Guided reading and material presentation by the students. Selected topics in group theory and differential geometry. Amount covered will depend on rate of progress in class. 

A) Introduction to groups and representations: semigroups and groups, morphisms, subgroups and, cosets, conjugacy classes, normal subgroups, permutation group. Representations, faithfulness, reducibility, Schur’s lemma,characters. Lie groups: continuous groups, generators and Lie algebras. 

B) Introduction to differential geometry and topology: Riemannian differential geometry manifolds, co-variant and contra-variant vectors, tensors and operations, metric tensor, covariant derivative and connection (Christoffel symbols), geodesics. Differential forms, wedge product, hodge dual, differentiation and integration. Homotopy,  topological defects.