Math 131AH (Winter 2024)
Instructor: Professor Robert Greene
Discussion Section Location: MS 5118.
TA Office Hours: Tuesdays 1-2 PM, Thursdays 11-12 PM in MS 2943 or by appointment.
You can find a course description through UCLA’s registrar. Official course materials are available on BruinLearn.
A lot of lower-division math puts an emphasis on knowing how to compute things: you may remember solving differential equations with variation of parameters, solving integrals with integration by parts, or taking determinants of \(5\times 5\) matrices by hand. But many of you are probably interested in pure math, where these computational skills are less relevant; in its place, you’re expected not only to know theorems and definitions, but also how to use them to prove other mathematical statements.
This transition can be quite hard, and I think lectures and discussions will play a complementary role to each other. In the former, you’ll (hopefully) learn the precise formulations and statements of various definitions and theorems. In discussion, we’ll look at how we can apply them to various problems.
You’ll be able to find fairly detailed notes for each week’s discussion at the bottom of this page. If you’re feeling sick or believe you may be potentially sick, please don’t come to class! You will have access to what we’re doing through this webpage.
The textbooks we’re using are Introduction to Topology by Gamelin and Greene and Introduction to Analysis by Rosenlicht. If you are allergic to either textbook, Principles of Analysis by Rudin is another standard textbook (often referred to as “Baby Rudin”), though we probably won’t be using it this quarter.
- 1. Some Practise with Sequences
- 2. Countability
- 3. Comments on Homework 1
- 4. Metric Spaces and Convergence
- 5. Metric Space Topology
- 6. Homework 2, Problem 3
- 7. Continuity and Compactness
- 8. Completeness of \(\ell^2\)
- 9. Homework 3, Problems 5 and 6
- 10. Connectedness
- 11. Studying and Problem-Solving
- 12. Derivatives
- 13. Comments about Homework 6
- 14. Contraction Mappings
- 15. Two Inverse Function Theorem Problems
- 16. Final Review
Fun fact: I actually took this very same class with Professor Greene himself three years ago (back in Winter 2021)! That was way back before I was even officially a pure math major. I’m quite pleased that I get to TA for this class, and I feel like things have gone full circle.