**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.

- Teacher: Rukmini Dey