William Lowell Putnam Competition | Department of Mathematics

# William Lowell Putnam Competition

The William Lowell Putnam Competition is the annual mathematical competition held on the first Saturday in December. This year's exam will be on December 7, 2019. The exam has a 3 hour morning session with 6 problems and a 3 hour afternoon session also with 6 problems. The problems are tough! Getting even one problem correct is an achievement! See some sample problems below.

2018 Participants - Rhythm Garg, Fernando Moreno

2017 Participants - Austin McGregor, Fernando Moreno, Ethan Seal

2016 Participants - Alvin Gao, Ethan Seal

2015 Participants - Mark Fincher, Ashley Miller

2014 Participants - Mark Fincher, Ashley Miller

2013 Participants - Pranav Davalla, Mark Fincher, Kevin Lin, Ashley Miller, Robert Tung. Coach Dr. Neal Brand. This team placed 40th from among the 557 participating institutions.

Current coaches - Dr. Joseph Iaia and Dr. Pieter Allaart

Problems from 1985-2018

(Also the AMS and MAA have two books of the Putnam problems (and solutions) from 1938-1964 and another which contains the problems (and solutions) from 1965-1984).

In the one hour course MATH 3010 - SEMINAR IN PROBLEM SOLVING TECHNIQUES - we will discuss strategies for solving some of the typical problems that come up on the Putnam exam. These are often fairly challenging problems and not for the faint of heart, so bring your best math skills and your thinking cap for a challenge and some fun for a class team taught by Dr. Allaart and Dr. Iaia. See some sample examples below.

1. Show that:
$$\lim_{x \to 1^{-}} \prod_{n=0}^{\infty} \left( \frac{1+x^{n+1}}{1+x^n} \right ) = \frac{2}{e}.$$
(from the 2004 exam)

2. Let $f$ and $g$ be real valued functions defined on an open interval containing 0 with $g$ nonzero and continuous at 0. If $fg$ and $f/g$ are differentiable at 0 must $f$ be differentiable at 0? (from the 2011 exam)

3. Let $S$ be a set of rational numbers such that:

a. $0\in S$,

b. if $x\in S$ then $x+1+\in S$ and $x-1 \in S$, and

c. if $x \in S$ and $x\neq 0$ and $x \neq 1$ then $\frac{1}{x(x-1)} \in S$.

Must $S$ contain all rational numbers? (from the 2009 exam)

4. Alan and Barbara play a game in which they take turns filling entries of an initially empty 2008 by 2008 array. Alan play first. At each turn, a player chooses a real number and places it in a vacant entry. The game ends when all entries are filled. Alan wins if the determinant of the resulting matrix is nonzero. Barbara wins if it is zero. Which player has a winning strategy?
(from the 2008 exam)

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