## What is the Putnam Competition?

The Putnam Exam (officially known as the William Lowell Putnam Math Competition) is a very challenging, six-hour mathematics exam administered by the Mathematical Association of America. This prestigious exam is taken by about 3,600 undergraduates in the United States and Canada each year. It is given on the first Saturday in December, and is composed of two 3-hour sessions, one in the morning and one in the afternoon, each with six questions. Each question is worth 10 points (for a total of 120).

William Lowell Putnam, a graduate of Harvard in the class of 1882, believed strongly in the value of academic competitions. To this end, Mrs. Elizabeth Lowell Putnam, the wife of Mr. Putnam, created a trust fund for supporting such competitions in memory of her husband. Two experimental competitions were held, one in English, and one in mathematics, before the competition assumed its present form in 1938. Scholarships and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools are given by the Putnam committee.

## Am I eligible?

If you are an undergraduate student and enjoy solving math problems, then YES, you are eligible to take part in this exam. There is no registration fee, and we submit your registration on behalf of the ISU mathematics department. There are a couple of minor restrictions. You should not have received a college degree and you may not participate more than 4 times. Keep in mind that Putnam is a very hard exam. Typically, the median score for all contestants is approximately one (out of 120). But let that not discourage you! It is fun to try and solve hard problems. Even a partial success after a long struggle with a hard problem can make you feel like a million dollars! Preparing for a Putnam competition can be an enriching mathematical experience for a good student, and success in the competition is definitely something students should proudly mention in their resumes. So why not give it a try?

## What topics does this exam cover?

The examination is constructed to test originality as well as technical competence. It is expected that the contestant will be familiar with the formal theories embodied in undergraduate mathematics. It is assumed that such training, designed for mathematics and physical science majors, will include somewhat more sophisticated mathematical concepts than is the case in minimal courses. For instance, the differential equations course is presumed to include some references to qualitative existence theorems and subtleties beyond the routine solution devices. Questions will be included that cut across the bounds of various disciplines, and self-contained questions that do not fit into any of the usual categories may be included. It will be assumed that the contestant has acquired a familiarity with the body of mathematical lore commonly discussed in mathematics clubs or in courses with such titles as “survey of the foundations of mathematics”. It is also expected that the self-contained questions involving elementary concepts from group theory, set theory, graph theory, lattice theory, number theory, and cardinal arithmetic will not be entirely foreign to the contestant’s experience. Here are some old Putnam exams which will give you a better idea of the nature and standard of this competition.

## How can I participate?

Each year the Putnam exam will be held on the first Saturday in the month of December. If you wish to participate (I hope you will), you must register by completing this fill this form There will be two sessions on the day of the exam. Sesssion A from 9:00 am – 12 noon and Session B from 2:00 pm – 5:00 pm. **Free lunch** will be provided between the two sessions (courtesy of the ISU Mathematics Department) for those who take this exam.

## Putnam Competition Sites

- Official Putnam Site – The official rules, regulations, and results of the competition.
- MAA/AMC Putnam Archive– An extensive archive of recent Putnam problems, solutions, and statistics.

## Putnam Preparation Web Sites

Here is a selection of Putnam Preparatory Seminars at various colleges. Note that some of these sites move frequently.

- Harvard Putnam website
- MIT’s Open Course Ware by Kedlaya, Roger and Stanley. Problem Solving Seminar in 2007 (18.S34)
- Richard Stanley’s Proposed Putnam Problems — from when he was on the committee that wrote the exam.
- Ravi Vakil’s Stanford Putnam Webpage.
- University of Waterloo Putnam Page
- Cornell Putnam Homepage
- Old Putnam Exams and Solutions

## Some Useful Problem Books

These books can be obtained from the library through ISHARE

Collection of Putnam probems:

*The William Lowell Putnam Mathematical Competition 1985-2000*by Kiran S. Kedlaya et al.

Putnam level and some easier problems grouped by subject.

*Problem-Solving Strategies (Problem Books in Mathematics)*by Arthur Engel*Problem Solving Through Problems*by Loren C. Larson*The Art and Craft of Problem Solving*by Paul Zeitz*Mathematical Olympiad Challenges*by Titu Andreescu, Razvan Gelca*Winning Solutions (Problem Books in Mathematics)*by Edward Lozansky, Cecil Rousseau

Collections of elementary problems appropriate for freshmen:

*Five Hundred Mathematical Challenges*by Edward J. Barbeau, Murray S. Klamkin, William O. J. Moser- Which Way Did the Bicycle Go? : And Other Intriguing Mathematical Mysteries — Joseph D. E. Konhauser, Dan Velleman

A classic on problem solving strategies:

*How to Solve It*by George Polya

## College Mathematics Journals with Problem Sections

- Math Horizons (MAA) is a magazine aimed at undergraduates with a very accessible problem section.
- Mathematics Magazine (MAA) is an expository journal of undergraduate mathematics, with an a good problem section for the undergraduate.
- The College Mathematics Journal(MAA) provides lively, well-motivated articles that can enrich undergraduate instruction and enhance classroom learning.
- The American Mathematical Monthly publishes articles about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional mathematicians as well as students of mathematics at all collegiate levels. The problem section is quite challenging, and often contains unsolved problems.

## Other Online Problem Competition and Sources

- Macalester Problem of the Week – Great and offbeat problems due to Stan Wagon and friends !!!
- The MAA/AMC Website has problems and solutions from other mathematics contests (USAMO, IMO, etc.).
- The Virginia Tech Regional Mathematics Competition is a Putnam-style competition.
- John Scholes site archives problems and solutions from a large number of competitions.
- Purdue’s Problem of the Week.
- The International Mathematics Competition perhaps could be described as a worldwide version of the Putnam.

## Online Mathematical Resources

- Math Fun Facts is Francis Su’s website with many amusing math facts for students of all abilities.
- Math Forum is a good starting place for K-12 resources.
- Eric Weisstein’s World of Mathematics – A very extensive encyclopedia of mathematics. Almost anything that you might want to know about math can be found here.
- MathSciNet – The best site for doing key word searches on journal articles.
- The Inverse Symbolic Calculator – A program that attempts to find a symbolic expression for a given decimal approximation to a number.
- Sloane’s On-Line Encyclopedia of Integer Sequences – An encyclopedia of many interesting sequences of integers.
- The Art of Problem Solving host a set of mathematical resources, publishes books, and runs courses aimed primarily at High School students.