teaching materials

I have taught quite a bit over the years, and have generated a lot of teaching materials along the way. Here I have collected the "nontrivial" ones, organized by topic. (You can find the quizzes and exams I've created by navigating from my teaching page.) This includes some of my syllabi: I sometimes like to include an extended overview of the material, perhaps including some context regarding how the material of the course fits into the broader landscape of mathematics.

Please feel free to use these materials. And if you do, please let me know how it goes!

In all cases, if you would like to see the context for the linked material, simply delete an appropriate amount of the end of the given url.

single-variable calculus

worksheet on epsilon-delta proofs, "The Ballad of the Gallant Hero and the Malicious Adversary" (2011)

worksheet on algebra prerequisites (2017)

summary of §§2.8-5.5 of Stewart's "Essential calculus", 2nd ed. (2017)

multi-variable calculus

syllabus (2018)

lecture notes at the bottom of the page (2019)

linear algebra

syllabus (2016)

abstract algebra

syllabus (2019)

lecture notes at the bottom of the page (2019)

worksheet on the graph isomorphism problem (2019)

category theory

worksheet on inverses and isomorphisms (2020)

worksheet on initial/final objects, groups as one-object categories, directed colimits and finality (2020)

algebraic topology

syllabus on algebraic invariants of topological spaces (e.g. fundamental group(oid)s and homology) (2020)

syllabus on homology, cohomology, and Poincaré duality (2021)

syllabus on characteristic classes (2022)

lecture notes at the bottom of the page (2020)

worksheet on the classification of covering spaces without basepoints or connectedness assumptions (2020)

worksheet simplifying Hatcher's proof of the refinement lemma for singular homology (2021)

higher category theory & higher algebra

picture of a big diagram attempting to summarize the relationship between relative categories, model categories, quasicategories, and ∞-categories (2016)

guide to some of the literature that one may be equipped to read after learning the basics of ∞-category theory (2017)

syllabus for homological algebra (2021)

textbook, "Higher Algebra: Chapter 0" (2021)

factorization homology

lecture notes (2016)

syllabus (2019)

homework problems (2019)

lecture notes at the bottom of the page (2019)

misc.

guide to getting started with writing math and writing tex (2019)