Ever since Fischer Black and Myron Scholes first determined a successful way to price options in 1973, Wall Street has increasingly been interested in using mathematics to price derivatives and hedge risk. Mathematical finance has since emerged as an interesting blend of many different fields of mathematics, ranging from probability and statistics to partial differential equations and numerical analysis. In this talk, will cover some of the basic definitions and concepts of mathematical finance, including puts, calls, and arbitrage. We will then look at a simple model for option pricing, known as the Cox-Ross-Rubinstein Binomial model. Finally, time permitting, we will discuss some more advanced topics such as the Black-Scholes formula. This talk should be accessible to everyone.