Math 323: Real Analysis

Instructor: Steve Abbott, Warner 503

Text: Understanding Analysis, 2nd edition

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 7 or 8 minute "historical moment" presentation sometime during the semester. You'll be asked to do this with a partner or two. 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!