The William Lowell Putnam Mathematical Competition 2003

The William Lowell Putnam Mathematical Competition will take place on Saturday, December 6, 2003.

It is a challenging opportunity for you to test your mathematical mettle. In the 2002 competition, 3349 individuals participated, representing 476 colleges and universities across Canada and the U.S. Stanford placed fifth, and many individuals did very well.

The competition emphasizes ingenuity rather than knowledge, so freshmen are not at much of a disadvantage compared to seniors. Interest in or experience with problem solving is a plus. Not just math majors have done well; some recent winners have come from nearby disciplines, including physics, computer science, and engineering.

Completely solving even one of the twelve problems is a significant achievement, and in almost all years would place you well above the median. (Keep in mind that the particpants are self-selected from among the best in the continent.)

THE COMPETITION WILL TAKE PLACE ON SATURDAY, DECEMBER 6, 2003. PLEASE CONFIRM WITH ME BY MONDAY NIGHT IF YOU ARE PLANNING ON TAKING IT! YOU SHOULD HAVE RECEIVED AN E-MAIL FROM ME (BY FRIDAY NOON) WITH MORE INFORMATION.

Links:

• The introductory poster.
• The introductory meeting will take place Tues., Oct. 7, 5:15-5:45 pm, in 380-383N. Here is the introductory handout.
• Meetings: We will have informal dinner-time problem solving practice sessions this quarter (likely six or seven), Mondays 5:30-7 pm. Practice problems will include some on the topics discussed, and some others. Handouts will appear here.
  • Monday, Oct. 20: general problem-solving strategy, induction and the pigeonhole principle. (I start with this every year.) Handout. Website of the week: Richard Schwartz' Lucy and Lily.
  • Monday, Oct. 27: Recurrences (with links to Fibonacci numbers and differential equations). Handout. Website of the week: Jordan Ellenberg's article Growing Apart: The mathematical evidence for Congress' growing polarization.
  • Monday, November 3: Number theory. Handout. Website of the week: a four-dimensional Rubik's cube.
  • Monday, November 10: Game theory Handout. Website of the week: the world's largest Klein bottle. (Also, some of you asked about the article with the "fourteen proofs of a result about a tiling a rectangle". Here it is. (This probably requires a Stanford account.)
  • Monday, November 17: Alok Aggarwal (alumnus of Putnam powerhouse Waterloo), on sums and series. Handout. Website of the week: a devastatingly good dots-and-boxes player by J.P. Grossman, sadly for windows only. (Click on "dabble" at the top of the page.)
  • Monday, November 24: Vin da Silva (IMO UK), on integration in geometry. Website of the week: the Riemann hypothesis (aka how to win a million dollars from the Clay foundation), which relates to the first question on last week's problem set. Handout.
  • Monday, December 1: Diane Maclagan (IMO New Zealand), on graph theory. Website of the week: William Wu's wonderful website of neat problems (and neat math). (Link goes to the "Sink the Sub" problem; from there, just browse.) Handout.
  • Saturday, December 6: THE WILLIAM LOWELL PUTNAM MATHEMATICAL COMPETITION. Plesae let me know if you will be writing! More information here soon! Website of the week: the article in last year's Time Magazine (Dec. 23 '02) about the Putnam.
• There will also be a masterclass for a few experts, Mondays 7:15-8:15 pm. (Everyone is welcome.)
  • Monday, October 27. Handout of problems to be discussed.
  • Monday, November 3. Problems.
  • Monday, November 10. Problems.
  • Monday, November 17. Problems.
  • Monday, November 24. Problems.
  • Monday, December 1. Problems.
• The official Putnam website.
• Recommended reading:
  • I really like Loren Larson's "Problem Solving Through Problems" --- definitely worth owning. It's great preparation for the Putnam.
  • It is also great help (more than you would think) trying many old problems. I'd especially recommend the collection of recent Putnams "The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary", by Kiran Kedlaya, Bjorn Poonen, and myself.
  • There are more good problems in the previous Putnam book, "The William Lowell Putnam Mathematical Competition Problems and Solutions: 1965-1984", by Alexanderson, Klosinski, and Larson (look especially at those in the 1980's).
  All of these books are in the math library (possibly on reserve), in Building 380. Also, on the web you can find
  • a compilation of old Putnam problems and solutions on the web, collected by Kiran Kedlaya;
  • to find solutions to older Putnams, you can read the official solutions in the American Mathematical Monthly, which you can see electronically (from any Stanford computer) here. At that page, 'Search this journal' for "William Lowell Putnam" in the title.
  • Some more links are available through this good UCSD site, by Patrick Fitzsimmons.
• Last year's Stanford Putnam website.

Want more? Additional suggestions for others? Please let me know.