Introduction to Mathematical Physics

The first few chapters of the book cover basic differential geometry, including the theory of manifolds, vector fields, and differential forms. These concepts are used to formulate Maxwell’s equations on arbitrary spacetime manifolds. The second part of the book presents the theory of vector bundles and connections and uses these concepts to discuss gauge theory and its relation to knots. The final part of the book explains Riemannian geometry and its applications in general relativity. Ideally, I would like to at least get to the section on knot theory, but in principle we could stop anywhere and it would still be a satisfying experience for the student. Actually, I think there’s a danger that we might finish the book too soon. If that happens, there are plenty of online materials and texts that I can share with the student. 

Book: 
John Baez and Javier P. Muniain, Gauge fields, knots and gravity
Term: 
Spring
Year: 
2016