Handouts
Condensed extracts of commonly recurring topics.
  • Vector calculus, pdf
  • Point set topology, pdf
  • Commutative rings and fields, pdf
  • Polynomial rings and irreducibility, pdf
  • Field extensions and Galois theory, pdf
  • Modules over commutative rings, pdf
  • Constructability and solvability (and origami), pdf
    • Elementary group theory
    Notes for videos from "Abstract algebra" playlist at Advanced Math Cafe
  • What is abstract algebra?, pdf, video
  • Sets and subsets, pdf, video
  • Logical statements, pdf, video
  • Set operations, pdf, video
  • Functions, pdf, video
  • Properties of the integers, pdf, video
  • Groups (definition, first examples), pdf, video
  • Basic properties of groups, pdf, video
  • Groups of orders 1-3, pdf, video
  • Groups of orders 4-8, pdf, video
  • Equivalence relations, pdf, video
  • Integers modulo n, pdf, video
  • Important facts about integers modulo n, pdf, video
  • Subgroups, pdf, video
  • Lagrange's theorem, pdf, video
  • Cyclic groups, pdf, video
  • Symmetric groups, part 1, pdf, video
  • Symmetric groups, part 2, pdf, video
  • Homomorphisms, pdf, video
  • Basic properties of homomorphisms, pdf, video
  • Cayley's theorem, pdf, video
  • More properties of homomorphisms, part 1, pdf, video
  • More properties of homomorphisms, part 2, pdf, video
  • Normal subgroups, pdf, video
  • Centers, centralizers, and normalizers, pdf, video
  • Quotient groups, pdf, video
  • First isomorphism theorem, pdf, video
    • Diophantine approximation and aperiodic order
    Lecture notes covering the following topics: background on Diophantine approximation, shift spaces and Sturmian words, point sets in Euclidean space, cut and project sets, crystallographic restriction and construction of cut and project sets with prescribed rotational symmetries, a dynamical formulations of pattern recognition in cut and project sets, a discussion of diffraction, and a proof that cut and project sets have pure point diffraction measures.
  • Full lecture notes, pdf
  • Slides: Historical background, point sets in Euclidean space, cut and project sets, crystallographic restriction, and constructing lattices and cut and project sets with prescribed rotational symmetries pdf
  • Slides: Review of fourier analysis, measures, tempered distributions pdf
  • Slides: Dynamical encoding of patches, LR classification for cubical cut and project sets, discussion of canonical cut and project sets, and examples pdf
  • Practice problems pdf
    • Introduction to tiling spaces and cut and project sets
    Handout for workshop at 18th Galway Topology Colloquium, June 2015
  • Tiling spaces and cut and project sets, pdf
    • Topology of tiling spaces
    Lectures given by Lorenzo Sadun at the University of York in April 2014.
  • Lecture 1, pdf
  • Handout 1, pdf
  • Lecture 2, pdf
  • Handout 2, pdf
  • Link to Lorenzo's paper on PE cohomology
  • Lecture 3, pdf
  • Handout 3, pdf
  • Lecture 4, pdf
    • Constructibility, solvability, and origami
    Slides from a public lecture given for the York University Math Society
  • Slides from lecture, pdf
  • Video of lecture is available here
    • Topological groups
    A reading course held at the University of Bristol in Fall 2012.
  • Review of measure theory, Sara Munday, pdf
  • Hausdorff measure and dimension, Adam Morgan, pdf
  • Review of point-set topology, Alan Haynes, pdf
  • Properties of topological groups and Haar measure, Efthymios Sofos, pdf
  • p-adic numbers, Martin Hauge pdf
  • Adeles and ideles, Matthew Palmer, pdf
  • Characters and the Fourier inversion formula, Daniel El-Baz, pdf
  • Pontryagin duality, Samuel Chow, pdf
  • An application to ergodic theory, Christopher White, pdf
    • Notice: Unauthorized reproduction of any material contained on this website is prohibited. If you wish to use any of the content or images here for any reason other than for personal edification, please contact me first to obtain permission.