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

Exercises with Solutions

For further applications in noncommutative geometry see Dan Rogalski's excellent notes. Here is Bergman's original paper on the subject.

In November 2024, I gave a lecture series titled: Deformation Theory of Associative Algebras.

The lectures were recorded and video is available here.

For more information see:

-Schedler's MSRI lecture notes,

-Witherspoon's amazing book, or

-Gerstenhaber's original paper.

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 how to build 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.

In Winter 2024, I taught Calculus with Analytic Geometry II. Here are 54 hard integrals with hints, answers, and solutions.

In Fall 2024, I taught Math 141 - Integral Calculus at UMass Boston.

Probability and Statistics

In Fall 2024, I taught Math 345 - Probability and Statistics. Each class begins with a "demonstration" like the derangement problem, the St. Petersburg Paradox, and the "class size" paradox. The first class began with the problem of points. I invited two volunteers to compete for a Snickers. One was head and the other was tails and the first to six wins. I flipped a coin five times and then with the score 3-2 lost the coin in midair (ahem, my pocket).

How should the volunteers split the Snickers?

Can you figure out which number is randomly generated?

a = 2023158152119581512419215208

b = 5689847268472147263000568421

c = 4355029835721084995915130994

d = 6345182790365481729634518279

e = 2134558914423337761098715972

f = 1592653589793238462643383279

Bonus: figure out how each other number was generated.

Commutative Algebra

In Fall 2025, I am teaching a graduate course on commutative algebra. Commutative algebra is a useful (albeit dry) tool in algebraic geometry, algebraic number theory, and homological algebra.

Riemann Surfaces

I am currently designing a course on Riemann surfaces for students with complex analysis.

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