William L. Putnam

In the December 1921 issue of Harvard Graduates' Magazine, the article "A Suggestion for Increasing the Undergraduate Interest in Studies" by William Lowell Putnam proposed academic competitions as a means of expressing idealism, interest in academics, and eagerness to win recognition for one's college or university. Later, the will of Mrs. Putnam established a $125,000 trust to make possible the kind of academic competition envisioned by her late husband. The first experiment was conducted in 1928, and involved a competition between Harvard and Yale English majors. The first trial competition in Mathematics took place in 1933, and the competing institutions were Harvard and West Point. West Point won. Finally, an annual competition, the William Lowell Putnam Mathematical Competition, began in 1938. The very first one included 163 students from 67 colleges, with 42 schools represented by three-member teams. The examination was prepared by members of the Harvard faculty, and Harvard students did not compete. The University of Toronto won the team competition, and the five highest ranking individuals, called Putnam Fellows, included Irving Kaplansky and George Mackey, both of whom went on to have distinguished scientific careers.

The Putnam has since become the premier competition for mathematically-inclined undergraduates from the U. S. and Canada. As one might expect, the list of Putnam winners since 1938 includes many famous mathematicians and scientists. Early winners also included Andrew M. Gleason, Harvey Cohn, and Felix Browder. Winners who have later achieved fame in physics include Richard Feynman, Tai Tsun Wu, James Bjorken, Robert L. Mills, Kenneth G. Wilson, and Barry Simon. Three Putman Fellows (J. W. Milnor, David Mumford, Daniel Quillen) have gone on to win the Fields Medal and two (Feynman and Wilson) later won the Nobel Prize in Physics. In Genius, the biography of Feynman by James Gleick, it is related that Feynman finished the exam early, and the graders were astonished by the gap between Feynman's score and that of his closest competitor. In case you are curious, John Nash was not a Putnam Fellow.

The Tigers team 2001 with coach, Prof. Rousseau. (L-R) David Bond, Catherine Frost, Eric Anderson.

In the December 1921 issue of Harvard Graduates' Magazine, the article "A Suggestion for Increasing the Undergraduate Interest in Studies" by William Lowell Putnam proposed academic competitions as a means of expressing idealism, interest in academics, and eagerness to win recognition for one's college or university. Later, the will of Mrs. Putnam established a $125,000 trust to make possible the kind of academic competition envisioned by her late husband.

In recent years, the ranks of Putnam Fellows have been well represented by "graduates" of the USA and Canadian Mathematical Olympiad Programs, the national teams which compete in the International Mathematics Olympiad. Read more about the IMO in a future newsletter.

At present, the winning team receives $25,000, and the Putnam Fellows each receive $2,500. In the 2001 competition, the first five teams were Harvard, MIT, Duke, Berkeley, and Stanford.

After a very long period in which the the University of Memphis did not participate, two of our undergraduates (Shabnum Kaderi and Matthew Kendall) competed in 2000, and a full team, Eric Anderson, David Bond, and Catherine Frost, represented the University of Memphis in the 2001 competition.

Eric Anderson

Out of 336 teams in the 2001 competition, our rank was 144. Eric Anderson ranked among the top 500 students out of nearly 3000 that participated.

Catherine Frost and David Bond

Our goal is not so much to field a team of Putnam Fellows, but rather to establish participation in the Putnam Competition as a yearly activity, to enjoy and profit from the time spent in preparation, and to aim to steadily improve our ranking in this prestigious competition.

Starting in September, students intending to take the Putnam gather weekly to study standard topics (analysis, combinatorics, geometry, number theory), learn problem-solving strategies, and practice on previously used Putnam problems and other problems of a similar nature.

The exam takes place on the first Saturday in the month of December. It consists of 12 problems. Problems A1 through A6 are given in the morning session (9 am -- noon) and problems B1 through B6 in the afternoon session (2 -- 5 pm). Generally speaking, A1 and B1 are the easiest, A6 and B6 are the hardest problems. However, the judgement of what is easy and what is hard may depend strongly on one's background and interests. For example, in the 1962 exam (when there were seven problems per session), problem B1 was a geometry problem with two parts and B7 was an analysis problem.

Problem B1. (i) Given line segments A, B, C, D, with A the longest, construct a quadrilateral with these sides and with A and B parallel, when possible. (ii) Given any acute-angled triangle ABC and one altitude AH, select any point D on AH, then draw BD and extend until it intersects AC in E, and draw CD and extend it until it intersects AB in F. Prove that

Problem B7. Prove that if f is continuous for a < x < b and for n = 0, 1, 2, then f is identically zero on (a, b).

Problem B1 is elementary, but requires a little work. On the other hand, B7 is "killed" immediately using the Weierstrass Approximation Theorem. For anyone with the appropriate background, B7 will be the "easier" problem. Our students took the 1962 exam for practice recently. The Weierstrass Approximation Theorem hadn't come up in Introduction to Real Analysis yet, so the students felt that neither problem was particularly easy.

In case you would like to try out some problems from the 2001 competition, here are two for your consideration.

Problem A6.
Can an arc of a parabola inside a circle of radius 1 have length greater than 4?

Problem B3. For any positive integer n let denote the closest integer to .
Evaluate
            .