## 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]