October 1: Josh Sparks
Title: Hyperpower to the Max!: An E-Z Look at Tetrations and Their Maximization
Abstract: Just when you just felt safe with exponents… here comes the hyperpower. Also known as the tetration or the repeated exponent, the hyperpower takes a number, x, and forms a chain x^(x^(x^(x^….) that, if extended to an infinite tower, tends to blow up pretty darn often. We will first explore a common math competition problem using this concept, and then look at graphical and calculus-based solutions to maximizing the function. From there we’ll discuss the creation of Lambert’s W function and the range of what values these infinite hyperpowers actually exist, overall showing that these crazy expressions are Easier than they appear!
October 8: Tim Ferguson
Title: Famous Proofs of the Pythagorean Theorem
Abstract: You have probably heard of the Pythagorean theorem, but can you explain why it is true? I will explain several different proofs of this famous theorem, including proofs by Euclid and President Garfield. If time permits, I will also discuss another famous result attributed to the Pythagoreans: the proof of the irrationality of the square root of 2.
October 15: Yago Antolin Pichel
Title: The Brouwer Fix-Point Theorem
Abstract: Play Hex, Prove Brouwer.
October 22: Brian Simanek
Title: Counting for Advanced Mathematicians
Abstract: Our mathematics education parallels the history of mathematics in that it all began with counting. At a very young age, we understood the idea of quantity and – more importantly – how to compare quantities. Then, somewhere along the way we vaguely became aware of this mysterious idea called infinity that somehow answered the question we all posed to our first grade teachers: “What is the largest number?” The main point of this talk will be to demonstrate that infinity does not really answer this question because there are different sizes of infinity! As strange as this may seem, we will try to understand how this can be the case and mention some different ways that mathematicians describe the size of a set when counting is not sufficient.
October 29: Alexandr Kazda
Title: What a computer can’t do
Abstract: Can you tell if a given computer program will ever stop? It turns out that once we abstract away properties of real computers like power running out and discs breaking down, we can’t give an algorithm that will tell us if a given program will ever halt. And it gets even stranger: A lot of mathematical properties are actually algorithmically undecidable. To talk about these matters, we will have to look into what does it mean to have an algorithm that solves a problem. On our journey, we will meet a couple Medieval and Ancient Greek scholars, and end in the 1930s.
November 5: 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.
November 12: Corey Jones
Title: Mathematical Knots
Abstract: An introduction to knot theory.
November 19: Zach Gaslowitz
Title: Combinatorics!
Abstract: Come see why combinatorial proofs are more fun than whatever else you have planned. A splendid time is guaranteed for all.