For a General Audience
Curvature of Polyhedra: A quick introduction to the idea of the curvature of a surface from the perspective of polyhedra.
For Math Undergrads
Coordinate-Free Linear Algebra: A tour of linear algebra from the perspective of universal properties, culminating in a coordinate-free presentation of many familiar concepts like the trace and determinant. The target audience has seen linear algebra before from a “coordinates and matrices” perspective and is comfortable with mathematical proof.
Differential Geometry: Definitions and Pictures: These are slides from a three-week lecture series I gave at Google about developing intuition for the basic definitions in differential geometry. The target audience has had a class in multivariable calculus and probably linear algebra. As always when reading slides without seeing the talk, some parts might not make sense out of context.
I’m working a series of articles on physics for mathematicians; more info can be found at that link. The articles in this series so far are:
- Hamiltonian Mechanics
- Quantum Mechanics I - Foundations
- Connections Crash Course. This article comes with two short supplements, on G-Bundles and Holonomy and Curvature.
- Electromagnetism as a Gauge Theory
- Thermodynamics and Statistical Mechanics. This article comes with one supplement, on A Toy Model of Thermodynamic Behavior.
My plans for future articles include (in no particular order):
- General Relativity
- Quantum Field Theory and the Standard Model (this will probably be several articles)
- Quantum Mechanics - The Feynman Path Integral
- Quantum Mechanics - Decoherence and Measurement
- Statistical Mechanics - Phase Transitions and Renormalization