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 ( March 8th, March 10th, March 16th : the first two contents overlap much and are complementary in a sense, with the first starting at a more basic level, and the last deals with exterior calculus. I hope to redo a video for this chapter in the near future in a more coherent manner. )

4. Riemannian Geometry ( March 21st ; after a long hiatus due to an instance of flu, I decided to jump to Chapter 5's version of Riemann curvature, which shall be more useful down the road. To appear before the end of April, as promised.)

5. Maurer–Cartan ( April 19th ; pending one final installment for examples and also for one key confusing fact about the definitions of Riemann curvature tensor often found elsewhere )