The Putnam Competition is a nationwide undergraduate mathematics competition held annually, usually on the first Saturday in December. The University of Texas always participates, and invites all interested students to join in the fun.

The format of the competition is a set of 12 questions which students answer as individuals -- you have from 9am until noon to tackle the first six questions, and from 2pm until 5pm to work on the other six. The topics of the questions range across much of the undergraduate curriculum; the tools needed to solve a question very frequently involve calculus, linear algebra, elementary number theory, and tools from high-school mathematics such as plane geometry. A smaller number of questions require knowledge of more advanced undergraduate topics like differential equations, abstract algebra, real analysis, or even topology. However there are frequently some questions that require nothing more than logic and an appreciation of patterns -- for example, a question might ask that the student analyze strategies for playing a peculiar abstract game.

This is an **EXTREMELY** difficult competition. Over four thousand
students sit for the competition every year, and usually almost half of them
will get no points at all (out of 120 possible points)! Really nailing three or
four of the questions will often put you in the top 5% or so of all
contestants --- and will attract the attention of people who run programs that
seek out good puzzle-solvers.

The top prize is a graduate fellowship in mathematics at Harvard University. There are substantial cash prizes for those in top five, the top ten, and so on. But let us be frank: you should take the exam because you enjoy challenging problems, and not focus on winning the prizes, because they are very elusive.

The UT Mathematics Department eagerly supports its student competitors. For starters, we'll feed you lunch on the day of the competition :-) Even better, we run coaching sessions about once a week during the Fall to help you sharpen the tools you'll use during the competition itself.

All UT students are eligible to participate; you need only sign up with the math department before the day of the competition (and it is possible to withdraw after signing up). We do need to order enough copies of the exam materials early in the Fall semester, so students are encouraged to sign up early; a few extra copies of the exam will be available on test day on a first-signed-up, first-served basis.

Here is a sample question to give you a flavor of the competition:

SupposeABCis a triangle in the coordinate plane whose three verticesA, B, Call have integer coordinates. Show thatABCcannot be equilateral.

**The 2020-2021 competition will be unusual because of the Covid-19 pandemic.
The competition has been postponed to February 20, 2021; students will
take the exam remotely; and it will be "unofficial" in the sense that no
prizes will be awarded. However we anticipate that the competition will be
otherwise normal: 6 difficult morning questions followed by 6 difficult
afternoon questions, and any substantive responses will be graded.
In Fall 2020 we ran some prep sessions by Zoom; you may wish to review the
2020 prep materials we developed.
**

For more information about the competition please contact Dave Rusin in PMA 9.140.