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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:

(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.

  • 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.

Olympiad Resources#

See also Geoff Smith’s page.


  • 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.


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


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.

Updated Sun 4 Feb 2024, 01:59:10 UTC by 20b2419e9046