**September 29**: 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.

**October 6**: 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.

**October 13**: Stacy Hoehn

**Title**: The Shape of the Universe

**Abstract**: To a topologist, two objects have the same shape if one object can be deformed into the other by simply stretching, bending, or twisting. With this understanding of shape, we will explore what 3-dimensional shape the spatial universe in which we live has. As 3-dimensional creatures living inside a very small part of the vast 3-dimensional universe, it is hard for us to imagine what the universe as a whole would like from the outside. However, recent experimental evidence suggests that there are only 10 possibilities! There will be lots of pictures to help us imagine what these shapes look like because some of the possibilities are truly bizarre!

**October 20**: 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 27**: Matthew Smedberg

**Title**: Euclid’s Proof of the Law of Cosines

**Abstract**: This talk will discuss ancient Greek geometry, and the methods used by the Greeks to prove many facts which we handle today with algebra. Starting with the proof (and the statement!) of the Pythagorean Theorem, both of which a modern reader might not recognize at first glance, we will discuss how the Greeks would have thought about such theorems as the distributive property, completing the square, etc., all of which, while interesting in themselves, also served as stepping stones to three Big Problems of Greek mathematics: “solving” arbitrary triangles, “squaring” arbitrary polygonal regions, and constructing geometric means.

**November 3**: Derek Bruff

**Title**: Cryptography: Nby Bcmnils uhx Gunb iz Wixym uhx Wcjbylm

**Abstract**: Cryptography is the science of secret writing—using codes and ciphers to conceal the meaning of messages and also cracking those codes and ciphers to discover the meaning of messages one is not intended to read. The history of cryptography is a game of one-upmanship between code makers and code breakers, a game that has played out in military settings (such as the cracking of the encoded Zimmerman Telegram that led to the entry of the United States in World War One), information security (such as the data encryption used to protect financial information online), and popular culture (such as the codes and ciphers used in Sherlock Holmes’ stories, books and movies like The Da Vinci Code, and online alternate reality games such as ones used to promote the TV show Lost). In this talk, we’ll take a quick tour through the history of cryptography and take a look at a few classical cipher systems, as well as some of the mathematics that makes them work.

**November 10**: Mikil Taylor

**Title**: Development of the Concept of Number

**Abstract**: Contrary to popular belief, the concept of number has not been static throughout history. Humans started in the most humble of conditions, counting on fingers, unable to write or even conceive of many numbers above 2. As time passed, the idea expanded to include written forms, both well and terribly suited for calculation, and other ideas of numbers, from fractions to irrationals to negatives, all the way to the imaginary. Join Vanderbilt Undergraduate Mikil Taylor on this exciting journey through the ever-changing ideas of what exactly constitutes a number.

**November 17**: 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…