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.

For Mathematicians

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:

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
  • Spin
  • Statistical Mechanics - Phase Transitions and Renormalization