Math 110A - Section 1

Geometric Analysis
Fall 2011

Instructor:

Luke Cherveny

Lectures:

TF 12:30-1:50pm in Goldsmith 317

Office:

Goldsmith 303

Office Hours :

F 10:30-11 and TF 2-3:45

Email:   

cherveny@brandeis.edu

Textbook:

John M. Lee, Introduction to Smooth Manifolds

Grading:   

Final grade is determined by the following scheme:

• First Exam: 20%
• Second Exam: 20%
• Problem Sets: 60%

In order to receive a letter grade for this course, you must take both exams!

Exams:

First Exam	Friday October 28th
Second Exam	Approx. Wednesday December 14th

Both exams will be oral exams lasting about 15 minutes. Details and scheduling will be addressed at a future date.

Problem Sets :

Problem sets are due at the time of lecture . Please read and follow the guidelines for homework.

• Problem Set 1 - Due Sept 9
  • Lee p. 28-29: 1, 3, 5, 7, 9
• Problem Set 2 - Due Sept 23
  • Lee p. 78-79: 2, 6
  • Lee p. 100-102: 1, 6, 13
• Problem Set 3 - Due Oct 7
  • Lee: 4-18, 5-7, 5-10
  • Prove S^1 x S^n is parallelizable.
  • Prove that the set of all lines in R^2 (not just those through the origin) is a manifold.
• Problem Set 4 - Due Nov 4
  • Lee: 8-6, 8-9, 8-11, 8-17, 8-24
• Problem Set 5 - Due Nov 22
  • Lee: 12-7b, 12-10, 13-6, 14-1
  • Prove that the total space of the tangent bundle to a manifold is always orientable.
• Problem Set 6 - Due Dec 9
  • Lee: 15-1, 15-5, 15-7, 15-8

Late assignments are subject to penalty.

COURSE SYLLABUS

FINAL SYLLABUS