Problems based on class lectures, as well as supplementary problems, are handed out 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 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.

Solutions to all of the problems are not provided, but a selection of hints and answers to supplementary problems are available.

1 The Pigeonhole principle

Pigeonhole problems (PDF)

Supplementary problems #1: 1-13 (PDF)

2 Probability theory

Probability problems (PDF)

Supplementary problems #2: 14-27 (PDF)

3 Congruences and divisibility

Congruence problems (PDF)

Supplementary problems #3: 28-38 (PDF)

4 Generating functions

Generating function problems (PDF)

Supplementary problems #4: 39-49 (PDF)

5 Integer part

Integer part problems (PDF)

Supplementary problems #5: 50-61 (PDF)

6 Inequalities

Inequalities problems (PDF)

Supplementary problems #6: 62-73 (PDF)

7 Zeros of polynomials

Zeros problems (PDF)

Supplementary problems #7: 74-83 (PDF)

8 Putnam practice Supplementary problems #8: 84-95 (PDF)
9 Hidden independence

Hidden independence problems (PDF)

Supplementary problems #9: 96-106 (PDF)

10 Putnam practice (cont.) Supplementary problems #10: 107-116 (PDF)
11 Limit problems

Limit problems (PDF)

Supplementary problems #11: 117-126 (PDF)


Putnam practice (cont.)

Linear algebra problems

Linear algebra problems (PDF)

Supplementary problems #12: 127-139 (PDF)


Solutions to all of the problems are not provided, but a selection of hints and answers to the Supplementary Problems are available.

Some Hints and Answers to Supplementary Problems (PDF)

More Hints and Answers to Supplementary Problems (PDF)