How to Solve It
Instructor: Tony Wong
Time & Venue: T 7:30-8:25pm, Sloan 151
Office Hour: T 8:30-9:25pm, Su 8:00-9:00pm Sloan 151
Email: tonywong (at) caltech (dot) edu
The goal of this course is to raise students' interests in mathematics, enhance their problem solving skills and help them better prepare for the William Lowell Putnam Competition.
In each weekly hour-long lecture, a focus will be chosen, and a selection of problems in the past papers of Putnam related to the focus will be discussed. Sometimes a complete proof will be presented, while at other times, only key ideas are mentioned. In any case, we shall always try to explore how we should start tackling the problems, how far we should push in a seemingly unsuccessful attempt, and how we should write a "precise and concise" proof.
During the office hour, students are encouraged to bring up questions on Putnam problems that they have worked on but could not solve. The class will then discuss on these problems together and try to solve them as a team work. If there are no questions brought up, the instructor will choose some problems related to the focus of the week for the class to work on.
Two to three problems will be assigned as homework each week, and grading will be based on the amount of efforts spent on the homework problems. Individual work is expected, as one of our goals of this course is to train for the Putnam competition.
There are several useful references for this course, and all of them are available online. The first one is the Putnam competition directory, which contains Putnam past papers from 1985-2011 and solutions from 1995-2011. There are also some interesting statistics for the competitions like the scores of the high achievers.
If this website does not provide enough past papers, one may go to the second one, which contains Putnam problems from the first competition in 1938 to the 64th in 2003. Again, this website also contains most of the solutions.
Finally, a website that may prove very useful is the course webpage of the Putnam seminar in Carnegie Mellon University, taught by a former Caltech undergraduate Po-Shen Loh. He is also the deputy team leader of the IMO (International Mathematics Olympiad) USA team.