A behind the scene look at how the toughest mathematics test, the Putnam Exam, is graded. If you thought taking the exam was grueling, you should try grading it. Have you ever wondered why the median score on the exam was so low? And what happens to all those erasure droppings left in the folder? By understanding the grading process, you might devise better Putnam taking strategies.

Trivia and statistics on Putnam performances through the years. Many of us are aware that the median score is very low. But do you know how many Nobel Prize winners were Putnam Fellows? Or the highest  team finish by a liberal art school? Or the number of perfect scores throughout the history of the competition? All these questions and more will be answered for your amusement.

How to participate and get prepared for the Putnam exam from seasoned coaches of a successful problem solving seminar. 

Who was Poincaré, what is his conjecture, how did it arise, why is it so important, and why is it taking the experts so long to decide whether or not the new proof is correct?  

Follow the two year development of a problem on the 2004 American Invitational Mathematics Exam involving  regular n-pointed stars. See how the definition was refined and the final problem was posed. After grappling with the problem, return to check your answer with the solution available here.

Melanie Wood is a rising star in the mathematical community. Her list of mathematical honors and prizes is impressive. She is currently a graduate student at Princeton University studying algebraic number theory. She reflects on some of her mathematical trials and successes with our Math Horizons correspondent.

While many mathematics graduate students fund their education through teaching assistantships, some get paid for doing the research they love. Learn how to put your best face forward on research fellowship applications with advice from seasoned reviewers for the NSF Graduate Research Fellowships.

Students review The William Lowell Putnam Competition 1985-2000: Probelms, Solutions, and Commentary by Kiran S. Kedlaya, Bjorn Poonen and Ravi Vakil and Count Down: Six Kids Vie for Glory at the World's Toughest Math Competition by Steven Olson. 

As a high school student, Steven Byrnes won a $100,000 scholarship in the Siemens-Westinghouse Competition for his insights into the theory of the game Chomp. This article introduces you to his winning work.

St. Olaf has an impressive record of producing mathematicians. See what an Olaf mathematics degree has done for Kevin Casson, Tom Halverson, Amy Stubbendick, and Theresa Wise. 

Undergraduates spend the summer working on the inverse problem for electrical networks.

Kimberly Hopkins, the 2004 winner of the Association for Women in Mathematics Alice T. Schafer prize, shares her winning "statement of purpose" with Math Horizons readers.

It is always a surprise when several people, despite their freedom of choice, come to the same results in the end. Your dozenal correspondent ponders twelve invariants inherent in a pile of buttons.

To be considered for publication, solutions to the following problems should be received by November 10, 2004. 

Do you have a favorite puzzle that is catch and appealing? The Mathematical Sciences Research Institute (MSRI) in Berkeley, CA, wants to promote the joy of mathematics across the nation. The plan: To place mathematical puzzles in advertising slots on busses, trains, and subways. MSRI seeks ideas for puzzles and will reward you with $200 if your idea in selected.  See the inside back cover for more details.