# Math 43900 - Problem Solving in Math

## Fall 2014

### Instructor: David Galvin

The William Lowell Putnam Mathematical Competition is a nationwide mathematical problem-solving competition that is held annually on the first Saturday of December. All undergraduates who enjoy solving mathematical problems (whether math majors or not) are invited to take part. Math 43900 is a course designed to help participants to prepare for the competition.

Here is some general information for the 2014 course.

**First meeting**: The first meeting is scheduled for Tuesday, August 26 (3.30pm, in Hayes-Healy 129), the first day of classes. This will just be an organizational/introductory session, where will go quickly over the organization of the class, and you can all introduce yourselves to me. We'll also talk briefly about high-level problem-solving strategies, and I'll hand out a sheet of warm-up problems.

**Weekly problems**: Throughout the semester I'll update the following document:

weekly problems
with problems, solutions, and discussions of problem-solving techniques.

- November 25: A final grab-bag, and Putnam tips
- November 18: Probability
- November 11: Graphs
- November 4: Games
- October 28: Modular arithmetic and number theory
- October 14: Another grab-bag
- October 7: Recurrences
- September 30: Polynomials
- September 23: Inequalities
- September 15: Binomial coefficients
- September 9: Pigeon-hole principle
- September 2: Induction
- August 18: A grab-bag of problems for the first week

**Recent Putnam Competitions and Solutions**

**2013**: problems, solutions (not the official solutions, which will appear in *American Mathematical Monthly* in October)
**2011-2002**: The official results and solutions, published every October in *American Mathematical Monthly*, can be found here. Your ND password is required.
**Earlier**: All earlier Putnam competitions are compiled in the three books mentioned on the general information page. These books are on reserve in the O'Meara math library.