ICTS Course no.: MTH 122.5

Venue: Online

Class timings: Tuesdays and Thursdays from 11:00 AM to 12:30 AM (1 hr tutorial once a week, tutorial timings to be announced later)

First meeting: 10th August 

Course description: 

Topology: Homotopy, retraction and deformation, fundamental group, Van Kampen theorem, covering spaces and their relations with the fundamental group, universal coverings, automorphisms of a covering, regular covering. 

Geometry: Differential geometry of curves and surfaces, mean curvature, Gaussian curvature, differentiable manifolds, tangent, and cotangent spaces, vector fields and their flows, Frobenius theorem, differential forms, de Rham cohomology.   

Grading policy:

20% assignments,  40% midterm,  40% final.