Course Synopsis. The course is an introduction to smooth manifolds. Topics to be covered include: smooth maps (including immersions, submersions and embeddings), Lie groups and homogeneous manifolds, vector bundles, vector fields and differential forms (including orientation, integration and Stokes's Theorem), integral manifolds (the Frobenius Theorem) and foliations. Additional topics (as time allows) may include connections on vector bundles.

Prerequisites. Math 532 (differential and integral calculus in several variables).

Text. We will not closely adhere to a text. Good references for the material we will cover include Boothby's An Introduction to Differentiable Manifolds and Riemannian Geometry and Jack Lee's Introduction to Smooth Manifolds. The latter is available as a free download through Duke Library. Before the first day of class: familiarize yourself with the contents of Lee's Appendix (Topology, Linear Algebra, Calculus, and Differential Equations), and keep this material in mind as a useful reference as we proceed through the course.

Lectures. Tuesday and Thursday, 4:40 - 5:55pm, Physics 205. No phones, computers or similar devices permitted.

Instructor. Prof. Robles, 023 Physics Building, robles {at} math.duke.edu.

Course Grade. Based on weekly assignments (50%), two midterms (15% each) and a final exam (20%).

Dates. Midterm 1: Oct 03 (Thu). Midterm 2: Nov 14 (Thu). Final exam: Dec 11 (Wed), 2:00 - 5:00pm

Homework. Submit all work single-sided and stapled. Late HW is not accepted. Missed assignments receive a score of zero; the lowest HW score will be dropped.

Make-up policy. Late HW is not accepted.
        There are no make-ups for the midterm exams: If you miss a midterm that score will be replaced by your score on Part 1 of the Final Exam.
        Exceptions to these course policies are made only as required by the University Policy.

Grade complaints. If you think an assignment or exam was graded incorrectly you have one week from the time the graded assignment was returned to you to bring the issue to the instructor's attention. No complaints after that time will be considered.