The William Lowell Putnam Mathematical Competition and the Polya Problem Solving Seminars 2009

For several years Ravi Vakil ran the wonderful Polya Problem Solving Seminar, one of whose goals is to motivate students to participate in the Putnam competition. Last year, Kannan Soundararajan took over for him, and this year I am running it.

The Putnam is a challenging opportunity for you to test your mathematical and problem solving skills. The exam is notoriously difficult; in most years the median score is 0, out of 120 possible points! Each year about 3600 students from colleges and universities across the US and Canada take the test. Stanford finished fourth in both 2007 and 2008, great achievements! Moreover, we placed many individuals in the top five hundred students.

The competition emphasizes ingenuity rather than knowledge, so freshmen are not necessarily 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; many 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.)

If you're interested in signing up for the Putnam, please come to the Introductory meeting, on Monday, September 28, or else please email me by Friday, October 2.

• Regular meetings will be on Mondays 6-7:30 in 380Y. You could drop by a little earlier, from 5:45 on, to discuss anything left over from the previous week. Rough schedule: from 6-6:10 we'll discuss some math: new technique, problem solving strategies ..., and then from 6:10-6:45 eat pizza and work on the problems. From 6:45--7:30 I'll have volunteers present solutions to selected problems. We'll also have a ``Masterclass" from 7:30-8:30 or so; this is aimed at more experienced problem solvers but everyone is welcome. Here a few volunteers each week will present a problem of their liking, together with ideas on how to think of the solution. If you'd like to volunteer for this, please let me know. You could either have a problem already in mind (please let me know what that is, so I can also think about it), or we can try and find a suitable problem together.

  Week 1: Monday, October 12: Pigeonhole principle. Problem set
  Week 2: Monday, October 19: Induction. Problem set
  Week 3: Monday, October 26: Inequalities. Problem set
  Week 4: Monday, November 2: Calculus. Problem set
  Week 5: Monday, November 9: Number theory. Problem set (Master class problems)
  Week 6: Monday, November 16: Algebra. Problem set and master class
  
  

  The Putnam will take place on Saturday, December 5 in (location TBA). The exam will be 8 AM-4 PM, with a break 11 AM - 1 PM for lunch (provided). Everyone should plan to show up by 7:40 AM, so we can sort out some of the formalities in an orderly way.