Each week there is a lecture (usually by a guest lecturer) on a specific topic or technique, accompanied by a homework problem set. In the following class, students present solutions to problems from the homework. In addition, each week the class is assigned a list of “supplementary problems” ranging from all topics, not necessarily related to the lecture.
Each problem set contains a (sometimes long) list of problems. You are encouraged to work on as many as you like, but only hand in your six best solutions, at least four from the topics problem set based on the lecture. For multi-part problems, you may decide what counts as “one solution,” as long as it is reasonable (i.e., not too trivial).
| SES # | TOPICS | ASSIGNMENTS |
|---|---|---|
| 1–2 | Hidden independence and uniformity | |
| 3–4 | Sums and integrals | |
| 5–6 | Analysis | |
| 7–8 | Recurrences | |
| 9–10 | Inequalities | |
| 11–12 | Probability | |
| 13–14 | Linear algebra | |
| 15–16 | Abstract algebra | |
| 17–18 | Congruences | |
| 19–20 | Combinatorial configurations | |
| 21–22 | Generating functions |
Additional Topics from Previous Editions of the Course
| TOPICS | ASSIGNMENTS |
|---|---|
| The Pigeonhole principle | |
| Integer part | |
| Roots of polynomials | |
| Limit problems |
Acknowledgements
Other than those listed below, all problem sets were created by anonymous guest lecturers.
- All supplementary problems, Hidden independence and uniformity problems, Probability problems, and additional topics assignments from previous editions are based on files created by Prof. Richard Stanley in earlier versions of the course.
- Sums and integrals problems courtesy of Even Chen, a guest lecturer in the class.
- Inequalities problems courtesy of Mehtaab Sawhney, a guest lecturer in the class.
- Congruences problems courtesy of Junyao Peng, a guest lecturer in the class.
All files are used with permission.
