The William Lowell Putnam Mathematical Competition 2002

The William Lowell Putnam Mathematical Competition will take place on Saturday, December 7, 2002.

It is a challenging opportunity for you to test your mathematical mettle. In the 2001 competition, 2954 individuals participated, representing 453 colleges and universities across Canada and the U.S. Stanford placed fifth, and many individuals did very well.

The results have arrived! A second banner year in a row! The results are here.

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 most years would place you well above the median. (Keep in mind that the particpants are self-selected from among the best in the continent.)

Links:

• The introductory poster, in dvi, ps, and pdf formats: dvi, ps, pdfA, pdfB. (If you prefer pdf, please try both pdf files, and let me know if one is better than the other. I've made them in two different ways, and I'm not sure which is better.)
• The introductory meeting will take place Thurs., Oct. 10, at 3:15 pm in 380-383N.
• Meetings: We will have informal dinner-time problem solving practice sessions this quarter, Tuesdays from 5 pm until 6:30 pm, in 380-383N. Practice problems will include some on the topics discussed, and some others. Handouts will appear here.
  • October 15: pigeonhole principle and induction. Here are the problems.
  • October 22: number theory, and Wythoff's game and Beatty's Theorem. Here are the problems. For the solutions to the problems which appeared on the Putnam: this file gives the Putnams on which each appeared. You can look up solutions online (see below), or in the books (see below) in the library. And you can also ask me.
  • October 29: complex numbers, with guest lecturer Alok Aggarwal. Here are the problems.
  • November 5: three impossible problems of antiquity (trisection of an angle, doubling the cube, and squaring the circle). Here are the problems.
  • November 12: no meeting.
  • November 19: analysis (aka calculus), with guest lecturer Lenny Ng. Here are the problems (dvi ps pdfA pdfB pdfC). The problem of the week (see the handout of problems): Find the hypervolume of the n-dimensional hypersphere!
  • December 3: guest lecturer Vin da Silva will speak on functional equations. The "website of the week" is about the related "Riemann hypothesis", perhaps the most important unsolved problem in mathematics. (If you solve it, you'll get a million dollars.) Here are the problems (dvi ps pdfA pdfB pdfC).
  • Saturday, December 7: The Putnam Competition! The Putnam will take place on Saturday, December 7, 8-11 am and 1-4 pm. We'll meet just outside of 383N (where the weekly seminar takes place) at 7:45 am. You can bring pencils (or pens) and erasers. (No calculators, rulers, etc. are allowed.) I'll bring another infinite pile of scrap paper. If you're up for writing, please send me an e-mail by Wednesday, so I can book rooms, and more importantly, arrange for lunch. (If you forget to respond until Thursday, don't worry.) Regarding lunch: I'm either going to order pizza from Pizza Chicago, or get sandwiches catered by Stanford (which I hear are quite good). So if you care, please let me know which you would prefer, and I'll go with the plurality's opinion. (Sandwiches currently lead.) Also, I'm going to get some snacks to keep your energy and spirits up, so if you have some favorites (chocolate, candy, carrots), let me know too.
• The official Putnam website.
• Recommended reading:
  • I really like Loren Larson's "Problem Solving Through Problems" --- definitely worth owning. (I just noticed that it's avilable at the bookstore, in the Springer "yellow-tag" sale. -- Nov. 3) 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.