Mathematics Events - Spring 2008
Friday September 21 at 1:40 in Copley 200
Mathematics Colloquium
What is the "birthday" of elliptic functions?
Dr. Adrian Rice, Randolph-Macon College
On December 23, 1751, Euler received a copy of a paper by Count Giulio Carlo de' Toschi di Fagnano on the lemniscate, which directly inspired the creation of Euler's general addition theorems for elliptic integrals. After his major contributions to the subject and the subsequent development and systematization of the theory by Legendre, elliptic functions became one of the dominant areas of mathematical research during the 19th century, leading Jacobi to call December 23, 1751 "the birthday of the theory of elliptic functions". But to what extent can the subject be said to have been born with Euler in 1751? After all, several other mathematicians, including Jacobi himself, are often credited with laying the foundations of what was to become the theory of elliptic functions, in which case its "birthday" could be anywhere from 1694 to 1829. By looking at the contributions of Euler, together with those of five other mathematicians, this talk will examine whether the theory of elliptic functions really did begin in 1751, or whether there is another date that could more accurately be described as "the birthday of the theory of elliptic functions".
Friday, September 28 at 1:40 in Copley 200
Mathematics Colloquium
Tossing a Coin: It's not as Easy as it Looks
Dr. Brian Sutton, Randolph-Macon College
It is a favorite pastime of mathematicians to imagine absolutely bewildering functions. In this tradition, I pose a challenge inspired by Daniel W. Stroock's article "Doing Analysis by Tossing a Coin" (Math. Intell. 22, No.2, 66-72, 2000). Here is the challenge. Draw a curve that
- starts at (0, 0) and ends at (1, 1)
- has length 2
- has no breaks
- always proceeds up and to the right, never dipping back down
- is never perfectly vertical
To demonstrate the difficulty, consider a "stair step" curve from (0, 0) to (1, 1). Such a curve travels 1 unit to the right and 1 unit up, so its total length is 2. It has no breaks and never "dips back down." Unfortunately, though, this curve is at times perfectly vertical. Can this be fixed? Why or why not?
Incredibly, there is a curve with all five of the properties, as we shall see.
Friday, October 5 at 1:40 in Copley 200
Mathematics Colloquium
How the Poles Broke Enigma Prior to World War II
Dr. James Kuzmanovich, Wake Forest University
In recent years a lot has been written about the British code breakers at Bletchley Park and how important their breaking of the German Enigma machine was to the Allied success in World War II. There have even been a NOVA television show and a popular movie (Enigma with Kate Winslet) devoted to the subject. Less, however, has been written about the Polish mathematicians who deduced the internal wiring of the Enigma machine and first broke Enigma messages starting in 1932. How they were able to accomplish this amazing feat using only the intercepted messages is the topic of this talk.
Most of this talk will be historical in nature, but there will be an attempt to give an idea about the mathematics that the Poles used. The mathematical maturity rating of this talk is PG.
Friday, October 12 at 1:40 in Copley 200
Mathematics Colloquium
The Lost Art of Condensation
Dr. Eve Torrence, Randolph-Macon College
Charles Dodgson, aka Lewis Carroll, is best known as the famous author of Alice in Wonderland. But despite his fame, Dodgson never gave up his day job as a mathematics lecturer at Oxford University. Dodgson was as original in his mathematics as he was in his literary pursuits. We will explore a little-known method discovered by Dodgson for computing determinants of matrices, and trace the history of the mathematics behind this method.
Friday, October 19 at 1:40 in Copley 200
Mathematics Workshop
Introduction to Mathematica 6
Dr. Bruce Torrence, Randolph-Macon College
This workshop is intended for new users to Mathematica 6, whether or not you have used previous versions of the software. We will explore some of the new interactive features of the program, and in the process look at many examples relevent to mathematics and science education. This talk is independent of the the talk to be given on Oct. 22.
Monday, October 22, 4:00-5:30 in Copley 200
Mathematics Special Presentation
Mathematica 6 in Education and Research
Cliff Hastings, Wolfram Research, Inc.
This talk illustrates capabilities in Mathematica 6 that are directly applicable for use in teaching and research on campus. Topics of this technical talk include:
- 2D and 3D visualization
- Dynamic interactivity
- On-demand scientific data
- Example-driven course materials
- Symbolic interface construction
- Practical and theoretical applications
Current users will benefit from seeing the many improvements and new features of Mathematica 6 (http://www.wolfram.com/mathematica/newin6), but prior knowledge of Mathematica is not required.
Friday, October 26 at 1:40 in Copley 200
Mathematics Colloquium
Modular Origami and the Trefoil Knot
Amy Winslow (08), Randolph-Macon College
Thomas Hull invented the PHiZZ origami module in order to make mathematical structures involving pentagons and hexagons. I will explain how I used these units to make a trefoil knot tessellated by polygons and then I will show how to use graph theory to explore the possibility of creating a proper three coloring for this structure.
Friday, November 2 at 1:40 in Copley 200
Mathematics Colloquium
Data Compression Using the Burrows-Wheeler Transform
Robert Pullin (08), Randolph-Macon College
The Burrows Wheeler Transform (BWT) is a block sorting data presort used in various compression techniques. Invented in 1994 by Micheal Burrows and David Wheeler, the algorithm rearranges data prior to compression in order to make the context of a given character a good predictor for the character itself. This summer I worked with the BWT in an effort to improve data compression prior to VLF radio transmission.
Pi Mu Epsilon Presents
Random Fractals
Dr. John Nolan, American University
Most people are familiar with (non-random) fractals, where some geometric construction is repeatedly applied to generate finer and finer detail. While it is less well known, there is also a field of random fractals, where shapes are generated by combining a geometric construction with a random component.
This talk will start with some common fractals, and then show how one can use randomness to construct similar random fractals. Examples include random Cantor sets, the Chaos game, random walks, random ferns, and random mountains. Pictures will be used to illustrate the ideas and unique, never before seen random constructions will be drawn in real time!
The talk will be accessible to a general audience.