Math Notes

Notes I’ve written from time to time.

Logic and Set Theory

• I wrote some notes for a (now defunct) Set Theory meetup.
• Scott’s Model of the Lambda Calculus. These are based on some notes I wrote up in the early 1970s, for a seminar on an early version of Dana Scott’s model of the untyped lambda calculus. These notes have nothing to say about Scott’s subsequent work on the typed lambda calculus, and the general notion of types. (Post)
• Algorithmic Information Theory. I wrote these notes sometime in the early 90s, based mostly on Chaitin’s book Algorithmic Information Theory.  (Post)
• Three items on recursion theory: Friedberg’s Enumeration without Duplication (post) and Simple Sets (post) and Shoenfield’s computation of the complexity level of the class of recursively enumerable sets.
• John Baez and I have been having a conversation about non-standard models of Peano arithmetic (PA). I have converted the story so far into pdf documents, formatted both for a small screen and a  medium-sized one. I will update these from time to time (but not that frequently).
• We’ve also been having a conversation about first-order categorical logic.

Other Stuff

• Algebraic Geometry Jottings, the story of my attempt to learn (more) algebraic geometry.
• Notes on Hatcher’s Algebraic Topology. Post.
• Notes on the wallpaper groups. Post.
• Notes on the de Smit-Lenstra article about Escher’s Prentententoonstelling. Post.
• Notes on Lie groups for a now defunct meetup.
• I participated in a meetup group that went through Leinster’s Basic Category Theory. I wrote up solutions to many exercises, plus supplementary material.
• Two notes on Stirling’s formula. First, easy derivations of parts of the formula, culminating in a determination of n! to within a factor of √2. Second, some notes on Ahlfors’ derivation (in the 2nd edition of his Complex Analysis). (Post)
• I translated Weierstrass’s paper on the Dirichlet Principle into English from the original German. Post.
• A post on Epstein relativity diagrams, formatted for small and medium screens.
• A very short note on principal and fiber bundles (small and medium formats), and a longer one on the Laplacian on the cube. Also Three takes on the tangent bundle. Post.
• Notes on quadratic reciprocity . Post.