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.
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.
See also Geoff Smith’s page.
- 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.
- Art and Craft of Problem Solving by Paul Zeitz, introduction to math olympiads in general.
- An olympiad combinatorics book, by Pranav A. Sriram. The individual chapters are located in posts #1, #11, #49.
- 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.
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: