Canada/USA Mathcamp is a yearly summer program for mathematically talented high school students. It lasts for five weeks, and it’s held at a different college campus every summer, and most of the classes are one week long. For some of the classes that I’ve taught there, I still have detailed lecture notes.

2023 (Champlain)

2022 (Colby)

  • The Category of Sets, an introduction to some of the basic ideas of category theory using the category of sets as a motivating example.
  • Special Relativity, a class I have now taught four times at Mathcamp but only now written notes for.

2016 (Colby)

  • Systems of Polynomial Equations, a problem-based class going through the basics of Gröbner bases. The entire class consisted of solving problems from the provided worksheet.
  • Multilinear Algebra, a short, intense introduction to tensor products culminating in the basis-free definition of the determinant.
  • Functional Programming, an introduction to programming in OCaml. This class was based on the Haskell class from 2013.
  • Quantum Mechanics, a whirlwind tour of some basic ideas from quantum mechanics, including the definition of quantum states and observables, entanglement, the uncertainty principle, and a few words about the quantum-mechanical treatment of position and momentum.

2013 (Colby)

  • Determinants, a short worksheet I wrote for the Linear Algebra class I taught. This material wasn’t covered in class; the students are given problems which work them through a natural definition of determinants from the perspective of area and volume.
  • Programming in Haskell, a one-week introduction to Haskell. This class was organized primarily around problem-solving and the students were encouraged to look up things they didn’t understand on the Internet. The file provided here includes a PDF with 22 problems and some files that are used in some of the problems.

2012 (University of Puget Sound)

  • The Line Without a Length, a one-week introduction to the construction of the Lebesgue measure, ending with a description of a nonmeasurable subset of the real numbers. (Unlike the other notes on this page, these notes were only used by me teaching and weren’t passed out to the students, so they are very clipped and difficult to read.)
  • Five Programming Languages in Ten Days, a very fast-paced introduction to declarative programming through Scala, Clojure, Haskell, Erlang, and Prolog, which received two days each. The homework is also available. Of all the notes on this page except the ones from 2016, these are by far the most detailed. This class was co-taught with Asilata Bapat.

2011 (Reed)

  • Analysis on the Hyperreals, a one-week introduction to nonstandard analysis, a way of making rigorous the infinity- and infinitesimal-based arguments that sometimes appear in calculus. (This class was co-taught with Waffle Wofsey, and these notes only cover the second half of the course.)

2010 (Mount Holyoke)

  • Group Theory, a one-week introduction to groups from the perspective of their actions on sets.
  • Greek Impossibilities, a one-week treatment of field theory, culminating in the famous result that it is impossible to trisect an angle or double a cube with a compass and straightedge.