Comments updated

Formative influence

Enjoyable activities


Algebraic and Differential topology

  • Jim Davis and Paul Kirk, Lecture notes in algebraic topology: fantastic notes for a grad student who has had a first course in algebraic topology.

  • Peter May, A Concise Course in Algebraic Topology: a logical next step, after having had some exposure to category theory as well. This fills in many topics that are left as “projects” in the previous notes.

  • Alexandru Scorpan, The wild world of 4-manifolds: gives useful intuition about all the non-intuitive (but not technically “wild”) things that one starts to see in dimension 4.

Category and Type Theory

  • Samson Abramsky and Nikos Tzevelekos, Introduction to Categories and Categorical Logic.

  • Emily Riehl, Categorical Homotopy Theory: a natural bridge between ideas from classical homotopy theory and category theory.

  • Many authors, The HoTT Book: doubles as an introduction to type theory and many other things.

Computer science

Reading list/Comments

  • R. Sadykov’s, “Elements of surgery theory”

  • Antti Laaksonen, “Competitive Programmer’s Handbook”

  • I’m also looking for material to teach me more mathematical physics, in order to understand better some of the challenges that fundamental physics is facing. If you have favorites, do let me know :-)

If anything should be added to the above, or doesn’t seem right, feel free to comment.