Here are some notes I have written up. They are all works in progress.

Quantum Invariants of Knots (pdf): In order to study for my orals, I am preparing notes on subjects related to knot theory. This piece deals with some category theory which is applied to quantum invariants such as the Kauffman and Jones invariants.

Categories (pdf): A little category theory.

2-Categories (pdf): The definition of 2-category.

Tangles (pdf): The category of tangles and the Kauffman bracket.

Axiomatic Introduction to the Riemann Integral (pdf): Wrote this up for my own edification.

Introduction to the Fundamental Group (pdf): Again for my own edification. So far it's got paths, homotopies, path-homotopies and the fundamental groupoid. More to come.

Rigid Body Mechanics and SO(3) (pdf): I wrote this up based on a talk I gave to SPS. I discussed an interesting application of Lie groups to classical mechanics.

Elliptic Functions (pdf): Notes for a talk i gave for a seminar class.

Differential Forms (pdf): It's got alternating and differential forms, wedge products, exterior derivatives, but as yet no De Rham cohomology.

Commutative Algebra (pdf): Notes I wrote up to study for a commutative algebra test.

Dirichlet's Theorem (pdf): Wrote this for a talk for my seminar class. It's on Dirichlet's theorem on primes in arithmetic progressions. Yay, L-functions.

Snake Lemma (pdf): Part of the proof of the snake lemma from homological algebra.

Fourier Analysis (pdf): Some very rough notes about some Fourier analysis.

Fundamental Theorem of Riemannian Geometry (pdf): A proof.