Splash Biography

Do you wish it was socially acceptable to spend all day playing with blocks and knocking down dominoes? Have you ever thought long and hard about what is really going on with a game of pick-up sticks or cat's cradle? It is a well kept secret that activities like these are actually a lot closer to the math that mathematicians work on than the numbers and symbols you think about in high school. In this class we will investigate cool abstract math problems which arise in children's games. The class will be very hands on, and we will sketch some really interesting proofs and think about cool mathematical concepts. We will avoid complicated notation and numbers and all that boring stuff.

Which way should you shoot in a penalty kick? How should ice cream vendors position themselves on beaches? What is the best strategy in rock, paper scissors? Game Theory is the study of strategic decision making. Mathematical models are utilized to represent rational individuals and attempts to determine the the best possible decisions given certain outcomes and constraints. Game Theory attempts to answer the questions listed before and some more serious ones, such as how companies like Coke and Pepsi should compete. It even goes so far to answer if these companies can collude without ever speaking. This course will present these models in the most basic form to illustrate how we can take certain "games" and attempt to determine a best possible choice. The games presented will be competitive, and will reward the cunning winners with delicious prizes. Topics to be included are normal vs extensive form, single vs. iterated play, the prisoners dilemma, and the pirate game. Come learn how we attempt to describe the choices of life and beat your friends in this competitive class.

Can a left handed person walk around the planet and come back right handed? Well, not on this one. But on another surface, this is quite possible. You can also walk around a knotted paths with out intersections or bridges, see yourself from behind without the help of mirrors, or be synonymously on the interior and exterior of the planet. In this class we will study a number of surfaces in three space, including the projective plane, the klein bottle, and multi-genus oriented an non-oriented surfaces.

How many integers are there? We all know the answer to that, there are infinitley many. Okay, but are there twice as many integers as positive integers? I claim that no, there are just as many, still infinitley many. Okay, then what about real numbers? It seems like if the above is true, there must be the same amount of real numbers as integers, still infinitely many. In fact this is not the case. There are measurably more real numbers than there are integers. And there are infinitley many of both. In this class we will learn some basic set theory which will allow us to discuss rigorously the cardinality of infinite sets, and we will describe one of the most fundamental open questions in mathematics, the continuum hypothesis.

Can a left handed person walk around the planet and come back right handed? Well, not on this one. But on another surface, this is quite possible. You can also walk around a knotted paths with out intersections or bridges, see yourself from behind without the help of mirrors, or be synonymously on the interior and exterior of the planet. In this class we will study a number of surfaces in three space, including the projective plane, the klein bottle, and multi-genus oriented an non-oriented surfaces.

How big is the universe? How big is the set of all real numbers? How big is the set of all integers? Are they all the same amount big? Are there bigger things than these? This class will explore the concept and sizes of infinity. It will introduce a definition of cardinality and some basic mapping theorems. But mostly we will be thinking about things too big to think about, and drawing conclusions about them.

How many rational numbers exist between 0 and 1? How many positive integers can be listed? How many real numbers? The answer to all of these questions is infinity. But the answers to all of these questions are not the same. This course will explore the sizes of unquantifiable sets, and the applications this has upon finite mathematics.

Suppose there exist a series of statements. The first is true. Each statement implies the next. Are all statements necessarily true? Can you prove it? This course will prove the mathematical theory of induction, and then use it to explore some important concepts in Number Theory.

"We all (or most of us anyway) exist in three spacial dimensions. But this is not the only dimensional possibility. Have you ever considered how the world would seem if you were flat? What if you were a line? What if you had a fourth spacial dimension that you cant even perceive because of the nature of your tri-dimensionality? This two part class will consider first the nature of the spacial dimensions, the worlds they view, and how different dimensions interact. Secondly, the class will discuss the dimensional nature of the universe, the structure it takes, and what this structure means to us. "