MATH  IN  ACTION Student Seminar Thursdays  at 2 p.m.  in ILB 430

Spring  2007

Date	Speaker	Title	Abstract
2/8	Dr. Scott Carter	An Introduction to Hypercubes	This story will begin by looking at powers of 2: 1,2,4,8,16,..., and methods of organizing things that can be counted by powers of two: the ends of binary trees, the terms in binomial expansions, the numbers from 1 up that power for example, and of course the vertices of the hypercubes. I will consider methods of cutting the hypercube into pyramidal sets to show an elementary, albeit higher dimensional, proof that the area under the n-power function is the reciprocal of n+1. I will try to show you some nice pictures, and movie illustrations of higher dimensional phenomena.
2/15	Dr. Boris Kalinin	Infinity and Beyond	What is infinity and how do we deal with it? Are all infinities the same? How do we measure and compare infinite sets? We will talk about these questions and explore countable and uncountable sets. We will discuss the notion of cardinality, Continuum Hypothesis, and Russell's paradox.
3/1	Dr. Victoria Sadovskaya	Fractals	Fractals can be described as self-similar sets that have a fine structure at arbitrarily small scales. We will consider a variety of fractals and discuss their properties such as non-integer dimension and infinite length. We will also explore self-similarity in nature and see how fractals are used to create art.
3/22	Dr. Kyle Siegrist (UAH)	How to Find the Woman (or Man) of Your Dreams	There are n candidates, totally ordered from best to worst. The candidates arrive sequentially, in random order. Our goal is to choose the best candidate; no one less will do. Unfortunately, we cannot observe the absolute ranks of the candidates, but only relative ranks. Once rejected, a candidate is no longer available. What should our strategy be? When n is large, is there any hope finding the best candidate? The answers are interesting and surprising.
3/29	Dr. Albert Gapud (Dept. of Physics)	From Measurement to Model, from Geometry to Gravity: A Story of Kepler and Newton	Johannes Kepler (1571-1630) spent much of his life trying to solve the greatest mystery of his era -- the motion of the planets. In 1609, he was the first to formulate a successful, mathematical model of the solar system. However, even though the model worked, he remained baffled as to why it worked, and two decades later he died a frustrated man. For half a century, this question remained unanswered until Isaac Newton (1642-1727) published his work based on a few simple rules. In this presentation, we explore how Newton successfully explained Kepler's model, an achievement that revolutionized humanity's view of the universe -- and was made possible by the synergy of science and math.
4/5	Dr. Boris Kalinin	Problem-solving Session	We will discuss select problems from 2004-2006 Mathematics Contests:   pdf
4/12	Dr. Dan Silver	Why Knot?	Why are mathematicians nuts about knots?

Fall  2006

Date	Speaker	Title	Abstract
9/19	Dr. Susan Williams	Mathematics of Chaos	Why are the weather and the trajectories of asteroids so hard to predict? And what's with those perpetual motion desk toys they sell in airports? We give a brief introduction to the mathematical theory of chaotic systems, which are not at all random even though they may look that way.
9/26	Dr. Madhuri Mulekar	Is Central Park Warming?	The temperatures recorded at the Central Park, New York over the last century show a large number of recent years with the mean annual temperatures above the median temperature of the century. Could this reasonably be attributed to variation due to chance (or randomness) in a process such as weather, or are we experiencing an unusually large number of warm years? Such a question could just as easily be asked for any other place. We'll use simulation for decision-making through hypothesis testing.
10/3	Dr. Victoria Sadovskaya	Problem-solving Session	Problem Set 1   pdf
10/10	Dr. Frank Jellett	Extreme Points of Convex Sets	Extreme points constitute a nice example of the interplay of geometry, analysis and algebra. It turns out that the extreme points of various naturally arising convex sets in functional analysis can be described in terms of the analytical or algebraic structure of the functions involved, and certain representation theorems, new and old can be revealed as a development of the idea of recovering a convex set from its extreme points.
10/17	Dr. Sherwin Kouchekian	Special Relativity	This will be an expository talk aimed specifically toward undergraduate and graduate students who are interested in learning/discussing the fundamental ideas behind the Einstein's special theory of relativity. In a "relative" non-hectic pace, we will try to explain the inertial reference frame, the principle postulates of special relativity, the coordinates of an event, the spacetime diagram, and Lorentz transformation. If time permits, "relatively speaking", we will discuss the effect of the theory on spacetime continuum.
10/24	Dr. Sherwin Kouchekian	Special Relativity II	By popular demand, we provide another lecture on special relativity. We start with Einstein's postulates and try to understand them well. From there, we prove the time dilation and length contraction in more details, where we also touch the topic of energy-mass with regard to special relativity. Moreover, we give a somewhat better understanding of the spacial relativity from the point of invariance theory of an interval in spacetime. Finally, we try to get a picture of special relativity by considering the worldline of a particle in spacetime diagrams and some demonstrations.
11/7	Dr. Elena Galaktionova	P-adic Numbers	In the land of 2-adic numbers all triangles are isosceles, every point inside a ball is its center, and the sequence 2, 4, 8, 16 ... converges to 0.  Do you think this is some exotic mathematical construction which has nothing to do with reality? Physicists consider  p-adic numbers just as relevant in describing our world as the real numbers.