(This has not been thought through particularly thoroughly, but I wanted to get this page posted.)
- I (=Ravi) really like Loren Larson’s Problem Solving Through Problems — definitely worth owning. It’s great preparation for the Putnam, but also great in general.
- Ditto for Paul Zeitz’ The Art and Craft of Problem Solving. It is ostensibly aimed at high school students, but there is no sell-by date on this stuff.
- It is also great help (more than you would think) trying many old problems. I’d especially recommend the collection of recent Putnams The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary, by Kiran Kedlaya, Bjorn Poonen, and Ravi Vakil.
- There are more good problems in the previous Putnam book, The William Lowell Putnam Mathematical Competition Problems and Solutions: 1965-1984, by Alexanderson, Klosinski, and Larson (look especially at those in the 1980’s).
Larson and Putnam ’85-’00 are in the math library. Also, on the web you can find
- a compilation of old Putnam problems and solutions on the web, collected
by Kiran Kedlaya (link to be added — but you can find them by google);
- to find solutions to older Putnams, you can read the official solutions in the American Mathematical Monthly, which you can see electronically (from any Stanford computer) here. At that page, ‘Search this journal’ for “William Lowell Putnam”
in the title.
- The Art of Problem Solving is terrific.
- Some more links are available through this good UCSD site, by Patrick Fitzsimmons.
Please pass on any suggestions you like!