Thursday,
Sept. 13th
Mizan
Khan, Eastern
Miscellaneous remarks about
Modular Hyperbolas
Let Hn be the modular hyperbola Hn = { (x, y) | xy = 1 mod n, 1 < x, y < n – 1
}. We restrict x, y to lie in the
interval [1, n-1] in order to view Hn as a discrete set of
points (of cardinality f(n)) lying in the square
[0,n]2. We will begin by showing some graphs of Hn generated by Maple, and
then proceed to make a number of geometric and number theoretic observations
and conjectures about these sets. The talk should be accessible to anybody who
has had some exposure to modular arithmetic.
Thurs., Sept. 27th
Jay Stine,
Pre-Hausdorff
spaces
The notion of using open sets to
separate points or closed sets from other points or closed sets is fundamental
in general topology. The classical T2 (a.k.a. Hausdorff) separation axiom is often
assumed in a first course in topology, and even in practice by working
mathematicians. Consequently, separation
conditions weaker than T2 are often given little consideration. However, there are many interesting and
useful topological spaces which are not Hausdorff. In this talk I will introduce a separation
axiom called pre-Hausdorff. This new
separation condition generalizes the Hausdorff axiom, and has advantages over
it topologically which I will discuss. I
will give some characterizations of pre-Hausdorff spaces, and a
characterization of Hausdorff spaces in terms of pre-Hausdorff. I will also discuss some classical Theorems
of general topology which can or cannot be generalized by replacing the
Hausdorff condition by pre-Hausdorff.
Thurs.,
Oct. 18th,
Emily
Dryden,
Bagels,
beach balls and the Poincare Conjecture
In 1904,
the French mathematician Henri Poincare made a conjecture about which
three-dimensional objects could be stretched and bent into spheres. Many mathematicians worked on this conjecture
and its generalizations over the next century, and in 2000, a prize of one
million dollars was offered for its solution.
Shortly thereafter, the conjecture was finally solved by an enigmatic
Russian mathematician. The journal
Science named this the scientific breakthrough of the year in 2006. We'll talk
about the general background and history of the problem and get our hands on
various shapes to better understand the topological ideas. Curiosity is the
only prerequisite.
Fri.,
Oct. 26th
Christopher Ariza,
An Introduction to Computer-Aided Algorithmic Music
Composition and athenaCL: Historical Models and New Approaches
The earliest application of computers to generate musical structures dates from 1956. The foundations provided by these early experiments, as well as the design principles inherited from modular synthesizers, has led to the development of generative music systems with general, reusable components. The open source, cross-platform athenaCL system, built in Python, provides a command-line and scriptable interface for computer-aided algorithmic composition (CAAC). While introducing foundational concepts of CAAC, this talk will demonstrate basic and advanced features of the athenaCL system
Thurs., Nov. 1st
Larry Gratton,
Who
really
done
it? Sampling and enhancement errors in digital fingerprint analysis
Digital imaging devices have put a new spin on the old
problem of identifying an individual by a fingerprint. Digital
fingerprint scanners now allow password-free access to secure information,
and police agencies around the world are converting stacks of old ink and paper
documents to efficient digital records. Questions arise, however, about
the reliability of these new digital images and the information they
contain. In this talk, we investigate the commonly used sampling and
enhancement techniques in digital fingerprint analysis focusing
on sources of error and potential consequences. A brief introduction
to Fourier analysis is included and provides the mathematical framework
for our investigation.
Tuesday, Nov. 27th (Senior Colloquium)
Mary Korch,
Entity
Identification Algorithm for Tracking Single Entities
In previous research, a probabilistic algorithm that
accurately tracks a single entity using a set of positive and negative
observations was developed and validated. The extension of this algorithm
to track several entities simultaneously introduces the problem of entity
identification; it must be determined for which entity a positive observation
is providing information. An initial framework of an entity
identification algorithm extends the original tracking algorithm to assign a
probability that an observation matches a given target or identifies a new
target based on four primary factors: location, unit type, heading, and
velocity. Unfortunately, initial tests to validate the current algorithm
have failed; the algorithm does not accurately identify and track a single, let
alone multiple entities. This talk outlines the procedures of the
entity tracking and identification algorithm, addresses the limitations of
extending the single entity tracking algorithm to multiple entities, and
establishes the necessary modifications to the algorithm to track single
entities within a multiple entity environment with sufficient accuracy.
Thursday, November 29th (Senior Colloquium)
Danielle Kahl,
The Mathematics of the
Rubik’s Cube
The Rubik’s Cube, becoming famous in the 1980s, is a very
popular toy among both young and old.
From people who pick up a cube and randomly twist its sides, to people
who compete at the Rubik’s Cube world championships for speed in solving the
cube, everyone uses math, whether cognizant of this fact or not, in order to
restore all the pieces to their original positions. For my colloquium I will present some of the
math needed to recognize how to restore the cube. Some useful topics will be presented that can
lead to restoration of a scrambled cube.
Some abstract algebra knowledge is useful, but not necessary as I will
be explaining how it relates to the cube throughout the colloquium. So bring a Rubik’s Cube if you want, and come
learn a few things to help you get on your way to solving your cube.
Tuesday, December 4th (Senior Colloquium)
Kate Haldeman,
Classifying Colored Patterns
Have
you ever wondered what makes different colored patterns different? Perhaps you were doing something like
choosing the best wallpaper for your house.
You were probably making decisions based on color schemes and the
patterns and figures. What you may not
have realized is that two wallpapers, although they may have looked different,
were actually considered the same colored pattern!
Authors Branko Grunbaum and G.C.
Shephard have introduced methods of classifying colored patterns. Our discussion will focus on classifications
such as underlying and color symmetry groups, pattern and colored pattern
types, as well as equicolor types. We
will begin to see how two patterns may or may not be classified similarly,
regardless of the differences and similarities noticeable at a first glance.
Wednesday, December 5th (Senior Colloquium)
Ashley McConnaughhay,
TBA
Unless otherwise noted, colloquia will begin at 4:15 p.m., in Seibert 017. (Light refreshments will be served at 4:05.)
For further information, contact Alex Wilce (wilce@susqu.edu) or Jeff Graham (graham@susqu.edu )