Teaching‎ > ‎

Math 761 (Fall 2017)

Announcements
  • Welcome to the class! The first lecture is at 9:55am on Wednesday, Sep. 6, in Van Vleck B235.

Lectures

Time: 9:55am-10:45am, on Mondays, Wednesdays, and Fridays
Location: B235 Van Vleck Hall


Instructor

Lu Wang
Office: 809 Van Vleck Hall


Office Hours

Time: 11am-Noon, 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. 29-31: #1-1, 2, 4, 6, 7, 8, 9, 10
  • HW#2 (due Oct. 6): [L] pp. 48-19: #2-1, 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, in-class 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. Make-up 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. 1-24 
  • Week of Sep. 11 
    • Smooth maps, diffeomorphisms: [L] pp. 32-40
    • Partition of unity: [L] pp. 40-47
  • Week of Sep. 18
    • Tangent vectors: [L] pp. 50-60
    • Coordinate representations: [L] pp. 60-65
    • Tangent bundles: [L] pp. 65-75
  • Week of Sep. 25
    • TBA
  • Week of Oct. 2
    • TBA
  • Week of Oct. 9 
    • Presentation I on Oct. 9 and 13
  • Week of Oct. 16 
    • TBA
  • Week of Oct. 23
    • TBA
  • Week of Oct. 30 
    • TBA
  • Week of Nov. 6  
    • TBA
  • 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 
    • TBA
  • Week of Dec. 4 
    • Presentation III on Dec. 8
  • Week of Dec. 11 
    • Presentation III on Dec. 11


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