Symposium

Department of Mathematics

Theodore Begeman

Professor Ken Shiskowski, Sponsor

Coding by the Numbers

Codes or Cryptology has been of intense interest in modern times to securely send messages as well as to encrypt data. One of the simplest and hardest to (theoretically) break methods is the PSA algorithm which uses large primes and modular arithmetic. The mathematical software Maple will be used to program the PSA algorithm and to examine its behavior.

Poster - Guild Hall - 9:00 a.m.~12:30 p.m.

Clarence Johnson, Jr.

Professor Ken Shiskowski, Sponsor

If Newton had a Computer, What Could He Have Done?

The Generalized Newton and Householder's methods for solving equations of the form f(x) = 0 produce wonderful and complicated fractal graphics which provide a great deal of information about each method. The mathematical software Maple will be used to generate these graphics in order to examine local versus global behavior for each method.

Poster - Guild Hall - 9:00 a.m.~12:30 p.m.

Daniel J. Mania

Professor Tim Carroll, Sponsor

Aristarchus of Samos and His Heliocentric Theory

Copernicus is recognized as the main person that laid the groundwork for our present understanding of our solar system. But up to about 1500 C.E. most people believed in the Geocentric Theory of the Universe as put forward mainly by Ptolemy around 150 C.E. Aristarchus of Samos actually had a Heliocentric Theory almost 300 years before Ptolemy came along and 'proved' his theory with some rigorous mathematics. Aristarchus also performed some interesting calculations involving a few celestial objects.

Session C - Gallery II - 12:00 p.m.~12:15 p.m.

Yiting Yu

Professor Ken Shiskowski, Sponsor

Visualizing Improvements to Newton's Method for Systems of Equations

There are several higher order of convergence methods which generalize Newton's method for solving a single equation f(x) = 0. Only one of these methods generalizes nicely to also solving square systems of equations - it is the Generalized Newton's Method. The mathematical software Maple will be used to produce the basins of attraction in several system examples to find the global behavior of the method.

Poster - Guild Hall - 9:00 a.m.~12:30 p.m.


			Department of Mathematics Theodore Begeman Professor Ken Shiskowski, Sponsor Coding by the Numbers Codes or Cryptology has been of intense interest in modern times to securely send messages as well as to encrypt data. One of the simplest and hardest to (theoretically) break methods is the PSA algorithm which uses large primes and modular arithmetic. The mathematical software Maple will be used to program the PSA algorithm and to examine its behavior. Poster - Guild Hall - 9:00 a.m.~12:30 p.m. Clarence Johnson, Jr. Professor Ken Shiskowski, Sponsor If Newton had a Computer, What Could He Have Done? The Generalized Newton and Householder's methods for solving equations of the form f(x) = 0 produce wonderful and complicated fractal graphics which provide a great deal of information about each method. The mathematical software Maple will be used to generate these graphics in order to examine local versus global behavior for each method. Poster - Guild Hall - 9:00 a.m.~12:30 p.m. Daniel J. Mania Professor Tim Carroll, Sponsor Aristarchus of Samos and His Heliocentric Theory Copernicus is recognized as the main person that laid the groundwork for our present understanding of our solar system. But up to about 1500 C.E. most people believed in the Geocentric Theory of the Universe as put forward mainly by Ptolemy around 150 C.E. Aristarchus of Samos actually had a Heliocentric Theory almost 300 years before Ptolemy came along and 'proved' his theory with some rigorous mathematics. Aristarchus also performed some interesting calculations involving a few celestial objects. Session C - Gallery II - 12:00 p.m.~12:15 p.m. Yiting Yu Professor Ken Shiskowski, Sponsor Visualizing Improvements to Newton's Method for Systems of Equations There are several higher order of convergence methods which generalize Newton's method for solving a single equation f(x) = 0. Only one of these methods generalizes nicely to also solving square systems of equations - it is the Generalized Newton's Method. The mathematical software Maple will be used to produce the basins of attraction in several system examples to find the global behavior of the method. Poster - Guild Hall - 9:00 a.m.~12:30 p.m.