Projects

I like (re)designing courses, and most of what follows came out of that. Notes and problem sets are written to be usable on their own, and most are accessible to undergraduates and to advanced high-school students.

How to Discover the Bell Curve

A week-long class deriving the normal distribution from least squares, following Gauss’ calculation of the orbit of Ceres.

Monte Carlo Methods

Course notes for a semester-long JHU AMS course on simulation and Monte Carlo estimation.

Visual Math Lab

A growing collection of interactive visualizations for teaching and learning mathematics.

Open Textbook for Linear Algebra

WeBWorK problem sets added to a PreTeXt open educational resources linear algebra textbook.

Introduction to Optimization

A quarter-long course on linear programming and duality, rebuilt around applications and modeling.

Algebraic Topology

Problem sets from a graduate course on the fundamental group, covering spaces, and singular homology.

Discrete Math, Fully Asynchronous

Rebuilding a second-year discrete math course for fully asynchronous delivery, with video lectures and hundreds of WeBWorK problems.

Theorem Proving in Lean

A fully interactive week-long class on the Lean theorem prover; you learn by solving exercises in the browser.

Riemann Surfaces

Constructing Riemann surfaces as graphs of holomorphic functions, ending with Fermat’s last theorem for function fields.

From High School Arithmetic to Group Cohomology

Group extensions and exact sequences, arrived at by taking carrying in multi-digit addition seriously.

Galois Correspondence of Covering Spaces

Covering space theory for graphs and surfaces, as an introduction to algebraic topology and its links to group theory.

Crash Course on Linear Algebra

A week-long, proof-based introduction to linear algebra in IBL format.

Expository Notes

Personal notes on spectra, h-principles, gauge theory, and assorted other topics.

Formalizing Mathematics in Lean

Contributions to mathlib, the Lean theorem prover’s mathematics library.

Would I Ever Lie Group to You?

Matrix groups, and how they arise as the symmetries of spaces.

How Curved Is a Potato?

Principal, Gaussian, and mean curvature, developed for potatoes embedded in three-space.

Cohomology via Sheaves

Čech cohomology on graphs, and cohomology computations for simple spaces.

Symmetries & Polynomials

A two-week intersession course taking non-math majors from group theory to the unsolvability of the quintic.

Honors Single Variable Calculus

Two semesters of calculus in one, taught IBL-style in a flipped classroom.

More Mathcamp Classes

Notes from several other week-long Mathcamp classes. Less polished, still useful.

Hitchhiker’s Guide to Algebraic Topology

A two-week intersession course introducing non-math majors to algebraic topology and its applications.