# Recommended Readings

This page has a bunch of links you might want to read. In addition, you might see the following sub-pages:

Please notify me of any broken links, suggestions, etc. by email.

An abridged version of this page for olympiad students can be found here.

## Mathematician autobiographies#

Two of my past mentors have really moving pieces about their lives:

- Joe Gallian’s story: A Break for Mathematics (interview)
- Ken Ono’s story: My Search for Ramanujan (book)

(If you are an undergraduate math student, Joe and Ken run summer programs that I recommend, at Duluth and UVa respectively. I am a proud alum of both.)

## PG essays#

I can’t help but link Paul Graham’s essays. Ones I felt hit closest to home: What You’ll Wish You’d Known, Undergraduation, The Age of the Essay, What You Can’t Say, Mean People Fail, The Lesson to Unlearn.

## Undergraduate Math and Computer Science#

If you check **Appendix A of Napkin**, you can find listings of lecture notes or textbooks that I like for most undergraduate (or early graduate) topics. Here are some additional links.

- MSci Category Theory notes by Tom Leinster. I highly enjoyed these notes; very carefully written and explains intuition. Some minimal knowledge of group theory and linear algebra is used in the examples. See also the corresponding print book.

- Analytic NT notes by AJ Hildebrand. A set of lecture notes for analytic number theory, suitable for self-study. A light introduction where you get to prove versions of the Prime Number Theorem and Dirichlet’s Theorem.

- Algebraic Geometry by Andreas Gathmann. My preferred introduction to algebraic geometry; short but complete. This was the source that finally got me to understand the concept of a ringed space.

- Manifolds and Differential Forms by Reyer Sjamaar. My preferred introduction to differential geometry; very readable and works with minimal prerequisites. Also, beautifully drawn figures.

- Harvard’s CS 125: Algorithms and Complexity has delightful lecture and section notes.

## Olympiad Resources#

See also Geoff Smith’s page.

### Handouts#

- My own handouts (sorry, couldn’t resist linking them again).

- Yufei Zhao’s site has several excellent handouts, especially in geometry. I consulted many of them when I was coming up with ideas for my geometry textbook. In particular, the Cyclic Quadrilaterals handout is especially worth reading.

- Alexander Remorov, in particular the projective geometry handout, which the corresponding chapter in my textbook is based off of.

- Po-Shen Loh, mostly combinatorics. See especially the handouts on the probabilistic method.

- A Journey to the IMO, an overview of the IMO written from Nepal student Yuvraj Sarda.

### Books#

- My own: olympiad geometry book EGMO and OTIS Excerpts for non-geometry.

- Art and Craft of Problem-Solving by Paul Zeitz, introduction to math olympiads in general.

- Olympiad Combinatorics, by Pranav A. Sriram. The individual chapters are located in posts #1, #11, #49. This is an intermediate-advanced textbook.

- Olympiad NT through Challenging Problems, by Justin Stevens, is an introductory olympiad number theory text, at a level somewhat easier than what my own number theory handouts assume.

- Modern Olympiad Number Theory, by Aditya Khurmi. More olympiad-oriented number theory textbook.

- Problems from the Book by Titu Andreescu and Gabriel Dospinescu. Intermediate-advanced textbook covering topics in inequalities, algebra, analysis, combinatorics, and number theory.

### Contests#

Each section is in alphabetical order. Obviously not an exhaustive list of good contests, there are too many; these are just ones I have seen recently.

- National olympiads:
- Other olympiads:
- Team selection tests:
- International contests: