Here's some stuff I've written for things. Read at your own risk.

James' Space

e is transcendental (need to finish pi and further topics)

Brauer Group

Groebner Bases and Applications

brief notes on topological K-theory

Notes on Analytic Number Theory (missing chunks~)

a handful of proofs of quadratic reciprocity(need to finish a couple, add a theta function proof?)

Ergodic Theory of Simple Continued Fractions (needs proofs of ergodic theorem and ergodicity of the Gauss map, doesn't address any hyperbolic dynamics)

A short derivation of Gauss measure on (0,1)

Sum of four squares via the Hurwitz quaternions

Slides from a talk on "super-apollonian continued fractions," JMM 2017

Summary/overview of A. L. Schmidt's continued fractions over Q(i)

A proof of the Banach-Tarski paradox

Parameterizing polygons with Grassmannians, (Interactive demonstration of the moduli of triangles by Sam Zhang)

the first and second Stiefel-Whitney classes; orientation and spin

The GNS construction, (every C^*-algebra is an operator algebra)

Lazard's theorem, (every flat module is a direct limit of finite rank free modules)

Some tables I made for fun

class numbers and reduced forms (negative fundamental discriminant D>-10000)

class numbers, reduced forms, Pell solutions, and c.f.e. (Q(sqrt(d)), 1000>d>1)

fundamental solutions of Pell's equation x^2-dy^2=+/-1, d!=1 mod 4, or x^2-dy^2=+/-4, d=1 mod 4, for d<200

singular points for imaginary quadratic fields, square-free m, 0<-m<1000

markoff triples of depth <= 11

Robert Hines MATH 340 robert.hines@colorado.edu