Solving Putnam Problems: Math Requirements

[qspeechc]

Hello.

I was just wondering, what mathematics do you need to do the Putnam Problems? I looked at one of the books, and I could not do most of the problems, because I didn't know the relevant mathematics. I'm thinking you need at least linear algebra and real analysis?

Thanks.

 

[snipez90]

You need to know the following topics:

Algebra: identities, inequalities (primarily AM-GM and Cauchy-Schwarz), polynomials, linear algebra, abstract algebra, functional equations, complex numbers
Real Analysis: sequences, series, continuity, derivatives, integrals, multivariable calculus

Geometry, Trigonometry, Differential equations, Elementary number theory (infinite descent, greatest integer function, theorems relating to prime numbers, diophantine equations), Combinatorics and Probability.

But just knowing these topics won't enable you to crack putnam problems immediately unless you are extremely creative or gain a lot of experience doing putnam/olympiad problems. The problems that could be considered part of a good elementary math curriculum such as those from number theory, counting, and elementary algebra could be as difficult as tough math olympiad questions.