Mathematical Notes

Here are my mathematical notes: short notes about well-known or research problems, notes from self-studying mathematical texts, and lecture notes from lectures. By "mathematics", of course theoretical computer science is included.

Lecture Notes

Topics in Mathematical Science VI (数理科学特論VI) (WIP)
Lecturer: Erik Darpö, Graduate School of Mathematics, Nagoya University, Fall 2019
A gentle introduction to module theory and homological algebra, accessible to anyone with a basic undergraduate background in abstract algebra.
[PDF] [LaTeX Source] (Latest build: November 1, 2019)

Formalized Mathematics

The Eckmann-Hilton Theorem
The higher homotopy groups are abelian. Mostly following the proof of Theorem 2.1.6 in the HoTT Book.
[GitHub]

Surveys

Securing Complex Software Systems Using Formal Verification and Specification
This was originally written as a course report for COMP 116, "Introduction to Computer Security", Fall 2017, Tufts University.
[PDF]

Short Notes

An Alternative Proof of Convergence for \( e^x \)
Proving that the exponential function converges using only the very basic facts about infinite series.
[PDF]

Project Reports

Formalizing the DFUDS Representation in Coq
Project report for CS 591K, "Foundations and Pragmatics of Dependently-Typed Systems", Spring 2019, Boston University.
(Note that the work reported is still very preliminary, and the approach outlined might turn out not to be the most best approach.)
[PDF]

Exploring Corpora-Based Music Classification: Classifying Japanese Popular Music using Lyrics
Project report for COMP 150WC, "Working with Corpora", Fall 2018, Tufts University.
[PDF]