Relativity and Geometry (late February ~ April)

A lean motivational introduction is confined to how Maxwell’s electromagnetism inevitably led to Special Relativity. Given the heavy mathematics that often precedes General Relativity, we offer the relativistic Kepler problem first, after the relativistic point-particle action is understood. The rest of Part I strives to give a comprehensive picture of modern differential geometry, although more abstract concepts such as bundles are relegated to the Appendix, in favor of computationally useful tools such as the Maurer–Cartan. For this preparatory part, lectures are planned to be more detailed. 

1. Electromagnetism and Special Relativity ( chapter_1_download )

2. Particle Motion under Relativistic Gravity ( February 25th )

3. Calculus on Manifolds

4. Riemannian Geometry

5. Maurer–Cartan