MATHEMATICAL ANALYSIS I
Basic information for Fall 2012
- Instructor: Professor Eugene Speer
- Hill Center 520
- 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:
- Other texts:
- Here is a link to a discussion of supplementary
reading, prepared by Prof. Stephen Greenfield for a previous year's 411
- 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.
The final exam is scheduled for Tuesday, December 18, 12:00–3:00
PM, in ARC 204.
- 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
- 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
- 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
- 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.