A collection of interactives, worksheets, and notes for my students and anyone else wandering through. I hope you find something you like!
Subject
Type
Interactive · Logic & Foundations · Discrete MathematicsFunctions on a Three-Element SetAll 27 functions from {a, b, c} to itself, sitting at the lattice points of a 3×3×3 cube. Toggle a property (bijective, constant, idempotent, a fixed point) or group them into the seven types up to relabeling.Open ↗
Worksheet · Real AnalysisAttracting and Repelling Fixed PointsThe derivative test for fixed points (|f′(p)| < 1 attracts, |f′(p)| > 1 repels), used to decide whether a recursively defined sequence converges, and to which limit.Open ↗Key
Worksheet · Abstract Algebra · Logic & FoundationsSets and CategoriesProblems on products, coproducts, and universal properties, following Aluffi’s Chapter 0.Open ↗Key
Worksheet · Number TheoryFarey SumsThe Farey sum a/b ⊕ c/d = (a+c)/(b+d) and the mediant procedure that builds the Farey sequence stage by stage.Open ↗Key
Thesis · ResearchDeformations and Products of Polish GroupsPhD thesis, University of Illinois at Chicago, 2019. Studies the large-scale geometry of Polish groups by way of deformation retracts and knit (Zappa–Szép) product decompositions.Open ↗
If something here is useful to you and you would like to go further, my tutoring contact form is on the home page. I also post the occasional video on YouTube.