Richard Evan Schwartz

Math Notes

These are notes on topics I've found
interesting and have tried to learn.
Sometimes I've written the notes for
a class I've taught, and sometimes
I've written them just for myself
A few have turned into expository articles.

Published Expository Articles

  • Pan Galactic Division Math Intelligencer
  • Conway's Nightmare: Brahmagupta and Butterflies Math Intelligencer
  • Kuehnel's CP2 triangulation Math Intelligencer
  • Two geometric pictures of Farey addition Math Intelligencer
  • PETs: Flux, Renormalization, and Compactification upcoming C.I.R.M. article

    Notes I'd like to publish

  • Dehn-Sydler Theorem (download the companion java program )
  • Expanders and Property T
  • Thurston's Shapes of Polyhedra
  • Mostow Rigidity
  • Alexander's Proof of the Jordan Curve Theorem
  • The Positive Dominance Algorithm

    Serious Topics

  • ZF, Choice, Zorn, Ordinals, Ultrafilters
  • Modular Forms and Fourier Series
  • NP Completeness
  • error correcting codes
  • Weierstrass uniformization
  • Notes on a Conjecture of Long and Reid
  • Notes on Manifolds

    Classic Theorems

  • transcendence of Pi & Lindemann's Theorem
  • Banach Tarski Theorem
  • Dehn Dissection Theorem
  • Kastelyn's formula for perfect matchings
  • The Cut Locus and The Jordan Curve Theorem
  • Existence of Bends on Paper Moebius Bands
  • Hadamard's Theorem
  • Link Universality
  • The Gauss-Salamin Algorithm
  • Erdos's Theorem on Random Graphs
  • Polya's Recurrence Theorem for Random Walks
  • The Isoperimetric Inequality
  • Sperner's Lemma and Homeomorphisms

    Short Notes

  • Machin's Formula for Pi
  • ArcTan relations
  • Multiplication and the Fast Fourier Transform
  • Basic Symplectic Geometry
  • Out(S6) and the Matthieu(12) Group
  • Components of the Fiber Product
  • Antoine's Necklace
  • Moebius maps preserve circles
  • Cayley's formula for labeled trees
  • Holonomy Proof of Morley' Theorem
  • Lily's Book of Math

    Research Notes I will never publish

  • Proving Disjointness with Foliated Patches
  • Billiards Obtuse and Irrational
  • Introduction to McBilliardsl (joint with Pat Hooper)
  • Outer Billiards, Arithmetic Graphs, and Multigrid Flows
  • A Textbook Case of Pentagram Rigidity