## Resources

### Undergraduate Research

#### List of Mathematics REU's

#### List of Mathematics REU's Compiled by the NSF

The NSF also has a list of REU's in other scientific fields. You can select a field here.

Also bear in mind that your professors tend to know a thing or two about research, asking them for suggestions is okay.

### Online Resources

#### Paul's Online Notes

A well-written set of notes covering calculus, the basics of differential equations, and high school algebra. About the same quality as any of the textbooks on this subject, and they're free.

#### Purdue Problem of the Week

Has a huge list of difficult problems.

#### Proof Wiki

Has a surprisingly large collection of proofs. Much easier to look here than hunt through the library for a specific proof.

#### Math Stack Exchange

Online community for answering basic math questions. If your question pertains to undergraduate mathematics, you should ask it here.

#### Math Overflow

Similar to math stack exchange, but for advanced mathematics, e.g. research level mathematics.

### Books that Are Actually Useful

#### General Topology

A reasonably accessible introduction to general topology. Covers all of the basics. Has quite a lot of content, and it's quite cheap.

#### Algebraic Topology

Relatively easy to read.

#### Advanced Linear Algebra

A genuinely enjoyable read. Covers the theoretical aspects of linear algebra.

#### Measure Theory

One of my favorite books. Measure theory is very interesting, and Halmos is an excellent writer.

#### Advanced Calculus

Try chapters three and four for a good minicourse in analysis. The rest of the book focuses on vector space calculus and manifolds.

#### Real and Complex Analysis

Rudin is pretty well known as a writer. The book's good. I suggest reading a book on measure theory first, because he moves very quickly at the start. You can find cheaper versions than the one here. Bear in mind that this book covers exclusively *graduate* analysis. If you want an introduction to analysis, look elsewhere.

### Books for Fun

#### A Course in Arithmetic - Jean-Pierre Serre

An easy introduction to arithmetic. Worth reading even if you already know arithmetic.

#### Basic Number Theory - Andre Weil

Another easy introduction to one of the core fields of modern mathematics.

#### Basic Algebra I and Basic Algebra II - Nathan Jacobson

The last of the three "Textbooks with Incredibly Misleading Names." Still pretty good, as mathematics books go.

#### Inter-Universal Teichmuller Theory I, II, III, IV - Shinichi Mochuzuki

Good luck.