Reading Recommendations

The world would be a great place if I could write about everything I knew about, but alas I have a finite amount of time. So in addition to the stuff I have on this website, here's a list of other resources I like.

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

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

Undergraduate Math and Computer Science

  • 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 instead 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. It doesn't officially cover schemes, but because it covers general varieties as ringed spaces the full-fledged scheme is not much harder.

  • 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.

Of course, see also Napkin.

Olympiad Resources


  • 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.



Each section is in alphabetical order.

Last modified: Tue Jan 23 10:12:41 2018


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