# Fall 2010 Talks

September 28: Michael Hull
Title: RSA – An Introduction to Public-Key Cryptography
Abstract: Ever wonder how you can safely send your credit card number over the internet? The answer is RSA, the first widely used public-key cryptographic communications system. Using only elementary techniques from number theory, RSA allows you to send secure communications over public channels without a pre-arranged code. In this talk, we discuss the difference between public-key and private-key cryptography, and cover some basic ideas from number theory. Then we will show how to use RSA to encode and decode messages, and explain why this process works and why it is so difficult to crack.

October 5: Jeremy LeCrone
Title: “IF You Believe That, THEN You Won’t Believe This”
SubTitle: “LOGIC: The Science of Argument”
Abstract: “If Mathematics is the language of science, as most people would agree, then the language of Mathematics is Logic. In this talk I will introduce you to some of the basics of this not-so-foreign language. As rational, educated human beings, you will see that learning logic is not like learning another language, but rather like formally defining the language you have been speaking since birth. Recognizing proper logic and knowing how to apply it can benefit you in all arenas of life. Not only will you see how logic is used in mathematics to prove and disprove claims, but also how it is used — and abused — in television, politics, the court system, philosophy, cartoons, movies, games, business, etc…”

October 12: William Young
Title: Proofs Everyone Should Know
Abstract: For the purpose of obtaining a well-rounded education, it is vital that everyone knows the basics of the most fundamental fields of study. For example, everyone should have read at least three Shakespearean plays, should understand the inner workings of the human body, should be able to name most of the British monarchs, and should have a basic comprehension of the proofs in this talk. Some ofthe results which will be discussed include that there are infinitely many primes, the irrationality of, the square root of 2, and Euler’s solution to the Königsberg Bridge Problem.

October 19: Emily Marshall
Title: An Introduction to Graph Theory
Abstract: What’s the Bacon number of Taylor Swift? How many colors do you need to color a map so that bordering countries have different colors? What’s the best traffic flow pattern through a city? These questions and more can all be answered using graph theory. To a graph theorist, a graph is a set of vertices and edges, not a Cartesian coordinate system. Graph theorists can apply their results to numerous other fields, particularly computer science. This talk explores some of the more fun applications of the field and introduces ways to use graphs to solve everyday problems.

October 26: Johnny Waite
Title: The Mathematics of Juggling
Abstract: Everyone has seen someone juggle at some point, probably at a circus or on the street. But anyone who has every tried to juggle knows that it is more involved and complicated than it looks. After further inspection, it is easy to see that juggling indeed has some very interesting mathematical properties. In this talk, these interesting properties will be explored. The juggling sequence notation will be introduced, and also many questions will be answered concerning juggling, such as: which sequences are valid juggling sequences, how many ways are there to juggle, etc.

November 2: Matthew Smedberg
Title: Early and Often: How voting systems affect democracy and math affects voting systems
Abstract: To most Americans, voting is an infrequent, simple civic activity: you learn a little about the candidates, choose the one you like the most (or dislike the least!), mark a paper or electronic ballot, and move on with your life. Few of us reflect on how the electoral system might shape our public institutions, and still fewer on how the electoral system might be different, and how such changes could affect the power and workings of public institutions. We will discuss a few such ideas during this talk, including why the U.S. has a two-party system while other nations have several parties; and Arrow’s Theorem stating (informally) that there is no perfect electoral system.
View the Slides from Matt’s Talk!

November 9: Justin Fitzpatrick
Title: Combinatorics: Pascal’s Triangle and More
Abstract: Ever wonder where the numbers in Pascal’s Triangle come from, or why they work out so nicely? In this talk, we’ll look at some basic techniques of counting by combinations and permutations and see how they lead us to some interesting results including the binomial theorem, which is the source of the numbers in Pascal’s famous triangle.

November 16: Stacy Hoehn
Title: Monopoly and Mathematics: Linear Algebra in Action
Abstract: Have you ever noticed when playing the board game Monopoly that you land on certain squares more than others? Do you know which square is the most common to visit? Do you know which properties are the most valuable to own? Using a few ideas from linear algebra which we will introduce in this talk, we will answer both of these questions and more.