expository [back]

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

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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)

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Some tables I made for fun

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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

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Robert Hines MATH 340 robert.hines@colorado.edu