# Fall 2007 Talks

Title: To Infinity and Beyond! (Tuesday, October 9)
Speaker: Tara Davis
Abstract: Infinity is a universal idea that has captured man’s imagination for centuries. It is ubiquitous in mathematics, art, philosophy and science. But what is infinity? We will discuss this question through the framework of history, anthropology, and mathematics, and along the way will meet some challenging questions which will illuminate just how mystical infinity really is.

Title: To Deal or Not to Deal, That is the Question.
Speaker: Justin Fitzpatrick
Abstract: Getting on a game show is a once-in-a-lifetime opportunity, so you had better go prepared! In this talk, we will prepare you specifically to play correctly on the wildly popular game shows “Deal or No Deal” and “The Price is Right.” We introduce the concept of expected value, a concept that is extremely integral to determining correct strategy for many games, and then apply it and other game-theoretic concepts to these two game shows. You will learn when to deal, when not to deal, when to spin again, and when to let the next person spin! And, since there is no substitute for experience, we will allow four lucky students to COME ON DOWN and compete for prizes!!

Title: What is Mathematics?
Speaker: Filjor Broka
Abstract: This lecture is a modest attempt to try and ask some questions on the nature of Mathematics, its goal, and its scope. The lecture will start with a brief survey of questions concerning Mathematics, which have interested many generations of mathematicians and non-mathematicians alike, and it will present some possible answers given by different people along the years. After this, I will try to give a very short introductory review of some of the major areas of modern Mathematics using elementary concepts. If you think you have an answer to the title question, please come and share it with us!

(Tuesday, October 30)
Title: The Brouwer Fixed Point Theorem
Speaker: Matt Calef
Abstract: The Brouwer fixed point theorem tells us (among other things) that if you take two identical sheets of graph paper, lay one flat on a table, crumple the other and place it on the first, then there is a coordinate on the flat piece that is directly below the corresponding coordinate of the crumpled piece. Formally the Brouwer fixed point theorem tells us something about continuous functions, but the proof of the theorem which we shall look will take us into far deeper material, showing us that in math sometimes the only way to solve a problem is to build some very new tools.

Title: Can the Circle be Untangled?: The Mathematics of Knots
Speaker: Thomas Sinclair
Abstract: Tie a knot in a piece of string. Now join the loose ends of the string together,and you have what mathematicians call a knot. Since the early 1980’s, mathematicians have noticed knots appearing in unexpected and surprising ways in such wide-flung areas as Quantum Physics, Chemistry, and Molecular Biology, as well as in many, seemingly unrelated, branches of Mathematics. This talk will introduce one of the basic methods mathematicians have used in describing and classifying knots, planar diagrammatics. Planar diagrams will then be used to prove that the trefoil knot cannot be untangled. The topics discussed in this talk are taken from chapter 1 of “The Knot Book” by Colin C. Adams.

Title: Graph Theory and Combinatorial Independence
Speaker: Jeremy LeCrone
Abstract: The concept of (in)dependence is encountered in many common, everyday situations. From a society’s dependence on oil, to the independence of college, away from one’s parents, we’ve all experienced some of the consequences of (in)dependence relationships. In this talk I will introduce and develop ideas of dependence as applied to graph theory, combinatorics and other branches of mathematics. These concepts will come together for a brief definition of matroids, an abstract combinatorial structure.

Title: Games in Mathematics
Speaker: Jeffrey Harris (Tuesday, December 11)