<p>Lecture, three hours; discussion, one hour. Manifolds, tangent vectors, smooth maps, tangent bundles and vector bundles in general, vector fields and integral curves, Sard theorem on measure of critical values, embedding theorem, transversality, degree theory, Lefshetz fixed-point theorem, Euler characteristic, Ehresmann theorem that proper submersions are locally trivial fibrations. S/U or letter grading.</p>

Mathematics

Combining rigorous, inclusive pedagogy with opportunities for co-curricular activities—including research, internships, and community engagement—the College provides students with diverse learning experiences that helps them thrive, become critical thinkers, and transform society.

College of Letters and Science

The department explores the frontiers of pure and applied mathematical research.

General Catalog

Differential Topology

MATH225A

4 units