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Teaching (OTIS)

Olympiad

  •  For beginners
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  •  EGMO book
  •  Napkin (v1.5)
  •  Course notes

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Advice and recommendations

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.

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#

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.

Updated Sun 28 Nov 2021, 12:13:12 UTC by 7fbfa8169e2c