Cover text

The Seventieth Annual William Lowell Putnam Mathematical Competition

Administered by the Mathematical Association of America

A competitive examination in collegiate mathematics to be given SATURDAY, DECEMBER 5, 2009 to contestants from colleges and universities in the United States and Canada

Address correspondence to
Leonard F. Klosinski, Director Putnam Mathematical Competition
Department of Mathematics
Santa Clara University
500 El Camino Real
Santa Clara, CA 95053-0374

The Seventieth Annual
William Lowell Putnam
Mathematical Competition
will be held on
Saturday, December 5, 2009

HISTORY

The competition began in 1938 and is designed to stimulate a healthful rivalry in mathematical studies in the colleges and universities of the United States and Canada. It exists because Mr. William Lowell Putnam had a profound conviction in the value of organized team competition in regular college studies. Mr. Putnam, a member of the Harvard class of 1882, wrote an article for the December 1921 issue of the Harvard Graduates' Magazine in which he described the merits of an intellectual intercollegiate competition. To establish such a competition, his widow, Elizabeth Lowell Putnam, in 1927 created a trust fund known as the William Lowell Putnam Intercollegiate Memorial Fund. The first competition supported by this fund was in the field of English and a few years later a second experimental competition was held, this time in mathematics between two institutions. It was not until after Mrs. Putnam's death in 1935 that the examination assumed its present form and was placed under the administration of the Mathematical Association of America.

RULES

The competition is open only to regularly enrolled undergraduates, in colleges and universities of the United States and Canada, who have not yet received a college degree. No individual may participate in the competition more than four times. An eligible entrant who is also a high school student must be informed of this four time limit. There is no provision for "unofficial" entrants.

A college or university with at least three registered entrants obtains a team rank through the positions achieved by three designated individual contestants.

No collaboration or outside assistance is permitted. Each contestant, even if designated as a team member, must work independently on the examination questions.

SCHEDULE

The examination will be held on Saturday, December 5, 2009. In order to assure uniformity and fairness to all, the examination shall consist of two periods of exactly three hours each with a two hour break between the two sessions, under the official supervision of a faculty member of the department of mathematics in the institution. The exact starting times are a function of the time zone in which the institution is located.

Time Zone: Mountain = Morning Session 8:30 am - 11:30 pm, Afternoon Session = 1:30 pm - 4:30 pm

Students who for religious reasons cannot take the examination at the scheduled hours may take the examination after sundown on December 5, upon request by the supervisor and approval of the Director. Such students must remain under the supervision of a faculty member, rabbi, or clergyman from the official starting time for that time zone on the day of the examination.

REGISTRATION

Any college or university desiring to compete should complete the registration material accompanying this announcement and return it so as to reach the Director not later than October 13, 2009.

When there are three or more contestants from the same institution, those chosen as the team should be numbered 1, 2, and 3. The others should be numbered in sequence as alternate team members with the understanding that contestant number 4 is to be a member of the team if one of the first three does not take the examination, and so on.

DESCRIPTION

The examination will be 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. Thus 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.

GRADING

Each problem is graded on a basis of 0 to 10 points. All the necessary work to justify an answer and all the necessary steps of a proof must be shown clearly to obtain full credit. Some partial credit may be given, but only when a contestant has shown significant and substantial progress toward a solution.

PRIZES AND SCHOLARSHIPS

WILLIAM LOWELL PUTNAM PRIZES

Prizes will be awarded to the departments of mathematics of the institutions with the five winning teams. In addition, there will be prizes awarded to each of the members of these teams. The five highest ranking individuals are designated Putnam Fellows by the Mathematical Association of America. Prizes will be awarded to each of these individuals and to each of the next twenty highest ranking contestants.

The trustees of the Putnam Fund also will award at Harvard University the annual William Lowell Putnam Prize Scholarship to one of the Putnam Fellows. This scholarship is available either immediately or on completion of the undergraduate course of the successful candidate and carries a value of up to $12,000 plus tuition at Harvard.

Institutions throughout the United States and Canada are encouraged to offer fellowships to high ranking contestants in the competition.

ELIZABETH LOWELL PUTNAM PRIZE

The Elizabeth Lowell Putnam Prize will be awarded periodically to a woman whose performance on the Competition has been deemed particularly meritorious. This prize would be in addition to any other prize she might otherwise win. Women contestants, to be eligible for this prize, must specify their gender.

ANNOUNCEMENTS

The names and addresses of the top five hundred contestants and the names of the top ten teams will be mailed to all participating institutions. The high ranking individuals will be grouped into the categories: Putnam Fellows, next highest ten, next highest ten, honorable mention, others in the top hundred, the next hundred, and the next three hundred. No other information on scores or rankings will be included in general announcements.

A report giving the scores and rankings of individuals at a participating institution and the team ranking (top 150 only) will be mailed to the supervisor of the examination at the institution. Contestants must obtain their ranking from the supervisor.

The lists of the top ten teams and the top hundred individual contestants, in the categories described above, will be published in the American Mathematical Monthly, together with the problems and solutions.

ADDITIONAL INFORMATION

More information on the Putnam Competition can be found in two articles in the May 1965 issue of the American Mathematical Monthly. Garrett Birkhoff described in one the early history and L. E. Bush gave in the other the later history and a summary of results up to that time. There are three Putnam problem books that contain collections of problems with solutions as well as historical information about the competition: (1) A. M. Gleason, R. E. Greenwood and L. M. Kelly, The William Lowell Putnam Mathematical Competition/ Problems and Solutions: 1938-1964, (2) Gerald L. Alexanderson, Leonard F. Klosinski and Loren C. Larson, The William Lowell Putnam Mathematical Competition/Problems and Solutions: 1965-1984, and (3) Kiran S. Kedlaya, Bjorn Poonen and Ravi Vakil, The William Lowell Putnam Mathematical Competition 1985-2000 Problems, Solutions and Commentary.

The questions on the Putnam examination are regularly published in the Monthly. The following issues of the Monthly contain questions, and sometimes solutions, for earlier competitions:

May 1942, Oct. 1946, Aug.-Sept. 1947, Dec. 1948, Aug.-Sept. 1949, Aug.-Sept. 1950, Aug.-Sept. 1951, Oct. 1952, Oct. 1953, Oct. 1954, Oct. 1955, Jan. 1957, Nov. 1957, Jan. 1961, Aug.-Sept. 1961, Oct. 1962, Aug.-Sept. 1963, June-July 1964, Aug.-Sept. 1965, Aug.-Sept. 1966, Aug.-Sept. 1967, Aug.-Sept. 1968, Oct. 1969, Aug.-Sept. 1970, Aug. Sept. 1971, Feb. 1973, Nov. 1973, Dec. 1974, Nov. 1975, Nov. 1976, Jan. 1978, Mar. 1979, Nov. 1979, Oct. 1980, Oct. 1981, Nov. 1982, Oct. 1983, Oct. 1984, Oct. 1985, Oct. 1986, Oct. 1987, Oct. 1988, Oct. 1989, April 1991, Oct. 1991, Oct. 1992, Oct. 1993, Oct. 1994, Oct. 1995, Oct. 1996, Oct. 1997, Oct. 1998, Nov. 1999, Oct. 2000, Nov. 2001, Nov. 2002, Oct. 2003, Oct. 2004, Oct. 2005, Oct. 2006, Oct. 2007, Oct. 2008

FIRST PLACE TEAMS

(in the last 10+ years)

competition / Date / Institution
50th 12/2/89 Harvard University
51st 12/1/90 Harvard University
52nd 12/7/91 Harvard University
53rd 12/5/92 Harvard University
54th 12/4/93 Duke University
55th 12/3/94 Harvard University
56th 12/2/95 Harvard University
57th 12/7/96 Duke University
58th 12/6/97 Harvard University
59th 12/5/98 Harvard University
60th 12/4/99 University of Waterloo
61st 12/2/00 Duke University
62nd 12/1/01 Harvard University
63rd 12/7/02 Harvard University
64th 12/6/03 Massachusetts Institute of Technology
65th 12/4/04 Massachusetts Institute of Technology
66th 12/3/05 Harvard University
67th 12/2/06 Princeton University
68th 12/1/07 Harvard University
69th 12/6/08 Harvard University

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