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 : instead of a lecture, Chapter 1 is offered in the form of a pdf file. )

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

3. Calculus on Manifolds ( March 8th, July 12th, March 16th : The middle installment, now replaced by a newer and leaner recording, may be used in place of the first which is a little too verbose. The first installment offers you more of the underlying thoughts, mathematical and physical, behind the framework here, so I kept it for the uninitiated.)

4. Riemannian Geometry ( March 21st ; I decided to jump to Chapter 5's version of Riemann curvature, which shall be more useful down the road. )

5. Maurer–Cartan ( April 19th, April 22nd )