February 7: 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.
February 14: Emily Marshall
Title: The Mathematics of Gerrymandering
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.
February 21: Justin Fitzpatrick
Title: Combinatorics: I Choose You!
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.
February 28: Michael Goff
Title: Voting power, coalition building, and the Electoral College
Abstract: Your voting power is the probability that your vote is decisive in an election. Does the Electoral College fairly allocate voting power among US citizens? How can voters form coalitions to maximize their voting power? Is any political system inherently unstable? We will survey some of the major ideas and consider the practical implications for our political system.
March 13: Colin Klaus
Title: Classical Mechanics
Abstract: Classical Mechanics represents an outstanding, theoretical achievement, one joining physical principal and mathematical theorem both into a single, concordant design. In this talk, we’ll trace the math-physics dialectic running throughout the subject, as well as narrate the origins of many technical constructs now become household words: e.g. , acceleration, mass, momentum, inertia, energy, etc … (Can you guess which belongs to math and which to physics?) We will be particularly interested in exploring the mathematical features of rigid body motion, which serves as an especially rich case study and is also commonplace in our everyday lives. (Ever ridden a bike or driven a car?) As soil the study of mechanics nourished a great many of the theories now in bloom and on display in our contemporary, mathematical garden. Here one may discover the roots to such subjects as differential geometry, lie theory, sympleptic geometry, ergodic theory. These reasons were alone to make classical mechanics a study of much interest, but as a matter of personality and flavor, it is also one of our most historied subjects and touched by the minds of many best geniuses.
This talk will be an appreciative and playful look at this inheritance. As Newton famously once quoted, “We stand on the shoulders of giants.”
March 20: Jianchao Wu
Title: Pizzas, Bagels, Pretzels, and Euler’s Magical Chi
Abstract: This talk is an informal introduction to topology, a vast mathematical field that studies the weakest notion of “shape”. Since its advent in the late 19th century, it has grown into one of the foundational pillars of modern mathematics. In this talk, I will tell you why to a topologist, a pizza is the same as a muffin, while fundamentally different from a bagel or a pretzel. Then we will continue with a survey of topological surfaces, meeting curious personae such as the Möbius strip and the Klein bottle. I will also shed some light on the pivotal role played by the Euler characteristic in the study of surfaces.
Free pizza! (No bagels or pretzels provided, but I will show you how a topologist would turn his pizza into a bagel or a pretzel)
March 27: Michael Northington
Title: Probability and March Madness
Abstract: Probability is one of the most important and, often, most misunderstood areas of mathematics. Applications of probability theory span from the most basic examples of flipping coins, to real world statistics used in everyday life, and even to the mechanics of the smallest particles that make up are universe. In this talk, we will cover some of the basic rules of probability theory and look at a few non intuitive results. Also, we will look at an interesting application where a probabilistic object called a Markov chain is used to predict the results of the NCAA tournament. As it turns out, this method, developed by researchers at Georgia Tech, has been overwhelmingly more successful than any other ranking system (such as RPI, AP poll, ESPN poll, Sagarin rankings, etc.) in predicting the outcome of NCAA tournament games. We will discuss the mathematics behind this model and some basics about the theory of Markov chains.
April 3: 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 of the 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.