Monty McGovern

Mathematical Reasoning

What do mathematicians do when they prove theorems? I will give an overview of the main techniques used in mathematical proof during the first week, and then apply these techniques to prove two major results in number theory (the two- and four-square theorems) the second week, though in fact you will be applying these techniques to a wide variety of problems throughout. What you learn will be very useful for other courses this summer as well.