In this course we will study mathematical finance. Mathematical finance is not about predicting the price of a stock. What it is about is figuring out the price of options and derivatives.The most familiar type of option is the option to buy a stock at a given price at a given time. For example, suppose Microsoft is currently selling today at $40 per share. A European call option is something I can buy that gives me the right to buy a share of Microsoft at some future date. To make up an example, suppose I have an option that allows me to buy a share of Microsoft for $50 in three months time, but does not compel me to do so. If Microsoft happens to be selling at $45 in three months time, the option is worthless. I would be silly to buy a share for $50 when I could call my broker and buy it for $45. So I would choose not to exercise the option. On the other hand, if Microsoft is selling for $60 three months from now, the option would be quite valuable.