September 23: Mikil Taylor, Vanderbilt University Undergraduate
Title: The Golden Ratio
Abstract: What is the Golden Ratio? In this talk, we will explore this mysterious number “phi” throughout its history. We will explain how to derive it, and how it naturally arises in all sorts of surprising situations, including geometry, music, art, poetry, and pineapples!
September 30: Justin Fitzpatrick
Title: To Deal or Not to Deal, That is the Question
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!!
October 7: Adam Weaver
Title: The People Have Spoken: but what did they say?
Abstract: Have you ever felt like there is something not quite right about the voting system? Is it a conspiracy or something intrinsic to voting? Think you could come up with a better system? How much impact does the choice of voting system have on the outcome, anyway? We’ll try to answer these questions with a mock election. We will consider some properties of an ideal voting scheme, and the possibility of achieving such an ideal. We will also discuss different ways to measure voting power.
October 14: Alan Wiggins
Title: Magic Computers
Abstract: In the 1980’s, Richard Feynman suggested building a computer based on quantum mechanical principles. What does that mean? What would such a machine look like? Are they out there right now? We’ll discuss these questions and what the theoretical limits on such machines would be. In particular, you CAN’T win a million dollars from the Clay Institute for making a “practical” quantum computer (unless you believe in traveling faster than the speed of light), but you CAN crack a host of security codes, which would get you even more from Microsoft.
October 28: Matt Calef
Title: Across the Eighth Dimension (Buckaroo Bonzai!)
Abstract: While the term dimension is used regularly it has many different definitions not all of which agree. An intuitive understanding is that the dimension is the maximum number of mutually perpendicular directions. However, dimension can be meaningful in settings where the notion of direction is not. The talk will start by considering the dimension of objects familiar to first year calculus students and then move on to examining dimension in more involved settings. We shall see that the questions: Can the dimension be infinite? and Can the dimension be non-integer? are both answered in the affirmative.
November 4: Alex Wires
Title: When is the Whole Equal to the Sum of its Parts?
Abstract: The number theoretic work of Euclid’s Elements culminates with the perfect numbers. But the ancient Greek geometers could only describe perfect numbers which were even. Are there infinitely many even perfect numbers? Are there any odd perfect numbers? In asking these two questions Edmund Landau wrote, “Modern mathematics has solved many (apparently) difficult problems, even in number theory; but we stand powerless in the face of such (apparently) simple problems as these.” Drop in to learn about the oldest unsolved math problem. There will also be the inaugural announcement of the Odd Perfect Cash Prize.
November 11: Dan Ramras
Title: A Tour through Topology
Abstract: Topology studies intrinsic properties of geometric objects: those features that remain unchanged if the object is deformed continuously. A basic goal of topology, and topologists, is to distinguish geometric objects. Sometimes this is easy. We all know the difference between a donut and a sphere; one has a hole, and the other doesn’t! But to distinguish more complicated, higher dimensional objects, subtler tools are needed. We’ll start off by discussing Euler’s theorem, which gives a topological invariant that can be computed for geometric objects built out of simple building blocks. Euler’s theorem has some nice applications, like Pic’s formula for the area of certain regions in the plane. We’ll move on to discuss the “fundamental group,” which describes loops inside a geometric object. This notion lead Poincare to make his famous conjecture about three-dimensional geometry, solved a hundred years later (in 2002) by Grigori Perelman.
November 18: Tara Davis
Title: To infinity and beyond!
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.