Math & CS Chats - Fall 2001
[ Wed. 12/12 | 11/26 | 11/12 | 10/28 | 10/15 | 10/1 | 9/17 ]
12/12/01 - Showing of "The Proof"
Wednesday 12:00 noon Dana 110
This GREAT movie introduces its audience to what may well be the most famous mathematical problem of all time, and the most exciting mathematical discovery we're likely to see in our lifetimes. It provides an excellent glimpse into the thrill of scientific discovery and what it means to be a mathematician! Moreover, the movie is accessible to mathematicians and non-mathematicians alike (although it should be of special interest to mathematicians and computer scientists). And John Conway (of Dickinson Priestly Lecture fame) appears in it. Everyone should see this movie!
Eureka! For Princeton math whiz Andrew Wiles, tackling an equation is like groping around in a dark mansion, finding the light switch, and suddenly seeing, with utter clarity, where you are. But in Wiles' case, the mathematical challenge of his childhood --- proving Fermat's Last Theorem, a famous enigma that had stumped experts for three centuries --- would take eight years of seclusion. With Wiles' apparent success came the triumphant glare of publicity... until a disappointing discovery forced him back undercover to retrace the steps of his difficult quest.
Follow a fascinating tale of obsession, secrecy, and the camaraderie of kindred souls. Enter a rarified world inhabited by the foremost mathematical minds, where the joy of finding an absolute solution is giddily contagious --- whether that proof is entirely your own or a bridge linking other mathematicians' conjectures. With the help of computer animation, see complex mathematical conceots, such as elliptical curves (the basis of elliptic curve cryptography) and modular forms, pictured in beautiful 3-D symmetry. And hear Wiles himself describe the "incredible revelation" that finally led him --- and three centuries of mathematicians --- out of the dark. "Fermat's Last Theorem has been responsible for so much," marvels John Conway, "What will we find to take its place?"
11/26/01 - "Dial M for Mathematics"
Prof. Barry Tesman
Department of Mathematics and Computer Science
Many great Theorems in mathematics have their roots in a very simple observation or question. In 1852, Francis Guthrie noticed that if regions on a map which share a common boundary are differently colored then four colors suffice for the whole map. This led to the proof of the four color theorem in 1976! Pierre de Fermat, around 1630, noted that x^n + y^n = z^n has no nontrivial integral solution for n > 2. It was not until 1995 when Andrew Wiles published his proof and finally settled this 300-year old conjecture. In this talk, I will show how a simple telephone number led to an abundance of mathematical research.
11/12/01 - Associativity in Human-Computer Interface Design: An Indicator of Remarkable Progress
Professor Sig Treu
University of Pittsburgh
The fact that the human mind is associative in nature has been known for a long time. It stands to reason, therefore, that the designers of human-computer interfaces should take advantage of such mental strength exhibited by computer users. However, for many years the objective of rendering the interface more conducive and complementary to the way people think was rather elusive. Vannevar Bush envisioned over half a century ago an associative system named "memex." Are we anywhere closer now to what he hypothesized? This talk portrays the remarkable progress that has indeed been made and uses it as one indicator of the importance of conducting graduate study and research in the discipline of computer science.
10/28/01 - Rubber sheets, hairy hedgehogs and the platonic solids: applications of the Euler characteristic
Prof. David Richeson
Assistant Professor of Mathematics
The Euler characteristic is a classical invariant of topological spaces. In this talk we will introduce the Euler characteristic and show how it relates to vector fields. We will show how the Euler characteristic relates to the hairy ball theorem, the classification of surfaces and uniqueness of the platonic solids.
10/15/01 - Ruler and Compass Constructions
Assistant Professor of Mathematics
Ruler and compass constructions, which were well-known to ancient Greek mathematicans, are a standard topic in today's high school geometry courses. Unfortunately these classes only provide a brief glimpse of the results that can be achieved with these "rudimentary" tools. In this talk we will consider one of the highlights of ruler and compass constructions, Hippocrates' Quadrature of the Lune.
10/1/01 - Unlocking the Mystery of Water Waves
Senior Mathematics Major
Water is encountered everywhere around us. While most times it is just accepted for its serenity and beauty, a mathematical system exists beyond what our eyes can see. I spent the summer researching this system with Professor Richeson, and we have developed a basic course teaching the basic theory behind water motion. Using some basic mathematical theory and computer programs, the chat should give a basic knowledge of the system behind water and hopefully inspire further thought for further research.
9/17/01 - Computer approaches to investigate biological questions.
Assistant Professor of Biology
The development of the wing in the fruit fly D. melanogaster is controlled by two proteins, Vestigial and Scalloped. These proteins function together, with Scalloped acting as a transcription factor that directly controls the expression of genes in the wing. The Scalloped protein recognizes a sequence of bases, or motif, in the DNA in the regulatory regions of genes. The Scalloped protein physically binds at these motifs, which results in a gene being turned on in the developing wing. I am using computational approaches to identify additional locations of these motifs in the D. melanogaster genome. In this manner, I hope to identify additional target genes of Scalloped activity. I will be discussing recent approaches and results.