# Putnam Mathematical Competition

### What is it?

The **Putnam Mathematical Competition** is the best known mathematics competition for undergraduate college students in the United States and Canada. The topics cover a range of material in undergraduate mathematics, but most problems require only calculus (MAT 295-296-397), linear algebra (MAT 331), and discrete mathematics (MAT 375). The problems are not like standard textbook exercises: they require creative thinking, followed by a rigorous demonstration (strong proof-writing skills are essential).

### Sample problems

A few examples of problems from the competition, to give an idea of what they are:

- Find all prime numbers in the sequence 101, 10101, 1010101, 101010101, ...
- Prove that it is impossible to place four points on a plane so that the distance between any two of them is an odd integer.
- Find all positive integers that are within 250 of exactly 15 perfect squares.
- Suppose A and B are square matrices of the same size such that ABAB = 0. Does it follow that BABA = 0?
- Does there exist an integer N such that any rectangular grid of size A⨯B, with A, B greater than N, can be tiled by 4⨯6 and 5⨯7 pieces?
- Let f be a function on the real line such that f, f', f'', and f''' are positive and f''' ⩽ f. Prove that f' < 2f.

These are sources of Putnam-type practice problems, listed in the order of increasing difficulty.

### Practice Sessions

Weekly problem-solving sessions are run in Fall semesters as a joint effort of the Mathematics Department and Pi Mu Epsilon honor society. Everyone is welcome to participate, even if you do not plan to take part in the competition.

### Participation

If you are interested in participating, email Leonid Kovalev to be added to SU Putnam team roster, and try to attend as many practice sessions as you can.

### Past Participants

- 2023: Spencer Evans-Cole, Anthony Mazzacane, Juliana Mini, Yutong Tang.
- 2022: Yuming Jiang, Anthony Mazzacane, Michael Perry, Connor Ritchie, Rongtian Ye.
- 2021: Yuming Jiang, Anthony Mazzacane, Michael Perry, Connor Ritchie.
- 2020: Shamil Askarov, Jason Curtachio, Anthony Mazzacane, Michael Perry, Aaron Pierron, Connor Ritchie, AiJing Wu, Yantao Wu
- 2019: Connor Ritchie, Yantao Wu, Xuerui Yang, Sifei Zhu.
- 2018: Yantao Wu, Xuerui Yang, Jinyang Zhou.
- 2017: Binyan Ding, Yijie Lu, Jiaxun Song, Xuerui Yang.
- 2016: Binyan Ding, Manxi Qin, Zhenyun Shi, Xuerui Yang.
- 2015: Binyan Ding, Kathryn Munster, Kaitlin O'Rourke, Manxi Qin, Grant Webster.
- 2014: Binyan Ding, Jiajin Lei, Stephen Sorokanich, Ju Yuan.
- 2013: Craig Allen, Dylan Hsu, Jiajin Lei, Stephen Sorokanich, Samantha Usman, Neill Warrington, Erin Zalewski.