Spring 2005 Schedule
The Incredible Shrinking Data (Thursday, January
27)Speaker: Casey Leonetti
In Clarksburg, West Virginia, the FBI maintains a database of 81 million sets of fingerprints. That's about 13,500 hard drives full of information! How does the FBI store all this data? They shrink it, of course, just as you might do to a song when you store it on your computer as an MP3. Join mathematics graduate student Casey Leonetti at this week's Undergraduate Seminar in Mathematics and learn about the mathematics behind the data compression used by MP3's, digital photos, and the FBI!
Speaker: Peter Hinow
Invented by the German mathematician Georg Cantor (1845-1918) in 1883, the Cantor set is probably the oldest fractal object. In this talk I will start with the standard construction of the Cantor set by removing the ''middle thirds'' of subintervals of the unit interval I=[0,1]. Then I will show that the points of the Cantor set are exactly those whose ternary (base 3) representation does not use the digit 1. The Cantor set can also be obtained as the attractor of an iterated function system, i.e., by applying a suitable function to I again and again. The concept of similarity dimension will be introduced and it will be shown that the Cantor set has the (non-integral) similarity dimension $\frac{\log 2}{\log 3}$.
Mathematics of Mosaics and Tilings (Thursday, February
10)Speaker: Yuliya Babenko
When confronted with a big flat space and a bunch of little pieces, it's just human nature to fit the pieces into it. Since every game has to have rules to make it fun and challenging, it only natural to want the pieces to fit together nicely. And voila! A tiling is born.
Every known human society and even mother nature have made use of tilings and patterns in some form or another: Alhambra Palace at Granada in Spain, ''impossible drawings'' of Escher, periodic wallpaper tilings and non-periodic Penrose tilings, crystals and quasicrystals, cell arrangements in skins and membranes of animals and plants. Join Yuliya Babenko to discover the geometry which makes all of it so structured and symmetric, so magically attractive and fascinating.
Order to Chaos (Literally!) (Thursday, February
17)Speaker: Les J-Man Carter (Literally!)
Much of the world around us seems chaotic and random. For instance, why are some rocks shaped the way they are shaped? Why do trees and plants grow to look as they do? What's up with DNA? And why did MC Hammer wear those disgusting pants in the 90s? Well, believe it or not, there is mathematics behind many seemingly chaotic phenomena. Come to the talk to hear about some of it! Perhaps MC Hammer will show up.
How to Guard a Museum (Thursday, February 24)Speaker: Dan Biebighauser
Suppose you have a one-story art museum, and you want to make sure that every point of the museum is watched by a guard. Guards must stay at fixed posts, but are allowed to turn around. How many guards do you need?
For example, if the floor plan is a rectangle (as in the figure), only one guard is needed, because the guard can see every point. Is this the case for every floor plan? Do you ever need more than one guard? If so, how does the number of guards needed depend on the shape of the museum?
The Prisoner's Dilemma and the Nash Equilibrium
(Thursday, March 3) SPECIAL ROOM: SC
5211 Speaker: Alex Popkin
You've just been arrested during an attempted robbery. If both you and your partner in crime confess, you face a lengthy prison sentence. If neither of you confesses, you can get by with a lesser sentence for breaking and entering. But if you testify against your partner, you can plea bargain and get no jail time at all. Can math help you decide what to do in this situation?
Of course! In this week's undergraduate seminar we'll explore a branch of math called game theory and learn about the concept of the Nash Equilibrium. The results can be applied to a huge variety of topics ranging from arms control treaties to bass fishing.
Alice and Bob: A Love Story (Literally!) (Thursday, March 17)Speaker: Matt Calef
In this crazy mixed up world of ours, how can two people communicate effectively? What problems will they face, and what tools are available to help them? Is there a relationship between privacy and trusted communication? What does the padlock icon signify in the corner of your browser? How can you make millions of dollars just by keeping a secret?
In this week's undergraduate seminar we'll explore cryptography in theory and in practice. We'll start with a discussion of modulo arithmetic and prime numbers, we'll examine the RSA algorithm, and then discuss how cryptography is put into service today.
You're Moving Where?!?: The Many-Fold Wonders of Manifolds (Thursday, March 31)
Speaker: Adam Richardson
Do you ever feel fenced in by the walls of your dorm room? Do you ever wish you could play a game of Tic Tac Toe with someone over the age of ten and win? Wouldn't it be nice if you could just pick up a pair of binoculars to determine once and for all whether or not those new jeans make your butt look big? In this week's seminar, we will discuss geometric boundaries and the ways in which they may be circumvented. While we're at it, we will explore some of the basic concepts of an exciting way of looking at geometry called manifold theory and use our newfound knowledge to play some of your favorite games ... with a twist (literally!). Finally, we will briefly touch on a few of the questions manifold theory raises about the nature of the cosmos and what, if anything, lies beyond.
Whistling Girls and Crowing Hens: Women in Mathematics from
Ancient to Modern Times (Thursday, April 14)Speakers: Dr. Jo Ann Staples and Fumiko Futamura
Recent remarks from Harvard president Lawrence H. Summers about the problems facing women in math and science have sparked a controversy about historical gender inequities in these disciplines. Jo Ann Staples and Fumiko Futamura take a look at some of the prominent women in mathematics from the time of the ancient Greeks to the twenty-first century. What led to the tragic murder of the Hypatia, the first woman mathematician on record? Who (or what) is the Witch of Agnesi? Who really invented computer software? Where did the silly title for this talk come from? Learn the answers as we explore the past, present and future for women in mathematics.
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Last Updated
April 12, 2005