Large language models have made it much easier to build interactive, visual material for teaching: explorers you can click through, sliders that show a model changing, exercises that check your work as you go. Things that once took weeks of programming can now be sketched in an afternoon. The results still need real refining, though: checking the mathematics, tightening the explanations, and finding out what actually helps students learn. Doing that work well is, I think, part of what math 2.0 looks like. Below are some early attempts from two of my courses, Applications of Linear Algebra (MATH 2LA3) and Number Theory (MATH 3H03).
Fall 2026
Review games
Pivot Peak — A pixel-art climbing game reviewing row operations, echelon forms, pivots and linear independence. Answer 12 randomized questions to reach the summit and unlock a bonus mode.
Corner Cabin — A pixel-art quiz on linear optimization by the geometric method and the simplex method. Twelve randomized questions; two wrong answers bring the cabin down.
Lectures: eigenvalues (Chapter 5)
Eigenvalues to Learning — Day 1: determinants as the route to eigenvalues, and why eigenvalues decide whether learning algorithms converge. Includes a clickable cofactor explorer.
Hawks, Mice and Eigenvalues (slides) — A predator–prey model that motivates eigenvectors, with a hunting-rate slider, a month-by-month matrix stepper and an eigenvector hunt.
Hawks, Mice and Eigenvalues (field notebook) — The same lecture as a single reading page, with exercises and answer checks.
Working the Long Run — In-class exercises on discrete systems x(k+1) = Ax(k): worked examples, seven mystery matrices to classify, and word problems.
Flowing to the Long Run — Solving x′ = Ax with eigenvectors: attractors, repellers and saddles, with phase-plane widgets you can run forward in time.
Practice and review
Gradient Descent Explorer — Lab 1: watch gradient descent move across a quadratic bowl and see how the eigenvalues of I − ηH decide whether it converges.
Eigenvalue Exercise Book — Ten applied problems on x(k+1) = Ax(k) (predators and prey, age classes, lakes) with step-by-step answer checking and hints.
Thinking in Eigenvectors — Test 2 review deck (sections 5.6–5.7): the six question types, a classification drill and a quick-fire round.
Test 2 Flashcards — Self-marking flashcards for Test 2 (sections 5.6–5.7) with topic filters, fresh numbers each time and worked answers.
Winter 2026
Roots of Unity — A nine-page walkthrough: roots of unity on the unit circle, why they sum to zero, cyclotomic polynomials, and arithmetic in ℤ[ω₃] and ℤ[ω₅] with the steps shown.
Number Field Explorer — Review degree, minimal polynomials and bases, then classify six number fields and pick the polynomial that builds a field with a given property.
Computing Legendre Symbols — Fifteen practice problems in three difficulty tiers using the supplements and quadratic reciprocity, with a review page and a strategy guide.
Gauss Sums: Reciprocity — A four-page route to a proof of quadratic reciprocity through Gauss sums, with the sums worked out for p = 3, 5 and 7.