18.101 - Analysis and Manifolds (Fall 2014)

PROBLEM SETS

Problem set 1 (in Munkres' book) - Due Monday, September 22

  1. Section 4, problem 3
  2. Section 6, problem 10
  3. Section 7, problem 4
  4. Section 8, problem 3
  5. Section 16, problem 1

Problem Set 2 - Due Monday, October 6

Problem Set 3 - Due Monday, October 20

Problem Set 4 - Due Wednesday, November 12

  1. Lecture 1, problem 2
  2. Lecture 2, problem 3
  3. Lecture 2, problems 6 and 7
  4. Lecture 3, problems 2 and 3

Problem Set 5 - Due Monday, November 24

  1. Lecture 5, problem 5 and part (b) of problem 6.
  2. Munkres, §24, problem 6.
    1. Show that O(n) is a compact n(n - 1)/2-dimensional manifold.
    2. Let I ϵ O(n) be the identity matrix. What is TIO(n)?
  3. Lecture 9, problems 4 and 5.
  4. Lecture 9, problem 10.

Problem Set 6 - Due Friday, December 5th

  1. Lecture 10, problems 3 and 10.
  2. Lecture 10, problem 8.
  3. Lecture 11, problem 7.
  4. Lecture 13, problems 5 and 6.