# Spring 2010 Talks

February 2: To Deal or Not to Deal
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 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!!

February 9: Puzzles, Riddles, and Games
Speaker: Michael Hull
Abstract: A good puzzle, as Peter Winkler of Dartmouth College describes, is easy to state, amusing, and catching, and it should have a sense of “universality” to it — that it is an exploration of a large interesting question rather than a specific curious instance. In this talk, we will discuss a few good puzzles, presenting elegant solution to some while leaving others for the audience members figure out for themselves. We will also discuss some common techniques for solving these puzzles, including parity and mathematical induction.

February 16: A Complex World, Simplified
Speaker: Justin Fitzpatrick
Abstract: The square root of -1 is a concept that most are at least familiar with. However, doing math with this number can sometimes seem like a mystical process, void of intuition. In this talk we will explore the complex numbers and their arithmetic by watching a series of movies that begins with map making and ends with fractals. You’ll be surprised how easy the transition will be!

March 2: How to Win at Monopoly… and Maybe Make a Billion Dollars
Speaker: Derek Bruff
Abstract: In the classic board game Monopoly, players take turns rolling dice, moving around the board, buying properties, and collecting rent from other players who land on their properties. All of the mechanics of the game are controlled by the dice roll except for one—players get to decide whether or not to buy the properties on which they land. So which properties should a player buy? Which properties are most landed on by other players? Which properties are most profitable? In this talk, we’ll see how to model the game of Monopoly using a few mathematical ideas that will help us answer those questions. We’ll also take a look at applications of those ideas in other settings—including the search algorithm the founders of Google used to become billionaires.

March 16: Fibonacci and the Golden Section
Speaker: Ayla Gafni
Abstract: The Fibonacci sequence is one of the most famous sequences in mathematics. Its terms are closely tied to the Golden Section, which the ancient Greeks found to be the proportion that creates the most aesthetically pleasing rectangle. In this talk, we will explore the life of Leonardo Fibonacci and some of the important contributions he made to mathematics as we know it. We will then look at the Fibonacci sequence, its relation to the Golden Section, and the importance of the Golden Section in nature, architecture, and art.

March 23: The Mathematics of Gerrymandering
Speaker: Emily Marshall
Abstract: The American Heritage Dictionary defines gerrymandering as the act of “dividing a geographic area into voting districts so as to give unfair advantage to one party.” The problem of gerrymandering has led to the development of several mathematical measures of shape compactness, some of which have been used in court cases to argue for or against the legality of congressional redistricting plans. In this talk, we will show how the notion of convexity can be used to detect irregularly shaped districts. We will explore both theoretical and empirical aspects of this convexity-based measure of shape compactness.

March 30: An Introduction to the Ontology of Mathematics
Speaker: Sam Nolen
Abstract: This is a philosophy talk in which I will consider a fundamental question in the philosophy of mathematics: “Do numbers, sets, and so on, exist?” A recurring theme will be the historical emergence of ideas about what mathematics is, from within mathematics itself. Due to personal biases, I will emphasize the perspective of the working mathematician.

April 6: Archimedes and Calculus: a look at Greek Mathematics
Speaker: Georgi Kapitanov
Abstract: Newton and Leibnitz are credited as inventors of calculus but the idea of finding the whole by approximating its parts was already known to Archimedes much earlier.For the first part of this talk we will look at early Greek mathematical ideas and give a proof of the Pythagorean theorem. Then we will concentrate on Archimedes and show how he used calculus ideas to prove the formula for the area of a circle.