
Mathematics, Computer Science and Statistics Department Seminar

Fall 2014
Friday, 5 September, 3:00 pm, Fitzelle 205
Fish, Forests, and Functions
Karl Seeley, Economics, Hartwick College
Abstract:
The workhorse models in environmental economics are some elegant applications
of a simple logistic growth function, tweaked in different ways to reflect
stylized facts about populations of fish, stands of trees, or some catchall
of renewable resources. This seminar will demonstrate these uses and what
can be learned from them, as well as discussing some important parts of
reality that get left out.
Friday, 3 October, 3:00 pm, Fitzelle 205
TBA
Jens Christensen, Mathematics, Colgate University
Friday, 7 November, 3:00 pm, Fitzelle 205
Bhāskarācārya: 900^{th} Birth Anniversary
Keith Jones and Toke Knudsen, Mathematics, SUNY Oneonta
Friday, 5 December, 3:00 pm, Fitzelle 205
My Favorite Groups
Rachel Skipper, Mathematics, Binghamton University
Spring 2014
Friday, 31 January, 3:00 pm, Human Ecology 105
Introduction to Lie Algebras
Jonathan Brown, Mathematics, SUNY Oneonta
Abstract:Algebraic Lie theory is an active and exciting area of
mathematics research with many applications to other areas of
mathematics and physics. At the heart of algebraic Lie theory are Lie
algebras. They arise naturally as tangent spaces of Lie groups. In
this talk I will give the basic axioms for Lie algebras as well as
some examples. I will also explain their relationship with Lie
groups, and I will talk about one of the connections between Lie
theory and physics. The talk is intended for math undergraduates,
and it will be accessible to anyone who has taken Calculus, though
knowledge of elementary linear algebra will help.
Friday, 28 February, 3:00 pm, Morris 104
Nontransitive dice and directed graphs
Alex Schaefer, Mathematics, Binghamton University
Abstract:
A set of three dice A, B, and C are said to be nontransitive if
the three probabilities (A beats B), (B beats C) and (C beats A) all
exceed 1/2. I will prove that such dice can be constructed with any number
of (at least 3) sides, and the number of dice can also in fact be
arbitrary. Then I will discuss the connections to directed graphs and show
that any directed graph has a set of dice that can be associated to it.
Friday, 21 March, 3:00 pm, Morris 104
POJOS, POGOS, and beans: Are these MREs or your employment future?
Dennis Higgins, Computer Science, SUNY Oneonta
Abstract:
POGOs and POJOs are "plain old" Groovy or Java objects which would typically
follow the bean convention  a standard way to build them and access their
fields or properties. Beans provide a simple mechanism that is leveraged in
Java and Groovy to facilitate object manipulation. In this talk I will
develop a few beans and show how they can be used in a variety of ways, like
application programs involving a database connection, web services and web
applications. Time permitting, I'll show how Grails uses beans and talk
about the vacation diary my students will build as one of their projects this
semester. No programming background is needed.
Friday, 18 April, 3:00 pm, Morris 104
Making a Really Cheap Quantum Graph
Kevin Schultz, Physics, Hartwick College
Abstract:
The study of quantum systems, whose classical counterparts are chaotic, is
called Quantum Chaology. In my talk I will describe quantum chaos and how we
can measure its effects as well as describing the experimental realization of
quantum graphs, which are an ideal test bed for investigating quantum chaos.
In particular how we can use acoustic analogs of quantum graphs, which allows
for low cost experiments (we use PVC from Home Depot and a sound card from a
computer), and a smaller learning curve for undergraduates.
Fall 2013
Friday, 20 September, 3:00 pm, Morris 104
Suspect Something Fishy? How Statistics Can Help Detect It, Quickly
Aleksey Polunchenko, Mathematical Sciences, Binghamton University
Abstract:
Suppose you are gambling at a casino in a game where you and a dealer take turns rolling a die. Suppose next that the die is initially fair, that is, each of its six faces has the same probability of showing up. However, at some point during the course of the game the evil dealer  without you seeing  replaces the die with an unbalanced one, and so from that point on the die's faces are no longer equally probable. Yet as the new die looks exactly the same as the old fair one, you continue to gamble without suspecting anything. The natural question is: as the game progresses, can you somehow "detect" that the die has been tampered with?
This question is a gamble on its own. On one hand, it would be desirable to find out that the die is no longer fair as fast as possible, so as to quit the game to prevent further losses and subsequently file a lawsuit against the casino. On the other hand, if you are too triggerhappy there is a risk of stopping the game too quickly, i.e., stopping the game before the fair die was replaced with the unbalanced one, which is not desirable. How does one go about solving this problem? Turn to statistics!
Statistics is a branch of mathematics concerned with rational decisionmaking among uncertainty. This is essential in real life, as only a wellthoughtout decision can enable one to take the best action available given the circumstances. This talk's aim is to provide an introduction to the nook of statistics that deals with cases when a solution has to be worked out "onthego", i.e., when time is a factor as well. Specifically, the talk will focus on the socalled quickest changepoint detection problem. Also known as sequential changepoint detection, the subject is about designing fastest ways to detect sudden anomalies (changes) in ongoing phenomena. One example would be the above biased die detection problem. However, there are many more, arising in a variety of domains: military, finance, quality control, communications, environment  to name a few. We will consider some and touch upon the subject's basic ideas.
Friday, 11 October, 3:00 pm, Morris 104
Decision Making using Analytical Hierarchies
Ronald Brzenk, Mathematics, Hartwick College
Abstract:
This presentation will discuss the decision making process, Analytical Hierarchies. I will describe how I have used it in my teaching. It has been the basis for students in my course Mathematical Modeling to actually do some "math modeling". I have also used it in some lower level courses. Finally, I will describe how it has also been the basis for senior projects in mathematics.
Friday, 8 November, 3:00 pm, Morris 104
Economics, Mathematics, and Job Market Signalling
Kristen Jones, Economics, Hartwick College
Abstract:
Economists use mathematical tools extensively in the analysis of consumer and producer behavior. This talk will cover the two core optimization problem used in microeconomic theory  utility maximization and profit maximization  focusing both on the mathematical tools used as well as the economic theory. The lecture will then turn to a more sophisticated application of mathematics, Gibbon's (1992) game theory model of the jobmarket dynamics introduced in Spence (1973). Spence's model of jobmarket signaling involves decisions of two parties (an employer and an employee) under uncertainty and we will discuss the structure and solution methodology of Spence's models as well as the interesting (and unexpected) results of the model.
Friday, 6 December, 3:00 pm, Morris 104
Generalizing Mundici's Gamma Functor
Joshua Palmatier, Mathematics, SUNY Oneonta
Abstract:
In this talk, we will discuss Chang's Gamma functor, a natural equivalence between the category of
MVAlgebras and the category of abelian lgroups with strong unit, as refined by Cignoli & Mundici,
and the possibilities of extending this functor to a natural equivalence between the category of
mzeroids and some category containing the category of abelian lgroups with strong unit.
Spring 2013
Friday, 25 January, 3:00 pm, Craven Lounge
Bumping and Sliding for Beginners: An Introduction to Young Tableaux
James Ruffo, Mathematics, SUNY Oneonta
Abstract:
The primary goal of this talk will be to present some of the basic properties
on an interesting class of combinatorial objects called Young tableaux.
After discussing the basic definitions and constructions, such as
the Jeu de Taquin and the RobinsonSchensted algorithm, we will
discuss an application to some problems in enumerative geometry.
Friday, 8 March, 3:00 pm, Craven Lounge
The Little Theorem that Could: Finding Pseudoprimes by Matching Terms of PolynomialValue Sequences
Robert Sulman, Mathematics, SUNY Oneonta
Abstract:
Pseudoprimes are counterexamples to the converse of Fermat's Little Theorem:
If p is prime and p does not divide a, then p divides a^{p1}1.
Thus, a pseudoprime (with respect to a∈Z^{+}) is any composite n
satisfying: n divides a^{n1}1.
In this talk, a modest set of divisibility relations are shown to generate
two polynomialvalued sequences. A match between them produces a pseudoprime
(with an additional nondivisibility condition). A generalization of this
construction is then given, which yields sets of pseudoprimes with respect
to a given base, and a variety of modifications are seen.
Finally, we describe primes q that are a divisor of a pseudoprime with
respect to a for all a=2,3,4,...,q1.
Friday, 22 March, 3:00 pm, Craven Lounge
Why Study Finite pGroups
Joseph Brennan, Mathematics, SUNY Binghamton
Abstract:
Given a prime p, a finite pgroup is a group whose order is
a power of p. Though major structures of a pgroup lie outside
the scope of a typical undergraduate abstract algebra course; I
would like to spark interest in finite pgroups by defining their
basics and outlining their role in the study of groups. If time
permits, I will outline some major developments in the field.
Friday, 26 April, 3:00 pm, Human Ecology 106
On Sums of Finitely Many Distinct Reciprocals
Donald Silberger, Mathematics, SUNY New Paltz
Abstract:
Let F denote the family of all nonempty finite subsets of N := {1, 2, 3, ...},
and let I ⊆ F be the family of all intervals
[m, n] := {m, m+1,..., n1, n}.
We define the function σ : F→Q^{+} by
σ : X → σ X := Σ_{k∈ X} ^{1}⁄_{k}.
Since the harmonic series 1 + ^{1}⁄_{2} + ^{1}⁄_{3} + ...
diverges to ∞, and since its terms are positive, with
lim_{k→∞} ^{1}⁄_{k} = 0, it is easy to see that the set
H := {σ[m, n] : m ≤ n ∧ {m, n} ⊂ N} of harmonic
rationals is dense in ℜ}^{+} . So it
is natural to ask: Is H = Q^{+}? In 1918 J. Kürschák
answered this question in the negative by proving that
σ[m, n] ∈ N only if m = n = 1.
We showed last year that in fact σ[m, n] = ^{1}⁄_{k}
for k ∈ N only if m = n = k.
This suggested a generalization, which we finally managed to establish:
Theorem:
σI is injective.
As of the present writing, my brother Allan, my daughter Sylvia and I
are attempting to pick the final burr out of a proof of the following
Conjecture:
The function σ is a surjection from F onto Q^{+}.
Indeed, if the approach we are using establishes this conjecture then it
will moreover, for each a ∈ N, facilitate the construction of a
partition S_{a} of N into infinitely many finite sets such
that σ X = a for every X ∈ S_{a}.
Furthermore, it will give us that, for each r ∈ Q^{+}, there are infinitely many
distinct Y ∈ F such that σ Y = r.
Fall 2012
Friday, 7 September, 3:00 pm, Room: Human Ecology 216
Lattice, You Have Seen One Don't Even Know It
Martha Kilpack, Mathematics, SUNY Oneonta
Abstract:
A lattice is a partially ordered set with some extra conditions.
We will look at these conditions and some examples of lattices.
We will then look at how these lattice are actually algebraic
structures and what questions then arise.
Friday, 5 October, 3:00 pm, Room: Human Ecology 106
Trying to understand evolution? Get help from the
Clergy (Three Cheers for the Good Reverend Bayes)
Jeffrey Heilveil, Biology, SUNY Oneonta
Abstract:
The study of evolutionary relationships, whether between or within
species, often requires a "backward view", as we are unable to observe
evolution in action for many species. Answering evolutionary questions
therefore requires heavy reliance on probability. One of the most
helpful analytical paradigms involves the application of Bayesian
statistics to evolutionary datasets. After briefly discussing the
nature of evolutionary research, Bayesian statistics will be explained
at a basic level, including showing how conditional probability impacts
our understanding of topics such as breast cancer. We will then look at
an example of how one can use Bayesian statistics to evaluate the
recolonization of the northern US following the retreat of the
Wisconsinan Glaciation.
Friday, 2 November, 3:00 pm, Room: Human Ecology 106
Hyperbolic Geometry: Logic Takes Us to a Strange Place
Charles Scheim, Mathematics, Hartwick College
Abstract:
The geometry that most people are familiar with from their high school
math days, Euclidean Geometry, has a long history and great importance
from both practical and intellectual viewpoints. But the discovery in
the 1800's of nonEuclidean geometries caused a revolution in the
fundamental assumptions about the relationship of mathematics with the
world around us.
This presentation will use the software Geometer's Sketchpad to reawaken
the basic principles of Euclidean geometry for the listeners and to help
them visualize a model of a nonEuclidean geometry. We'll explore this
new geometry and examine some of the philosophical questions that arise
because of its existence.
Friday, 30 November, 3:00 pm, Room: Human Ecology 106
Games, Fractals, and Groups: From Hanoi to Sierpinski
Keith Jones, Mathematics, SUNY Oneonta
Abstract:
The longstudied game The Tower of Hanoi has a fascinating connection
to the famous Sierpinski Gasket fractal, which provides a clear
visualization of the recursive nature of its solution. This connection
is strengthened by a group structure, which exhibits the same selfsimilarity.
The fractal nature of the group lends itself to a natural description in
terms of a finite state automaton a theoretical model for computing. In
this expository talk, I will introduce the various concepts involved,
and illustrate how these seemingly disparate concepts are tightly intertwined.
Spring 2012
Friday, 3 February, 3:00 pm, Fitzelle 206
From the Four Color Theorem to Thompson's Group F
Garry Bowlin, Mathematics, SUNY Oneonta
Abstract:
The Four Color Theorem states that given any map on the
sphere (or plane) one can color the map with four colors
so that no two regions that share an edge are the same color.
The question was first posed by Francis Guthrie in the early
1850's and likely publicized by him in The Athenæum
in 1854. We will discuss various reformulations of the Four
Color Theorem, which will take us from the world of graphs
and topology into the realm of group theory. No prior knowledge
of group theory or graph theory is necessary.
Friday, 2 March, 3:00 pm, Fitzelle 206
Statistics: The Good, the Bad, and the Ugly
Grazyna Kamburowska, Statistics, SUNY Oneonta
Abstract:
``There are three kinds of lies: lies, damned lies, and statistics.''
The statement, attributed to Benjamin Disraeli, refers to the persuasive
power of numbers, the use of statistics to bolster weak arguments, and
the tendency of people to disparage statistics that do not support their
positions. There are many researchers who are passionate about exposing
poor studies but, unfortunately, the incorrect use of statistics is still
common. Many researchers still shy away from the rigorous application of
statistical methods or, worse, use them incorrectly.
We will discuss various examples of the misuse and abuse of statistics.
Friday, 30 March, 3:00 pm, Fitzelle 206
Perturbations of Fourier Bases and the Haar Wavelet
Min Chung, Mathematics, Hartwick College
Abstract:
A Riesz basis is the image of an orthonormal basis
under an invertible continuous linear mapping.
Both orthononal basis and Riesz basis provide us with
a simple representation of an element in Hilbert
space. Since perturbing an orthonormal basis in a
controlled manner yield a Riesz basis, this is an
important subject of study which goes back to Paley
and Wiener who were interested in the question of
which perturbations {1/(2π)e^{λnx}} of
the orthonormal basis {1/(2π)e^{nx}} are
still a Riesz basis for L^{2}[π,π].
In this context, it is then natural to consider when
the sequence {&lambda_{n}n} is small, so that the
perturbations of local Fourier bases are still a Riesz basis.
In this talk, first we find Riesz basis for L^{2}[0,1]
of the form {sin(λ_{kx})}, by perturbing
the local sine and cosine orthonormal bases of Coifman
and Meyer. Second, the Haar function, the simplest
compactly supported but discontinuous wavelet. By
using the properties of Bessel sequences, we
provide an explicit and more practical way of
constructing locally continuous perturbations of the
Haar wavelet. In this way, we can generate the continuous
or even smooth perturbation of the Haar wavelet
which then will lead to an alternative way to the approach
given by Aimer, Bernardis, and Gorosito, but
we provide better conditions for perturbations and frame bounds.
Friday, 27 April, 3:00 pm, Fitzelle 206
Ruler Constructions
Marius Munteanu, Mathematics, SUNY Oneonta
Abstract:
Ruler and compass constructions have a rich and fascinating history
going back more than two thousand years. We will see that many of
these constructions can be carried out with a ruler alone, as long
as an appropriate ``starter set'' is given.
Fall 2011
Thursday, 1 September, 3:20 pm, Fitz 308
From Galaxy Clusters to Cosmology:
Using Mathematics to Solve Some of Astronomy's Biggest Problems
Parker Troischt, Physics, Hartwick College
Abstract:
In the last decade or so, astronomy has advanced extremely rapidly due
to technological advances used in telescopes, satellites and large sky
surveys. We now have quantitative data on hundreds of extrasolar planets,
countless stars and over a million galaxies. Future telescopes like
the Large Synoptic Survey Telescope (LSST) promise to extend this much
further and will survey the entire visible night sky every three days.
Here, we discuss how mathematics is used to study the properties of
everything from nearby stars, to galaxies, to clusters of galaxies
located over 100 million light years away. In addition, we will show
how solutions to Einstein's equations can be used to study some of the
most interesting questions about the universe starting with the Big Bang.
Friday, 23 September, 3:00 pm, Fitz 221
Cantor's Diagonalization Revisited: Constructing Transcendental
Numbers
LuiseCharlotte Kappe, Mathematics, Binghamton University
Abstract:
An evolving awareness of the deep nature of the real numbers began
over 2,500 years ago, when the Pythagoreans were startled by their discovery
that numbers such as the square root of 2 were not rational. A recurring
theme in their history is that the set of real numbers is richer and much
more complex than is generally assumed. The demonstration by Cantor, that
the reals cannot be enumerated, is a wellknown landmark of these
developments. Knowing that the rationals can be enumerated, it follows from
Cantor's diagonalization that there exist irrational numbers. Similarly,
knowing that the algebraic numbers can be enumerated, it follows that there
exist transcendental numbers.
But can one use Cantor's diagonalization for the construction of such
numbers? The topic of this talk is the explicit construction of a
transcendental number using Cantor's diagonalization.
Friday, 21 October, 4 pm, Fitz 221
Computational Thinking in 24Point Card Game
Sen Zhang, Computer Science, SUNY Oneonta
Abstract:
The 24point game is a mathematical game in which the object is to construct
an arithmetic expression using four integers (usually from 1 to 10) and three
out of four possible elementary arithmetic operations (addition, subtraction,
multiplication and division) so that the expression evaluates to 24. For
example, given a hand of four integers 4,7,8,8, (78/8)*4 would be a possible
solution. Notice that all four integers need but not every operation needs to
be used in the expression. The game is relatively easy but entertaining enough
to play for almost any people who have elementary arithmetic knowledge. Two
questions that tend to captivate many people who have played the game are how
to find out all the hands that have at least one possible solution and how to
find out all possible solutions for each of such hands. Obviously these are
the problems we don't want to solve manually. This talk will first examine a
set of mathematical and computational thinking techniques that can help answer
the above questions. After that, a straightforward software that implements
the techniques will be presented as a typical computing solution where
mathematical thinking and computational thinking go hand in hand perfectly.
Friday, 11 November, 3pm, Fitz 221
From Ordinary Differential Equations to Geometric Control Theory
Laura Munteanu, Mathematics, SUNY Oneonta
Abstract:
Many real life processes can be modeled by (systems of) ordinary differential
equations. More complex processes involve a parameter/control that can be
adjusted in order to affect their outcome. Due to the large number of
variables or the nonlinear nature of these control systems, one seeks to find
simpler systems whose solutions mimic (in a certain sense) the solutions of
the original system. In this presentation, we look at how geometric objects
such as differentiable manifolds and vector fields can be used to better
understand the aforementioned problem.
Spring 2011
Friday, 4 February
Chess Endgame Composition: Proofs in Pictures
Robert Sulman, Mathematics, SUNY Oneonta
Abstract:
Although primarily viewed as a game to be played between two
individuals, the very nature of chess leads to configurations of the
pieces (called "positions") in which one player has a forced win, or a
forced draw. Such positions have been composed as well, that is, they
have not come about naturally from an actual game. The freedom to
create such problems enables one to highlight a given theme in which
the pieces interact on the 64 squares.
Whether one tries to solve such a composition, or simply read the
solution, the moves leading to the end result are intended to be
surprising and beautiful.
A brief review of the moves of the pieces will be followed by a series
of endgame studies (as they are also called), beginning with
relatively simple examples. The more subtle studies, including those
by pioneer Alexey Troitsky will (I hope) draw you into this wonderful
area of chess.
Friday, 4 March
Fibonacci's Not Just Counting Rabbits Anymore
Gary Stevens, Mathematics, Hartwick College
Abstract:
In 1202, Leonardo of Pisa, son of Bonacci, published his pioneering work,
Liber Abaci, the book of calculation. In this book, Fibonacci
presented a problem relating to the breeding of rabbits whose solution
gave rise to a sequence of numbers which now bears his name. The Fibonacci
Sequence has been studied and generalized for the last 800 years and is
now one of the cornerstones of the area of mathematics known as combinatorics,
the art of counting. The sequence shows up in some unexpected places and
provides solutions to many counting problems. This lecture will look at
some of the myriad uses of the sequence and will provide a gentle overview
of and introduction to the subject of combinatorics.
Friday, 8 April
Techniques in Atmospheric Dynamics and Weather Forecasting
Melissa Godek, Meteorology, SUNY Oneonta
Abstract:
Within the field of meteorology, the study of atmospheric dynamics
focuses on macroscale motions and their ability to create the
weather phenomena and climate patterns experienced at the surface.
These circulations are described by fundamental and apparent Earth
forces as well as the governing equations of motion. It is through
calculus that atmospheric scientists learn how to apply these equations
in dynamics to obtain a new set of equations referred to as
QuasiGeostrophic Theory. Just as important to meteorologists are
Numerical Weather Prediction (NWP) models, which are used every day in
short and longterm weather predictions. These NWP models are
essentially algorithms that represent the QuasiGeostrophic Theory
that describes macroscale atmospheric circulations. This talk will
describe how atmospheric scientists incorporate the science, mathematics
and computer model predictions to produce multiple forecasts each day.
Friday, 29 April
Not So Boring Statistics
JenTing Wang, Statistics, SUNY Oneonta
Abstract:
In this talk, we'll discuss three real court cases, which involved
different types of statistical reasoning. In particular, we'll see
the statistical evidence found in a serial killer case and how it
was used in court. This presentation is accessible to everyone and
no previous statistical knowledge is required.
Fall 2010
Friday, 10 September
Bounded Analytic Functions with Unbounded Parts
Angeliki KazasPostisakos, SUNY Oneonta
Abstract:
For any analytic function on the unit disc,
f &isin H^{p}, there exists
a factorization f(z)=g(z)F(z) where g is inner and
F is outer.
The properties of g and F are well known and in particular the
function g is a bounded analytic function on the unit disc. More
generally, for an inner function φ, there exists a
factorization f(z)=h(z)F(φ(z)) where h is a
φp
inner function and F is outer. We will construct a function that
is bounded and analytic on the unit disc with unbounded φp
inner part. All the terms above will be defined and the talk should
be accessible to students that have completed the calculus sequence.
Friday, 8 October
The Fundamental Theorem of Calculus: History, Intuition, Pedagogy,
Proof
V. Frederick Rickey, US Military Academy at West Point
Abstract:
The Fundamental Theorem of Calculus (FTC) was a theorem with Newton
and Leibniz, a triviality with Bernoulli and Euler, and took on the
concept of "fundamental" when Cauchy and Riemann defined the
integral. FTC became part of academic mathematics in the 19th
century, but waited until the 20th century to take hold in classroom
mathematics. We will discuss the transition from clear intuition to
rigorous proof that occurred over three centuries.
Friday, 5 November
Mathematics and the Methods and Models of Morality
Michael Green, Philosophy, SUNY Oneonta
Abstract:
Mathematics and moral theorizing have had a long and tangled
history. Philosophy has nurtured mathematical forms of thought that
have, in turn, had a profound influence on ethical theorizing. The
aim of this lecture is to reflect upon the relationship between
mathematics and moral theorizing in Plato, Aristotle, Augustine,
Hobbes, Spinoza, Bentham, and Rawls.
Friday, 3 December
On Symmetries, Supersymmetries, and Akan Symbolism
Michael Faux, Physics, SUNY Oneonta
Abstract:
Some of the intricate mathematics used by physicists to
probe the laws of nature are rendered helpfully perspicuous
by the use of symbolic representations. In some cases, such
symbols exhibit a mathematical significance which transcends
their original motivation. In this talk I will explain how a colorful
graphical paradigm, reminiscent of West African tribal symbols,
invented to represent supersymmetry algebras, which I will explain,
have exposed an unexpected, fascinating, and rich connection between
an emergent quantum theory of gravitation and the mathematics of
coding theory.
Spring 2010
Friday, 5 February
Math Anxiety
Lynne Talbot, SUNY Oneonta
Abstract:
The presentation will outline the causes and symptoms of
math phobia, as well as suggestions for instructors to alleviate the
anxiety that some students feel when confronted with a math problem.
Myths regarding math, such as math is not creative, will be
dispelled. A pamphlet will be distributed for instructors to
reference to assist in identifying math phobic students.
Friday, 5 March
Knot a Graph? Why Not?
Susan Beckhardt, SUNY Albany
Abstract:
Choose any seven points in space, and connect each pair of
points with a curve in such a way that none of the curves intersect.
No matter how you arrange your points and curves in space, I can
always find a closed loop that is tied in a knot. The choice of
points and curves is called a spatial embedding of K7, the complete
graph on seven vertices, and a graph with the property that every
spatial embedding has a knotted cycle is said to be intrinsically
knotted. Although topological in nature, the remarkable fact that K7
has this property can be proved with little more than some basic
combinatorics. We'll go over the proof, and then look at some
further results in the field of intrinsically knotted graphs.
Friday, 26 March
Embarrassing Moments in the History of Calculus
Kim Plofker, Union College
Abstract:
The development of modern calculus wasn't the smooth transition
pictured in today's textbooks, but rather a long struggle between
practicality and precision. Handling the tricky quantities known as
infinitesimals, which might be zero or not as the situation
required, led early modern mathematicians into some awkward
contradictions and some vehement disputes. This talk surveys some of
the peculiar innovations in calculus that you won't find in your
calculus book, and the controversies, shock, and outrage that they
provoked in their day.
Friday, 16 April
The Power Residue Problem and Arithmetic Geometry
John Cullinan, Bard College
Abstract:
If an integer is an nth power, then it is an nth power mod p for
all primes p. However, the converse is not always true  there exist
integers which are nth powers mod p for all primes p, yet are not the nth
power of an integer. In general, given a polynomial with integral
coefficients, it can be quite difficult to describe its integral (or
rational) roots. One technique that has proved fruitful is
instead to find roots of the polynomial mod p for prime numbers p, and
from these roots deduce the existence (or nonexistence) of a rational root.
The success or failure of this approach often gives new insight into the
original problem. This talk will focus on the example given above, and
a similar problem phrased in terms of points on elliptic curves and
abelian varieties.
Friday, 7 May
Let's Pack! An Introduction to Hyperspheres and Hypercubes
David Biddle, SUNY Oneonta
Abstract:
It is commonly said that beauty is in the eye of the beholder, but what if the eye is incapable of seeing something in its entirety? Higher dimensional geometry affords us the opportunity to explore beautiful objects and phenomena using a plethora of tools from all parts of mathematics. In this talk we compare the 'look and feel' of higher dimensional analogues of the circle and sphere (hyperspheres) and the square and cube (hypercubes) and come to the conclusion that exploring higher dimensions leaves plenty of room for the bizarre!
Fall 2009
Friday, 11 September
MZeroids: Structure and Its Effect
on the Additive Operation
J. Palmatier, SUNY Oneonta
Abstract:
An mzeroid is an algebraic structure with both operations and an inherent
order on its elements.
If we remove the order by making it totally ordered and finite, only the
additive operation remains
important. In this talk, we will discuss how the structure of the finite,
totallyordered mzeroid,
both algebraic and pictorial, restricts the additive operation table and
allows you to generate
such an mzeroid with a minimum of fuss.
Friday, 9 October
The Mathematics of Origami
L. Bridgers, SUNY Oneonta
Abstract:
With paper folding, we can complete geometric constructions that are
impossible using the classical geometry tools of a straight edge and
compass. In this talk we will explore some origami constructions and
the geometry proofs behind them. This will include both constructions
that we could complete with a straight edge and compass, such as the
construction of an equilateral triangle, and those that are impossible
using a straight edge and compass, such as the trisection of an angle.
Friday, 6 November
Number Theory and Music
L. Alex, SUNY Oneonta
Abstract:
In this talk connections between musical intervals and
Diophantine equations in number theory will be described.
In particular the intervals will be viewed as "superparticular"
ratios of the form (n+1)/n. In this form the octave would
be viewed as the ratio 2/1. The ten superparticular ratios
corresponding to the intervals preferred by the Western ear
will be listed. Each of these ratios corresponds to a solution
of a certain Diophantine equation in number theory. An elementary
number theoretic method for solving the equation will be
illustrated.
Diophantine equations in number theory will be described.
In particular the intervals will be viewed as "superparticular"
ratios of the form (n+1)/n. In this form the octave would
be viewed as the ratio 2/1. The ten superparticular ratios
corresponding to the intervals preferred by the Western ear
will be listed. Each of these ratios corresponds to a solution
of a certain Diophantine equation in number theory. An elementary
number theoretic method for solving the equation will be
illustrated.
Friday, 4 December
Disappearing Messages: Basic Steganography
J. Ryder, SUNY Oneonta
Abstract:
The practice of steganography involves surrepetitiosly hiding a
secret within some object at a source location then allowing that
object to be carried to some destination. At the destination, a
receiver extracts the secret from the carrier. Steganography is secret
communication in which only the sender and receiver of the secret
know of its existence yet it travels through hostile territory
unnoticed.
In Ancient Greece, troops at one location would tattoo a secret onto
a slave's shaved head. When the slave's hair had once again become
sufficiently long, the slave would be sent to another camp some
distance away. Upon arrival, the slave's head was shaved and the
secret message was read. This brief talk will show a few ways that
steganography is used today in the digital world. Examples will show
methods of hiding secrets in images, in Internet web pages, in
music, and even in plain text.

