For a 3rd year essay, I think you have to choose a topic you already know something about, or at least are extremely interested in, or you will find writing the essay very hard work.
So what are your areas of interest? Pure? (e.g. Analysis? Group Theory? Galois Theory? Combinatorics? Complex Variable?) Or Applied? (e.g. Quantum Mechanics, General Relativity, Numerical Methods, Information Theory?)
Oh, and if there are any requirements for the essay (e.g. it must / must not be closely related to a course you are currently studing), that would be useful to know as well.