Math 323: Real Analysis

__Instructor:__ Steve Abbott, Warner 402

__Text__: *Understanding Analysis*

__Goals:__ I see three main goals for us:

i) To learn how to write
extended, rigorous mathematical proofs.

ii) To understand why an intuitive understanding of calculus (learned in Math
121 and 122) is insufficient as a foundation for building more complicated and
powerful mathematical tools.

iii) To enjoy the payoff of analytical rigor and abstraction by studying
some newly accessible topics.

__Regular Assignments__: I will assign a few problems at the conclusion
of each class, which are usually due in a few days. These are not pledged so you are allowed and encouraged to work together, share ideas, and get
help from me.

PLEASE DO NOT USE ANY SOURCES OTHER THAN YOUR TEXT, ME, AND EACH OTHER. Do not consult peers outside of our class, and no internet! The idea is to wrestle with the ideas of the course using just the resources given to you in class and in your book.

__Pledged assignments: __Twice during the semester I will assign a longer
and more challenging problem set that must be done on your own. These will constitute
a review of the previous 2 or 3 chapters as well as a synthesis with what is
happening in lecture.

__History__: The mathematics covered in this course was largely developed
between 1807 and 1901 (with a few exceptions). I have found that to understand
this subject it helps to understand who these mathematicians were and why they
were worried about the questions that we will be studying. Thus I'd like everybody
to be responsible for a short 10 minute "historical moment" presentation sometime
during the semester. You'll be allowed to do this with a partner if you like. Specifications for what to include in your presentations
will be forthcoming.

__Grades__: Your
grade will be computed from the following recipe:

25% regular assignments and class participation

25% pledged set #1

25% pledged set #2

5% historical presentation

20% final project

Including class
participation in the above formula is meant to make the point that I expect you
all to be present, sharp, and ready to contribute to discussion. Let's all work
hard, be smart, and have a great semester!