**The Pólya Problem-Solving Seminar** is a series of informal dinner-time problem solving practice sessions this fall quarter, on Mondays 6-8 pm. Some faculty and graduate students always turn up with wise words. The seminar can be taken for credit (in the guise of Math 193).

**There will also be a Masterclass for a few experts (everyone is welcome),** on Mondays (an hour, immediately after the regular seminar, starting roughly at 7:45 or 8).

The Pólya Seminar can be useful preparation for the William Lowell Putnam Competition, but is logically independent.

(For information about the Putnam competition, click here. For some resources, click here. For the Math 193 Coursework site, click here — those not in the class but students at Stanford can still sign up here.)

If you are (even potentially) interested in hearing about the seminar, please let us know (by emailing either of us). We maintain an email list (**not** the coursework list associated to Math 193) for those interested, where we send announcements.

Practice problems will include some on the topics discussed, and some others. Handouts will be posted on this page.

*Monday, September 21:*introductory meeting. Here is the introductory handout.*Monday, September 28:*warming up: induction, and the pigeonhole principle. Here is the handout.*Monday, October 5:*number theory. Here is the handout. We also had the first meeting of the Masterclass. The Masterclass problems are here. At risk of making you hungry, here is a picture of a cake Lisa Sauermann’s mom baked in summer 2011 (relevant to one of the masterclass problems):*Monday, October 12:*combinatorics. Here is the handout. Here are the Masterclass problems.*Monday, October 19:*invariants. Here is the handout. Here are the Masterclass problems.*Monday, October 26:*inequalities. Here is the handout. Here are the masterclass problems.- Here is Zeb Brady’s one-line (but evil) proof of the Arithmetic-Geometric Mean Inequality: For any , we have

which is manifestly nonnegative.

- Here is Zeb Brady’s one-line (but evil) proof of the Arithmetic-Geometric Mean Inequality: For any , we have
*Monday, November 2:*probability and expected values. Here is the handout. Here are the Masterclass problems.*Monday, November 9:*recursions and generating functions. Here is the handout. (No Masterclass this week.)

*Monday, November 16:*analysis. Here is the handout. Here are the masterclass problems.*Monday, November 23:*no meeting (Thanksgiving break).*Monday, November 30:*general problem-solving practice. Here is the handout. Here are the masterclass problems. Also, Gyujin Oh has collected some nonstandard techniques that have appeared on the Putnam that he is willing to share. Here it is!*Saturday, December 5:*The Putnam Competition!

Want more? Additional suggestions for others? Please let us know!