Mathematical Methods of Physics II

The course is one in a series of several courses devoted to teaching modern mathematical techniques in physics. On one side, it further develops topics of Symmetry and Group theory in Physics offering a more profound discussion of Lie groups and Lie algebras, including weight space description and classification of the latter, as well as elements of the representation theory. On the other side, it introduces elements of abstract topology and then differential geometry with their application in physics. Topics include smooth manifolds, tensors, differential forms, metric spaces, introduction to Riemannian, symplectic, and complex geometry. The course is designed for physics students interested in theoretical studies. It serves as a prerequisite for a follow-up course Geometrical Methods in Theoretical Physics and also provides a valuable mathematical complement to the course Gravitation and Cosmology.