Teaching
Uganda Lecture Series
In August 2023, I gave a lecture series titled Modern Applications of the Diamond Lemma at Makerere University in Kampala, Uganda. The lecture series was part of the 2023 East Africa Algebra Research Group workshop. Here are drafts of the lecture notes, exercise sheets, and solutions:
Lecture1 - Reduction systems.
Lecture2 - Diamond Lemma
For further applications in noncommutative geometry see Dan Rogalski's excellent notes. Here is Bergman's original paper on the subject.
I am returning to Kampala in December to teach a course on Deformation Theory of Associative Algebras outlined here.
Homological Algebra Class
Winter 2022 I taught Topics in Algebra to 3rd year undergraduate students at University of Hasselt. The course is an introduction to homological algebra with focus on projective resolutions and Ext and with applications to group cohomology and the space form problem.
Here are the lecture notes:
Lecture 0 - motivation and ring theory
Lecture 1 - introduciton to modules
Lecture 2 - functors, hom functor, induced maps
Lecture 3 - free modules, projective modules, universal properties
Lecture 4 - tensor products (following Conrad's notes), flat modules
Lecture 5 - complexes, exact sequences, resolutions
Lecture 6 - maps of complexes, Ext and Tor are (well-)defined
Lecture 7 - snake lemma, LES is homology, LES in Ext
Lecture 8 - group cohomology, bar resolution, extensions of groups
Lecture 9 - groups acting freely on spheres
Computing Ext - supplemental notes on how to compute Ext by hand
Here is an (experimental) explainer video about lifting modules maps to chain maps of projective resolutions.
An example of building a free resolution by taking successive kernels (the red maps), finding their projective covers (the blue maps) and then using the composition (the purple maps).
Differential and Integral Calculus Classes
In Fall 2023, I taught Calculus with Analytic Geometry I as part of Florida State University's Broad Curriculum Program in London. The class included excursions to Hyde park and the Tate Modern as well as a guest lecture from a data scientist. I am currently teaching Calculus with Analytic Geometry II. Email me if you are interested in course materials including: (1) 54 integrals with hints, answers, and solutions, (2) theoretical true/false questions, and (3) an introduction to neural networks.