Problems based on class lectures, as well as supplementary
problems, will be posted during the week of the lecture. You are
expected to solve on your own problems which you hand in. Some
collaboration with other students in the seminar is o.k. as long as
you don't simply copy someone else's work. You should also not hand in
any problems whose solution you are already familiar with. If you get
completely stuck you can hand in solutions from another source,
provided: (1) the solution is written up in your own words, (2) you
understand the solution, and (3) you indicate on your paper the source
of the solution. You should hand
in **exactly** six problems
each week, at least
four from the problem set based on the lecture. Do not hand in
supplementary problems rated less than [2]; these are too easy. Please
do not hand in more than six problems, as this creates extra work
for the graders.

Problem sets will be due in class the first Tuesday after they are handed out, unless otherwise specified.

- Lecture of September 5 (the Pigeonhole Principle)

Pigeonhole Problems

Supplementary Problems #1: 1-13

- Lecture of September 12 (Congruences)

Congruences Problems

Supplementary Problems #2: 14-27

- Lecture of September 19 (Linear Algebra) notes

Linear Algebra Problems

Supplementary Problems #3: 28-39

- Lecture of September 26 (Inequalities)

Inequalities Problems

Supplementary Problems #4: 40-50

- Lecture of October 3 (Polynomials)

Polynomials Problems

Supplementary Problems #5: 51-63

- Lecture of October 10 (Invariants) - guest lecture by Tanya Khovanova

Invariants Problems (all six problems from this problem set)

- Lecture of October 17 (Recurrences)

Recurrences Problems

Supplementary Problems #6: 64-76

- Lecture of October 24 (Analysis) notes

Analysis Problems

Supplementary Problems #7: 77-87

- Lecture of October 31 (Probability)

Probability roblems

Supplementary Problems #8: 89-100

- Lecture of November 7 (Generating Functions) - guest lecture by Richard Stanley

Generating Functions Problems

Supplementary Problems #9: 101-110

- Lecture of November 14 (Hidden Independence and Uniformity) - guest lecture by Shan-Yuan Ho

Hidden Independence and Uniformity Problems

Supplementary Problems #10: 111-122

- Lecture of November 21 (Abstract Algebra)

Algebra problems

Supplementary Problems #11: 123-133