Introduction
The Vanderbilt University Undergraduate Seminar in Mathematics is designed to show the undergraduate community at Vanderbilt some fascinating and exciting sides of mathematics. During the course of each semester, we'll feature talks by graduate students and professors on a variety of topics in mathematics, from set theory and abstract algebra to analysis and applied mathematics. Each talk will be interesting and accessible to undergraduates, whether they're math majors or not.
Our goal is to show students the beauty and power of mathematical ideas they might not see in their regular coursework. Our hope is that those same students will develop a better idea of, and a keener interest in, what mathematics is and what mathematics can do.
For more information, e-mail mathnpizza@gmail.com.
Read the Vanderbilt Register story about the Undergraduate Seminar in Mathematics!
Spring 2006 Schedule
The talks for Spring 2006 will begin on February 9. Any date without a speaker listed is still available for a volunteer to present on that day.
The talks will usually be from 7:00-8:00 PM, Thursday evenings in Stevenson Center 1206.
FREE PIZZA will be provided!
Secret periodicity in the Fibonacci numbers (Thursday, February 9)Speaker: Alex Powell
This talk will survey some basic concepts concerning the Fibonacci numbers and modular arithmetic (i.e., "clockwork addition"). The Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, ..., are defined by a well-known recursion, and have many familiar properties. We shall take a slightly different look at the Fibonacci numbers within in the world of modular arithmetic and discuss some interesting Fibonacci properties in this realm.
This talk requires no prerequisites and will be accessible to all undergraduates interested in mathematics. In fact, the math discussed in this talk is even accessible to research by undergraduates.
Sudoku (Thursday, February 16)Speaker: Dan Biebighauser
You know the rules (complete the grid so that every row, column, and 3 by 3 box contains every digit from 1 to 9, inclusive). You've seen them everywhere (even The Vanderbilt Hustler). Now learn some of the mathematics behind the amazingly popular Sudoku puzzles. We will explore some, if not all, of the following questions:
- How many filled 9 by 9 grids satisfy all of the rules?
- Is there always just one correct answer?
- How many squares need to be filled initially in order to make the solution unique?
- What are some strategies for solving Sudoku puzzles?
- How can we create Sudoku puzzles?
Speaker: Lin Shan
In mathematics we need to prove many statements and compute tons of exercises. Maybe you need more than one piece of paper to write down one proof. Could you imagine that we can really prove or compute something by a picture? Come to this Thursday's talk! This talk consists of pictures which prove mathematical statements. From this talk you will see that with a little geometric help, you could save lots of time in your study.
Lies, Damn Lies, and Statistics: Exploring the value of numerical
literacy (Thursday, March 16)Speaker: Jake Woods
One only needs to watch a few minutes of television to understand how completely addicted to numbers American society really is. Whether we are hearing a political advertisement, absorbing a news story on tv or in print, or having conversation with a (doctor, stockbroker, lawyer, mom, dad, whoever) it is nearly inescapable that some numerical "spin" will present itself for evaluation. Based on the books of Temple Mathematics professor John Allen Paulos, this talk will present some examples of how a well-developed knack for being sensible about numbers, probability, and statistics can provide profits, prevent embarrassment, and, at the very least, provide some amusement at the abject silliness of some of the numerical "truths" we espouse.
How to Win at Monopoly (Thursday, March 23)Speaker: Derek Bruff
In the classic board game Monopoly, players take turns rolling dice, moving around the board, buying properties, and collecting rent from other players who land on their properties. All of the mechanics of the game are controlled by the dice roll except for one -- players get to decide whether or not to buy the properties they land on. So which properties should a player buy? Which properties are most likely to be landed on by other players? Which properties are most profitable?
In this talk, we'll see how to model the game of Monopoly using a few mathematical ideas that will help us answer those questions. We'll also see how those mathematical ideas can help us do things that are perhaps more important than winning at Monopoly.
Do Bees Know Math? (Thursday, March 30)Speaker: Sergiy Borodachov
If you ever looked at a bee honeycomb, you have noticed that the cells are equal regular hexagons. Did the bees choose this shape and arrangement at random? No! They turned out to be good mathematicians and solved a number of beautiful problems before building their honeycomb.
These are the problems of discrete geometry. One of them is how to arrange non- overlapping quarters on the surface of a table in order to fit the largest possible number of coins on it, or how to place N antagonistic dictators on a given territory so that they were as far as possible from each other?
Another problem, dual to this one, is how to cover a table by equal circular napkins using the least possible number of napkins, or which is the same, what is the smallest number of oases one needs to have in a desert so that for any point in the desert there was an oasis within a given distance a? Join us this Thursday for more interesting examples and to see how the bees reasoned while creating their honeycombs.
Summing Infinite Collections of Numbers (Thursday, April 6)Speaker: Brett Wick
How do you sum an infinite collection of numbers? For example, what does
$$\sum_{k=1}^\infty\frac{1}{k^2}$$
mean? An even better question is what, if anything, is the exact number of this infinite sum?
This question has an answer using calculus, but the answer doesn't tell you what the actual sum is. In fact, it is easy to tell when a sum of infinite numbers is finite, but it is difficult, if not impossible, to compute the exact value of an infinite sum.
In this talk, we will review the concept of a series, talk about some simple examples of series where we can compute the exact sum, and then end with some simply stated questions for which an answer isn't known.
Past Talks
2005 Fall Schedule
2005 Spring Schedule
2004 Fall Schedule
2003 Spring Schedule
2002 Spring Schedule
2001 Fall Schedule
2001 Spring Schedule
Site Maintained by Dan Biebighauser
dan.biebighauser@vanderbilt.edu
Last Updated
April 4, 2006