Robert Komara - Delgarno-Lewis Methods for Second Order Energies of Neon
The Delgarno-Lewis methods bypass the older
extrapolation methods by combining the solutions of normalized second order
differential basis equations of hydrogen. These stiff differential equations
must be approximated using special techniques to avoid divergence caused
by round off error.
Scott E. Clark - Extensions of the Tower of Hanoi
~~ Best Talk Award ~~
The Tower of Hanoi uses 3 pegs and 64 discs
increasing in size from top to bottom stacked all on one peg. One must
transfer all the discs, one at a time, to another peg, never placing a
larger disc atop a smaller disc. Solutions to the puzzle will be discussed
and variations to the puzzle considered.
Vincent Lucarelli - The KGB, Espionage, and RSA Encryption
~~ Best Talk Award ~~
RSA public key encryption will be applied
to a message from a Russian spy so that it can be securely sent to his
superiors. In the event that American authorities recover the operative
and his encryption system, methods for decoding the message will be presented.
Key to decrypting the message is factoring a 200 digit number by a non-traditional
factoring algorithm. A detailed description of the factoring algorithm
and its application will be discussed.
Bryan Treusch - Days of the Week from Dates
An illustration of the algorithm used by computer
operating systems to calculate days of the week from dates. Mathematical
properties of the Gregorian calendar allow the algorithm to be reduced
to a simple congruence which functions efficiently on even the most basic
8-bit computers.
Kim Jordan - Graceful Creatures of the Sea
~~ Best Talk Award ~~
Graceful labelings of (p,q) graphs requires the
vertices to be distinctly labeled from the set {0,1,..., q} in such a way
that the edge labelings, |i-j|, yield the labels 1,2,...,q for the edges
of the graph. I will examine several families of graceful graphs, including
paths, stars, and catepillars. Several conjectures will be discussed concerning
the gracefulness of graph types Bermond introduced as lobsters and what
I have nicknamed the pinwheel problem. Other families of graphs including
cycles, crowns, and octopi will be examined.
Nakia Rimmer - Cubic Splines vs. Lagrange Polynomials for Multistep Approximation
Methods
~~ Best Talk Award ~~
A predictor-corrector for solving initial-value problems is a combination
of explicit and implicit techniques. The method discussed will use explicit
and implicit methods derived from cubic splines. Comparisons will be given
with the classic Adams Bashforth-Moulton methods, which are derived using
Lagrange interpolating polynomials.
