University of British Columbia, Department of Mathematics

MATH 425 September-December 2012

Course Information

Classes: Mon/Wed/Fri 10-11am in room MATH 204;

Textbook: Introduction to smooth manifolds, by John M. Lee, 2003, Graduate texts in mathematics, Volume 218.
(the e-book version can be accessed online at Also, a pdf of the whole book can be found at

In this course we study the basic theory of smooth manifolds. We will consider fundamental constructions/objects on manifolds including vector bundles, tensors, differential forms and submanifolds. Depending on time, we may also discuss one or more of the following topics: Integration on manifolds, De Rham Cohomology and Lie Groups and Lie algebras.