This year we (Ravi and Sound) will be running the Polya seminar, one of whose aims is to motivate students to participate in the Putnam competition. The Polya seminar was first started by Ravi many years back, and his website contains much useful information. The seminar is named after George Polya (1887-1985), a great mathematician and problem solver. He was a Professor at Stanford from 1940 to 1953, and lived in Palo Alto for the rest of his life.

The Polya seminar is also being offered as a 1 credit course Math 193. You do not need to sign up for the course in order to participate in the seminar. But if you do sign up for the course, then to get credit it is expected that you will attend all of the seminars, and take part in presenting solutions from time to time. If you miss more than two meetings, you may not receive credit for the course.

The Putnam is a challenging opportunity for you to test your mathematical mettle. This year the Putnam will take place on Saturday, December 3; there are two sessions, morning from 8 to 11 and afternoons from 1 to 4. The exam is notoriously difficult; in most years the median score is 0, but in some recent years the exam has gotten slightly easier with a median score of 1! Each year there are about 3600 students from colleges and universities across the US and Canada who take the test. Stanford has been doing phenomenally well in the last several years. Last year the Stanford team finished fourth, and Gyujin Oh was named a Putnam Fellow. In addition, a number of students placed in the honor roll of top 500 students in the competition.

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; 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.)

The Polya seminar is also supported by Two Sigma Investments, and in the spring we will award cash prizes (thanks to Two Sigma!) based on performance in the Putnam.

Our goal in the seminar is to have a relaxed and friendly atmosphere. There'll be pizza and drinks, and you are strongly encouraged to talk and work with others. Ultimately the focus is on developing a broader appreciation for mathematics, in addition to problem solving skills, and to have fun in the process!

Some useful links:

More info on the Putnam plus a sample year: 16introhandout copy.pdf

Kiran Kedlaya's Putnam Archive

Po-Shen Loh's Putnam Seminar Page

You may also find useful the books by Larsen (Problem solving through problems), or Engel (Problem solving strategies), or the compendia of past Putnams (an old book by Alexanderson et al, and a newer one by Kedlaya, Poonen and Vakil). These will be on reserve in the math library; also the library may have online copies of some of these books that you can access directly.

Week 1 (Oct 3) : Topic: Induction, Parity, Pigeonhole. Problem1.pdf

Week 2 (Oct 10): Topic: Number Theory. Problem2.pdf

Week 3 (Oct 17): Topic: Recurrences, Combinatorics, Generating Functions. Problem3.pdf

Week 4 (Oct 24): Topic: Analysis and Inequalities. Problem4.pdf

Week 5 (Oct 31): Topic: Algebra, Polynomials, Complex numbers. Problem5.pdf

Week 6 (Nov 7): Topic: Invariants and Monovariants. Problem6.pdf

Week 7 (Nov 14): Topic: Probability and Combinatorics. Problem7.pdf

Week 8 (Nov 28): Miscellaneous Putnam Problems. Problem8.pdf

Week 9 (Dec 5): Putnam Post Mortem. PPutnam2016.pdf