Difficulty Rating of Problems

I have included a difficulty level for each problem as follows:

  1. Easy: most students should be able to solve it
  2. Moderately difficult: many students should be able to solve it
  3. Difficult: a few students should be able to solve it
  4. Horrendous: no students should be able to solve it (without already knowing how)
  5. Unsolved

Further gradations are indicated by + and -. Thus a [3-] problem is about the most difficult problem that makes a reasonable homework exercise, and a [5-] problem is an unsolved problem that has received little attention and may not be too difficult.

"Reasonable" collaboration is permitted on problems unless stated otherwise. You should not simply copy another person's solution or obtain a solution from an outside source. If you have collaborated on a problem, please state so (with the name of the collaborator(s)) on your problem set.

The problem sets are due during the lecture noted in the table below.

Problem Set 1 (PDF) Hand in two from 1.1-1.7. Ideally you should work on all seven problems, but you should hand in only your two "best" problems, i.e., the ones whose solutions you feel are the most difficult and/or interesting Lecture 7
Problem Set 2 (PDF) Hand in two from 2.1-2.10 Lecture 11
Problem Set 3 (PDF) Hand in two from 3.1-3.7, 4.1, 4.3, 4.10-4.11, 4.20 Lecture 16
Problem Set 4 (PDF) Hand in one from 4.4-4.9, 4.12-4.19, and one from 5.1, 5.4, 5.6-5.9 Lecture 22
Problem Set 5 (PDF) Hand in two from 5.10-5.18, 5.24-5.29 Lecture 27
Problem Set 6 (PDF) Hand in 6.1 and one further problem from 6.3-6.8 Lecture 32
Problem Set 7 Make up two problems of your own and hand them in (with solutions). Problems may have multiple parts. Some of the parts can be unsolved (or, at least, you were unable to solve them), but each of the two problems should have at least one part with a (nontrivial) solution included. The problems can be on any material covered during the course Lecture 37