My Undergraduate Senior Thesis

HERE is the writeup, titled Fourier Analysis on Groups of Finite Measure, accompanied by a slide show and a poster.

Notes on Functional Analysis (in progress)

HERE are my own notes, being continuously written as I learn the subject. I would like to be able to turn these into a textbook, someday. Currently, however, I only consider chapters 1-3 and 5 to be readable. I'd be grateful to anyone who points out mistakes.

Analysis Proofs (in progress)

HERE I rewrite the proofs of Baby Rudin in my own words. These notes are intended to serve as a companion piece to Rudin's text. Omitted sections exist, but are less polished. I'd be grateful to anyone who points out mistakes.

My TeX Template

HERE should be suitable for an intermediate level TeX-er (such as myself), and ought to be particularly useful for when you either need to include pseudocode in your documents, or would otherwise like demonstrate code verbatim. Also, for those not familiar with the phenomenal leftbar and noncompile environments, allow me to be the one to introduce them to you! (thanks to prof. Darij Grinberg, from whom I learned of them, myself).

List of Tricks

HERE I am actively compiling a reasonably succinct list of tricks (mostly inequalities) which I found obscure and wouldn't otherwise be able to remember. As such, it might be missing some tricks which I remember but the reader doesn't, and it may include "dead weight" which the reader remembers but I don't.

All Roots of the First Hundred Legendre Polynomials

HERE (that is, up to and including degree 100) computed in R using the bisection method (since Newton's proved to be unstable) with arbitrary precision rational arithmetic (the class "bigq" from "Rmpfr") and afterwards converted to decimal form.

A Presentation on the λ-π Theorem

HERE is the slide show, wherein the Theorem is presented, and we use it to prove Tonelli's theorem.

Secant Interpolation

HERE are my personal notes on an operation I've defined which essentially "blends" two functions. The result is particularly interesting when the operation is defined recursively, resulting in a seemingly convergent sequence. The name needs improvement... and, sadly, I cannot manage to prove convergence. Collaborators would be welcome! I have python code which implements the procedure, available upon request.