distributed 12/10 and available below, will not be covered. There will probably be some emphasis on Chapters 4 and 5.
• I will hold special office hours on reading day and during the exam period (there is a slight change here from the office hours I announced in class):
  • Thursday 12/13/2012: 11:00–12:00 and 3:15–4:00, Hill 520
  • Monday, 12/17/2012: 1:45–3:00 and 3:45–4:30, Hill 520

Announcements

• 12/10/2012: Here are some brief notes covering a few simple results that we will not have time to prove in class. These are really at the level of exercises, and many of them are so treated in Rudin, but since we are moving fast at the end of the semester it seems worthwhile to provide proofs or proof sketches.
• Here is a write-up of the proof of l'Hôpital's rule that I gave in class Monday, November 26, and here is an alternative and perhaps simpler version of the proof.
• The second exam is Monday, November 19. It will cover Chapter 3, omitting summation by parts and the proof of Theorem 3.54, and Chapter 4, up to but not including the section on ``Continuity and Connectedness'' which begins on page 93. We should finish almost all of this material on Monday, November 12, but a little may carry to Thursday.
• The first exam is Monday, October 15. It will cover all our work from Chapters 1 and 2 of Rudin.
• Here is a summary of some of our results about compactness.