# 18.A34 Mathematical Problem Solving (Putnam Seminar)

**Fall 2018, MIT**

**Class meetings:** Tuesdays and Thursdays 3–4pm in 2-147

**Instructor:** Yufei Zhao (see website for contact info)

**Grader:** Yau Wing Li

Please include “18.A34” in the subject line of your emails

## Course description

18.A34 is a seminar intended for undergraduate students who enjoy solving challenging mathematical problems, and to prepare students for the Putnam Competition.

**William Lowell Putnam Mathematics Competition:** The Putnam Competition is an annual mathematics
contest for undergraduates in the USA and Canada. This year it will be held Saturday, December 1, 2018.
**All students officially registered in the class are required to participate in the competition.** MIT students can **sign up** to take the Putnam Competition by completing this form by noon, Friday, November 9.

**Grading.** Based on homework and in-class presentations. Beyond grading for correctness, the grader may deduct points or grant bonus points based on the elegance of the solution and clarity of the writing. **Class attendance is required.** Please email me in advance if you cannot make it to class. Too many unexcused absences is cause for concern.

**Listeners.** MIT students who are not officially enrolled in the subject are welcome to sit in and participate, but should not hand in homework.

Student Support Services (S^{3}) and Student Disability Services

## Schedule and homework

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** (please do not submit more than six), at least four from the topics problem set based on the lecture. Do not hand in supplementary problems rated strictly less than [2]; these are too easy. For multi-part problems, you may decide what counts as “one solution”, as long as it is reasonable (i.e., not too trivial).

Homework submissions are due at the end of class. Please type or write legibly. They will be graded similarly to the Putnam competition. (Non-registered students should not hand in solutions.)

*Sources.* At the top of each assignment, you must write either “**Sources consulted: none**” or a list of all sources consulted other official course material. Examples include: names of people you discussed solutions with (whether or not they are taking the class), books, Wikipedia and other websites. Do not look up solutions to homework problems online (or offline).

*Collaborations.* “Reasonable” collaboration is permitted, everyone must write their solutions individually and acknowledge their collaborators in *sources consulted*.

(Schedule subject to change)

Lecture date | Topic | Guest lecturer | HW due & presentations | Supplementary set |
---|---|---|---|---|

R 9/6 | Hidden independence and uniformity | T 9/11 | #1 | |

R 9/13 | Sums and integrals | Evan Chen | T 9/18 | #2 |

R 9/20 | Analysis | Ashwin Sah | T 9/25 | #3 |

R 9/27 | Recurrences | Yunkun Zhou | T 10/2 | #4 |

R 10/4 | Inequalities | Mehtaab Sawhney | R 10/11 (Tuesday holiday) |
#5 |

No lecture | Probability | T 10/16 | #6 | |

R 10/18 | Linear algebra | Allen Liu | T 10/23 | #7 |

R 10/25 | Abstract algebra | Zilin Jiang | T 10/30 | #8 |

R 11/1 | Congruences | Junyao Peng | T 11/6 | #9 |

R 11/8 | Combinatorial configurations | David Stoner | T 11/13 | #10 |

R 11/15 | Generating functions | Ben Gunby | T 11/20 | #11 |

(No homework submissions required for 11/27–12/6)

T 11/27: Students present solutions to Putnam 2017 exam

R 11/29: Students present solutions to Putnam 2016 exam

**Saturday 12/1: Putnam Competition**

T 12/4: Students present solutions to part A of Putnam 2018 exam

R 12/6: Students present solutions to part B of Putnam 2018 exam

**Final homework**: Create your own Putnam-style problem. Submit your problem and solution separately on Stellar by **Saturday Dec 8**. Your problem submissions will be visible to other students in the class, and the solutions will be made visible by Sunday afternoon as well.

T 12/11: Presentations of student-created problems

## Additional resources

You may find the following optional resources helpful for additional preparation. The books can be found at Hayden Library.

**Previous Putnam problems and solutions**

- Putnam archive by Kedlaya
- The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions and Commentary by Kedlaya, Poonen and Vakil

**Additional books helpful for preparation**

- Problem-Solving Through Problems by Larson
- Putnam and Beyond by Gelca and Andreescu

Previous course homepage from Fall 2017