For a General Audience

Curvature of Polyhedra: A quick introduction to the idea of the curvature of a surface from the perspective of polyhedra.

Generating Functions I - How to Count with Power Series: An introduction to generating functions, a powerful counting technique, for students with some exposure to calculus.

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.

The Riemann Zeta Function and the Distribution of Primes: An exploration of the relationship between the famous Riemann zeta function and number theory, including an explanation of what the Riemann Hypothesis would tell us about the distribution of the primes. The target audience has seen enough complex analysis to know the Residue Theorem, but might not know anything about the zeta function, the Riemann Hypothesis, or any analytic number theory at all.

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:

• Hamiltonian and Lagrangian 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.
• Quantum Mechanics II - The Path Integral
• Quantum Field Theory I - Free Fields
• Quantum Field Theory II - Interacting Fields and Scattering
• General Relativity. This article comes with a supplement on The Lagrangian Approach to General Relativity.
• Quantum Field Theory III - Perturbation Theory and Feynman Diagrams

My plans for future articles include (in no particular order):

• Quantum Field Theory (this will probably be one more article)
• Topics in Quantum Field Theory, possibly including:
  • Unstable Particles
  • Discrete Symmetries and the CPT Theorem
  • Spontaneous Symmetry Breaking
  • A Tour of the Standard Model
• Quantum Mechanics - Decoherence and Measurement
• Spin
• Statistical Mechanics - Phase Transitions and Renormalization