Math writing

A compilation of things I've written for courses and my research. (All the ones that I like enough to put online, anyway.)
  • I completed my master's essay in spring 2016 under the supervision of Rahim Moosa; I studied applications of model theory to the study of formal languages.

    Formal languages and the model theory of finitely generated free monoids

  • In winter 2016, I took PMATH 945, a topics course in category theory and homological algebra. For the final project, I wrote a paper on monads, algebras over monads, and an interpretation of the latter via universal algebra.

    A brief introduction to monads (Now with universal algebra™!)

  • In fall 2015, I took PMATH 753, a course in functional analysis. For the final project, I wrote a paper on trace class operators on a Hilbert space. I should note that the proof of theorem 3.6 is flawed, though I believe it is easily fixed. I'll get around to correcting it sooner or later.

    A brief introduction to trace class operators

  • In fall 2013, I took CS 758, a course in cryptography and network security. For the final project, Eddie Cheung, Patrick Lee, and I wrote a paper on secure computations using playing cards. The paper gives a broad overview of the field, presents a new perspective on existing techniques, and presents a new card-based algorithm for computing the AND of two bits.

    Secure Computation with Playing Cards

  • I did a research term in model theory under the supervision of Rahim Moosa during the spring term of 2013. This resulted in the following documents being brought into being: