Announcements Welcome to the class! The first lecture is at 9:55am on Wednesday, Sep. 6, in Van Vleck B235.
Lectures
Time: 9:55am10:45am, on Mondays, Wednesdays, and Fridays Location: B235 Van Vleck Hall
Instructor
Lu Wang Office: 809 Van Vleck Hall
Office Hours
Time: 11amNoon, on Mondays and Wednesdays Location: 809 Van Vleck Hall
Textbooks [L] Introduction to smooth manifolds (2nd Edition), by John M. Lee, ISBN 13: 9780387954950(required)
 [W] Foundations of differentiable manifolds and Lie groups (2nd Edition), by Frank W. Warner(required)
 [S] A comprehensive introduction to differential geometry; Vol. 1 (3rd Edition), by Michael Spivak
Syllabus  Differentiable manifold, differential map
 Tangent space, vector bundle
 Immersion and embedding
 Vector field, Lie derivative
 Frobenius Theorem
 Tensor and exterior algebra
 Integration, Stokes' Theorem
 De Rham cohomology, Poincare Lemma
 Sard's Theorem, degree of a map
Homework
There will be homework assignments on a regular basis, mostly selected from the textbooks of Lee and Warner. Assignments are usually posted here about two weeks before the due date. Homework will be collected in beginning of the lecture on the due date and graded only on completeness. No late homework will be accepted.  HW#1 (due Sep. 22): [L] pp. 2931: #11, 2, 4, 6, 7, 8, 9, 10
 HW#2 (due Oct. 6): [L] pp. 4819: #21, 5, 13, 14 (to be continued)
 HW#3 (due Oct. 27): TBA
 HW#4 (due Nov. 10): TBA
 HW#5 (due Dec. 6): TBA
Presentations
There will be three short, inclass presentations of solutions to homework assignments that have been collected. You will be assigned the problem(s) to present about a couple of days in advance. Makeup presentations will not be provided. Tentative presentation times are listed here.  Presentation I: Oct. 9 and 13, in class, based on HW#1 and 2
 Presentation II: Nov. 13 and 15, in class, based on HW#3 and 4
 Presentation III: Dec. 8 and 11, in class, based on HW#5
Grading
 Homework: 10%
 Presentation I: 30%
 Presentation II: 30%
 Presentation III: 30%
Letter grades will be assigned roughly according to the following standard:  A: 90+
 AB: 86+
 B: 77+
 BC: 72+
 C: 60+
 D: 48+
 F: 0+
Lecture Schedule
The following lecture schedule will be updated during the semester.  Week of Sep. 6
 Introduction
 Manifolds and smooth structures: [L] pp. 124
 Week of Sep. 11
 Smooth maps, diffeomorphisms: [L] pp. 3240
 Partition of unity: [L] pp. 4047
 Week of Sep. 18
 Tangent vectors: [L] pp. 5060
 Coordinate representations: [L] pp. 6065
 Tangent bundles: [L] pp. 6575
 Week of Sep. 25
 Week of Oct. 2
 Week of Oct. 9
 Presentation I on Oct. 9 and 13
 Week of Oct. 16
 Week of Oct. 23
 Week of Oct. 30
 Week of Nov. 6
 Week of Nov. 13
 Presentation II on Nov. 13 and 15
 Week of Nov. 20
 No class on Nov. 24 due to thanksgiving recess
 Week of Nov. 27
 Week of Dec. 4
 Presentation III on Dec. 8
 Week of Dec. 11
 Presentation III on Dec. 11
