Our main focus will be on the material found in Chapters 2, 3, 7 and 11 of the text. Specifically, this involves the following topics: metric spaces, compactness, sequences and series of functions, and measure theory. As time allows, we may try to cover the implicit and inverse function theorems.

1. To learn and apply ideas, concepts and proof techniques from analysis, particularly from the topics listed above.
2. To practice (and improve at, hopefully) writing rigorous proofs.
3. To get a flavor of what graduate-level mathematics is like.
4. To become familiar with a classic text in mathematics.

It will be assigned and collected nearly every day. Exercises will usually require formal proofs and, even when not, all statements that seem pertinent should be supported. You should feel free to discuss ideas with your classmates, but you should be alone when writing up your own response. Make a rough draft outlining the most direct path from assumptions to conclusions before writing up your final submission. If you are planning to head to graduate school, it would be a good idea to learn how to use LaTeX, and typeset some of your homeworks using it. “The Not So Short Introduction to LaTeX 2e,” subtitled “LaTeX in 139 minutes,” is a good document for how to get started using LaTeX.

Homework submissions are due by 3 pm on the due date, and may be placed in the folder outside my office marked for “New MATH 362 homework”.

There will be 2-3 exams during the semester. The specific dates are, as yet, undetermined.