Seth Albert:
"Fractal Dimension and the Wavelet Transform Modulus Maxima method"
An introduction to fractal dimension and a look at
characterizing multifractal surfaces by its singularities through the
Wavelet Transform Modulus Maxima method.
Matthew Brenc:
"Dirichlet's Theorem on Primes in Arithmetic Progressions"
Johann Dirichlet proved in 1837 that for coprime integers a and
k, there exist infinitely many prime numbers congruent to a modulo k. In
this talk I will provide an outline of Dirichlet's proof, focusing in
particular on his key insight that the characteristic function of the
integers congruent to a mod k can be written as a linear combination of
multiplicative functions on the group (Z/kZ)^{*}.
Matthew Breton:
"Vibrations of a Drumhead"
This talk will focus on how to describe the vibrations of a drumhead
using polar coordinates.
Timothy Buchak:
"Mathematics of Sudoku"
My talk will be on the mathematics behind the popular puzzle game
Sudoku. I will summarize what work has been done related to Sudoku, and look at
some of the more advanced solution algorithms. I will also briefly talk about the
relation between Sudoku and graph theory.
Nicole CurtisBray:
"Applications of Bessel Functions in Electrical Engineering"
An introduction to the origins and applications of Bessel functions and
waveguides. In addition, Maxwell's equations for electromagnetic waves will be
used to derive Bessel's equation.
Cormick Frizzell:
"An Introduction to Card Counting"
I will discuss a few methods of card counting and
will prove parts of the Fundamental Theorem of Card Counting.
Paige Gallagher:
"Introduction to Fibonacci Numbers"
This presentation will be an introduction to Fibonacci numbers, their
properties, applications and other interesting mathematical connections
these numbers share.
Travis Goodwin:
"The Concepts of Communication Theory"
An introduction to the basic concepts that were developed by
Claude E. Shannon, and consequently mathematically proved, in his
famous paper, "The Mathematical Theory of Communication".
Jodi Harnden:
"A Perspective on Polyominoes"
An introduction to Solomon W. Golomb's polyominoes
and their tiling capabilities. There will also be a discussion on how generating
functions play a role in computing the possible tilings of specific rectangles
with trominoes.
Stuart Lawson:
"The Analytic Continuation of The Riemann Zeta Function"
This presentation will provide a detailed walkthrough of one of the
many proofs of the analytic continuation of the Riemann Zeta Function; that is, it
will show how the zeta function can be extended in a way that its domain is
(nearly) all of the complex plane, and not just numbers whose real part is greater
than 1. This particular proof utilizes the theta function and the Mellin
transform, as well as Poisson summation and Fourier transforms.
Tim Michaud:
"Fractal Coastlines"
A look at how coastlines are selfsimilar under different magnifications and thus
are fractal in nature. We will also look at the fractal dimension of the coast of
Maine and how it compares to that of other coastlines.
Mahadi Osman:
"Composites in Diferent Bases that Remain
Composite After Changing Digits."
Filaseta et. al. proved that there are infinitely many composite
numbers that remain composite after changing any digit in the decimal
expansion by constructing an infinite arithmetic progression of such
composite numbers. We show that there are infinitely many composite
numbers in base b that have this property for b=2,...,9. We then attempt to
show that there are composite numbers in base b that remain composite
after replacing any two adjacent digits in the base b expansion.
Dean Pelletier:
"A Little to Say About RSA"
RSA cryptography is a modern and secure form of secret communication. In
this talk I will cover the basics of RSA cryptography and how it differs from
private key cryptography. I will also discuss enciphering keys and algorithms as
well as how to develop the deciphering key, and how having one does not give a
person the ability to find the other.
Anne Witick:
"Fractals: A Basic Overview"
An exploration of the evolution of fractals, with emphasis on the history
and development. Examines some famous fractals and the Iterated Function System.
Jennifer Wood:
"Google's PageRanking System"
An introduction to Google's search engine and the PageRank equation that
calculates the popularity score of webpages by applying the power method to the
Google Matrix.
Hannah Woodruff:
"Primes of the Form x^{2}+y^{2}"
In this talk, I will be proving Fermat's observation that an odd prime p
can be written as x^{2}+y^{2} if and only if
p≡1 mod 4. This proof will be based on
Euler's proof which he completed in 1749.
