— Differential Topology

Prerequisites & course information

This version has ended; see updated course, below. Course Description: Differentiable manifolds, vector fields, transverse intersections, Sard's Theorem, orientations, intersection theory, the index of a vector field, differential forms, integration on manifolds, Stokes' Theorem, deRham cohomology, Morse functions, the Morse lemma, and the index of critical points. Learning Activities: Lecture 3 hour(s), Discussion 1 hour(s). Grade Mode: Letter. MAT 239 — Differential Topology (4 units) Course Description: Differentiable manifolds, vector fields, transverse intersections, Sard's Theorem, orientations, intersection theory, the index of a vector field, differential forms, integration on manifolds, Stokes' Theorem, deRham cohomology, Morse functions, the Morse lemma, and the index of critical points. Prerequisite(s): MAT 201A ; or consent of instructor; Vector calculus, point-set topology; MAT 250A & MAT 250B highly recommended. Learning Activities: Lecture 3 hour(s), Discussion 1 hour(s). Enrollment Restriction(s): Open to graduate students; open to undergraduate students with consent of instructor. Grade Mode: Letter. This course version is effective from, and including: Winter Quarter 2027. Learning Activities: Lecture 3 hour(s), Discussion 1 hour(s). Grade Mode: Letter. MAT 239 — Differential Topology (4 units) Course Description: Differentiable manifolds, vector fields, transverse intersections, Sard's Theorem, orientations, intersection theory, the index of a vector field, differential forms, integration on manifolds, Stokes' Theorem, deRham cohomology, Morse functions, the Morse lemma, and the index of critical points. Prerequisite(s): MAT 201A ; or consent of instructor; Vector calculus, point-set topology; MAT 250A & MAT 250B highly recommended. Learning Activities: Lecture 3 hour(s), Discussion 1 hour(s). Enrollment Restriction(s): Open to graduate students; open to undergraduate students with consent of instructor. Grade Mode: Letter. This course version is effective from, and including: Winter Quarter 2027.