# 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.

### 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. In **Fall 2018** the sessions take place **Sunday 2-3 in Carnegie 120**.

### Participation

The 2018 Putnam Competition takes place on Saturday, December 1, in two sessions (10am-1pm and 3pm-6pm). There are six problems given in each session. 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.