Math 8302: Manifold and Topology
Time
3:35pm - 4:25pm MWF
Location
Vincent Hall 20
Office
Vincent Hall 365
Zoom Meeting ID
Office hours
Wednesday 1pm-2pm in office, Friday 12:30pm - 1:30pm in office, or by appointment
Textbooks
I will very loosely follow
- Introduction to smooth manifolds by John M Lee.
Contents
Smooth manifolds, tangent spaces, embedding/immersion, Sard’s theorem, Frobenius theorem, differential forms, integration, curvature, Gauss-Bonnet theorem. Time permitting: de Rham, duality in manifolds. A detailed day by day plan can be found on Canvas.
Prerequisites
Knowledge of basic point-set topology and multivariate calculus will be essential for this course.
Homework
Homework will be assigned on weekly on Canvas. Collaboration on homework is encouraged.
Exams
There are one midterm exam and one final exam. Both exams are take home exams. No collaboration is allowed. You can use books or notes, but you are not allowed to use internet for the exams.
Midterm exam: Exam time: 3/14-3/18
Final exam: Exam time: 5/2-5/6
Grading policy
Your grade is based on homework(60%) and the exams(40%).