Abstract: 

A partition is a way of writing a number as an unordered sum of numbers. For example, three of the five partitions of 4 are: 4, 3+1, 2+2. Can you find the remaining two? The partition function p(n) counts the number of partitions of n.

We give a proof of the simplest of Ramanujan's congruences for the partition function, and a related result for the tau function. The proof rests on results of Euler, Gauss and Jacobi. The talk will be accessible to undergraduates as long as they are willing to believe a few things about infinite products. We prove an infinite family of congruences for powers of the eta function, which contain the two congruences in question. This is joint work with Hartosh Singh Bal.