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# William Lowell Putnam Mathematics Competition

The *William Lowell Putnam Mathematics Competition*, known more briefly as the *Putnam Exam* or the *Putnam*, is an annual mathematics competition open to undergraduates in the United States and Canada. Administered by the Mathematical Association of America (MAA), the Putnam is widely regarded as the most challenging undergraduate mathematics examination given in America. The exam is written to test both technical competence in undergraduate mathematics and problem-solving skills.

The Putnam is given the first Saturday in December. It consists of twelve problems; six are given during the three-hour morning session (10 a.m. - 1:00 p.m.) and six are given during the three-hour afternoon session (3:00 - 6:00 p.m.). The two sessions are separated by a two-hour lunch break.

The Putnam supervisor for St. Bonaventure University is Dr. Chris Hill.

### Registration

A student must register to take the Putnam Exam. To register, contact Dr. Hill (De La Roche 301 C, chill@sbu.edu) during the fall semester. Students will be alerted in mathematics classes and by email when they may register for the next Putnam Exam. Registration is free. The deadline for registration tends to be mid-October. Note that a student who has registered to take the exam is free not to take it, but a student who has not registered may take the exam only if someone who had registered does not take the exam.

### Preparation

As a practical matter, a student should have taken MATH 152. Calculus II and have taken or be taking MATH 207. Discrete Mathematics I before attempting the Putnam Exam. See **Putnam Resources** and **The Problem-Solving Seminar**, below, for avenues of additional preparation.

### How Challenging?

The Putnam is exceedingly challenging: if a student solved just one of the twelve problems on the 2006 Putnam, he or she would have ranked in the top 20% of the over 3000 participants. What makes a Putnam problem so challenging? It’s not so much the subject matter, which is taken from undergraduate mathematics, but the necessity of finding the right insight. The solution of a Putnam problem can be quite short, once one has the right insight.

### Free Lunch!

By tradition, Bona's Putnam participants eat lunch during the two-hour break at the Beef `N Barrel Restaurant, paid for by the Department of Mathematics.

### Putnam Resources

- The official Putnam website contains a helpful description of the Putnam, the history of the exam, and the complete set of rules, but it does not include past exams.
- A collection of past Putnam exams and solutions, courtesy of Kiran Kedlaya of UCSD. The exams (1985 to present) and the solutions (1995 to present) are provided as PDF and TeX files.
- Another collection of past Putnam Exams, courtesy of Dr. Patrick J. Fitzsimmons of the University of California at San Diego. The collection includes exams from 1980 to 2010 as postscript, Adobe Acrobat, and dvi files.
- Free paper copies of several of the most recent Putnam Exams may be found in the "Resources" bookcase in the Mathematics Suite (De La Roche 301).

### The Problem-Solving Seminar

MATH 281. The Problem-Solving Seminar is offered during the fall semester and prepares students to take the Putnam Exam. In this one-credit course, techniques of mathematical problem-solving are studied and applied to a wide range of problems (including problems from previous Putnam Exams). The prerequisites for Math 281 are MATH 152. Calculus II and MATH 207. Discrete Mathematics I. MATH 281 may be repeated for credit. During previous Problem-Solving Seminars, students solved problems posed in the problems sections of the national undergraduate journals *Math Horizons*, *The College Mathematics Journal*, and the *Pi Mu Epsilon Journal*. Note that students who register for the Putnam are not required to take the Problem-Solving Seminar and students who take the Seminar need not take the Putnam Exam.

### Aftermath: The Putnam-Free-for-All

Early in the spring semester, the SBU Student Chapter of the MAA sponsors a Putnam Free-For-All, which is an informal discussion of the problems on the previous year's Putnam Exam, hosted by Dr. Hill.

### The University of Rochester Mathematical Olympiad

*The University of Rochester Mathematical Olympiad* (URMO) is an annual mathematics competition for undergraduates in Western New York. The URMO occurs on a Saturday in March. The University of Rochester Mathematical Olympiad was created to be a challenging competition, but friendlier than the Putnam Exam. For example, the URMO is a three-hour exam consisting of four problems. For more information, visit our URMO web page or contact Dr. Hill.