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.
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.
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.
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.
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: