February 3: 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.
February 10: Speaker: Tara Davis
Abstract: Let’s play Sudoku! Sudoku is a number puzzle that has recently become popular in America. It is a generalized version of a centuries old mathematical puzzle called Latin squares. In this talk we will discuss some history of and strategies for playing Sudoku. We will also look closer at how to engineer Sudoku puzzles, and focus on how to ensure a unique solution. Finally, we will explore some of the symmetry and mathematics of Sudoku squares.
February 17: Alex Wires
Title: Frank Ramsey and his Innesential Theorem
Abstract: In his short academic career, Frank Ramsay was influential in philosophy, economics, and logic. However, in one of his logical papers he proved a little theorem (which turned out to be unnecessary) in order to answer positively a result (which turned out to be not true). What was this inessential theorem? Why does it tell us complete disorder is impossible, or that an infinite universe may contain all possible worlds – including a world with your own doppleganger? Along the way we may make the acquaintance of a number so big it will make the Sand Reckoner look like a day at the beach.
February 24: 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.
March 10: Mrinal Raghupathi
Title: Spam, Netflix, the FBI, ZIP Codes, and Math.
Abstract: You may have wondered how spam ends up in the spam folder, how Netflix learns your taste in movies, how the FBI (or the team on CSI) match fingerprints, or how your mail gets forwarded. We’ll talk about these issues, and look at other mathematical challenges that arise in making sense of large datasets.
March 17: Mikil Taylor, VU Undergraduate
Abstract: Zero is one of the strangest numbers we have. Why even bother expressing something that, by definition, is nothing? Topics covered include why division by zero destroys all logic, and the development of zero from a placeholder to a full-fledged digit, and the problems it causes.
March 24: Sam Nolen, VU Undergraduate
Title: God’s Algorithm for Solving the Rubik’s Cube
Abstract: A hypothetical “God’s Algorithm” for solving the Rubik’s Cube would give a solution with as few face turns as possible. In August 2008 Tomas Rokicki gave a computational proof that God’s Algorithm would never need more than 22 face turns. The maximum is now known to be either 20, 21, or 22. In this general-audience talk we introduce basic concepts of combinatorial group theory in the context of the Rubik’s Cube and discuss recent computational work on problems related to God’s Algorithm.
April 7: Tyler Smith
Title: A Complex World, Simplified.
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!