Possible syllabus
Below is an outline of the course. The textbook is the third edition
of Rudin's Principles of Mathematical Analysis. There will be 2
exams in class, and students will be notified about them at least a
week in advance. I do notice that the sum of exams plus the lectures
suggested is 25. There are 28 class meetings, but my best guess now
(before the semester begins) is that we will not finish all of
the first 7 chapters. We (students included!) may discuss homework
solutions in some classes, etc. We likely will only begin chapter 7
and so progress more slowly than last year's instantiation of Math
411.
I strongly suggest you glance at the chapter contents before class discussion of the material begins, and that you then seriously read each chapter as the class discussion continues. I also suggest that you look at most of the problems in each chapter. At least understand the questions (just this is sometimes not so easy!). Even if you are not required to write solutions and hand them in, you may want to consider how to solve many of the problems.
| Chapter number and title | Number of lectures planned | Homework problems | Due date |
|---|---|---|---|
| 1 The Real and Complex Number Systems | 2 Done in only 3.5 |
First assignment | 9/15/2008 |
| 2 Basic Topology | 3 | ||
| 3 Numerical Sequences and Series | 4 | ||
| 4 Continuity | 3 | ||
| 5 Differentiation | 4 | ||
| 6 The Riemann-Stieltjes Integral | 4 | ||
| 7 Sequences and Series of Functions | 4 |
How to do homework
A previous 411 instructor wrote the following paragraphs. I
emphatically agree with these statements.
One important way to learn mathematics is to talk about it. You are strongly encouraged to discuss problems -- and indeed, all the material in the course -- with me or with other students. After you have finished discussing a problem, however, you must write your solution independently, not in concert with others. Your ideas and approach to the problem may come from discussion, but you should express those ideas in your own words.If you have trouble with homework problems, or with any material in the course, I urge you to come in during my office hours, or at some other time, and discuss them.
Grading
Course grades principally will be based on a weighted average of
homework and exams.
| Homework | 20% |
| Class exams (each 20%) | 40% |
| Final exam | 40% |
Maintained by greenfie@math.rutgers.edu and last modified 8/31/2008.