MATH 448 - Introduction to Differential Geometry

3 units (fi 6)(EITHER, 3-0-0)

Topological and smooth manifolds; continuous, smooth, and invertible maps between manifolds; submanifolds; vector fields and their flows; Lie groups and algebras; left-invariant vector fields on a Lie group; differential forms, vector bundles and tensor fields; integration on manifolds; de Rham cohomology. Time permitting, additional topics at the discretion of the instructor. Prerequisite: one of MATH 209, 215, 217, 315 or MA PH 351, and one of MATH 225 or 227.

MATH 521 - Differential Manifolds

3 units (fi 6)(EITHER, 3-0-0)

Topological and smooth manifolds; continuous, smooth, and invertible maps between manifolds; submanifolds; vector fields and their flows; Lie groups and algebras; left-invariant vector fields on a Lie group; differential forms, vector bundles and tensor fields; integration on manifolds; de Rham cohomology. Time permitting, additional topics at the discretion of the instructor. Prerequisite: one of MATH 209, 215, 217, 315 or MA PH 351, and one of MATH 225 or 227. Note: Credit cannot be obtained in both MATH 448 and MATH 521.