Geneseo Mathematics Colloquium Schedule
Fall 2008
Schedule to be determined. Please visit again to find updates.
For a taste of the type of talks to expect, here are quite a few previous
talks.
Patrick Rault, University of Wisconsin
Mathematical game theory
Mathematical strategies and solutions
of various games will be discussed. Recent developments in the
game theory of Checkers and Rubik's Cube will be presented within a historical context.
Sharon McCathern, University of Illinois at Chicago
The Triangle Game, Symmetry, and Dihedral Groups
Using a simple arithmetic game as an
introduction, we will discuss the symmetries of an equilateral
triangle. I will introduce the dihedral groups, which consist of the
symmetries of regular polygons, and briefly mention some of their nice properties.
Palalanivel Manoharan, Penn State University
The Angel of Algebra and the Devil of Geometry - or is it the other way around?
We will discuss the history of cordial
(or uneasy?) relationship between Algebra and Geometry, two
ancient pillars of mathematics. We will look into some specific
incidents in mathematical history when unexpected bridge developed
between Algebra and Geometry to create duality among them.
Jeff Johannes & Gary Towsley, SUNY Geneseo
A Concise History of Calculus
A lively overview of over two thousand years of calculus history.
Not only who-did-what along the way, but the cultural and sociological
causes and effects of the calculus. Strongly recommended for
anyone who has taken or is taking calculus.
Patrick van Fleet, University of St. Thomas
Basic Image Processing with Wavelets
On my desk sits a digital image of my children. The camera my wife used
to take the picture allows the user to save the image to disk in either
raw format or as a JPEG file.
We saved the image using both options. The raw format produced a file
whose size is 861KB while the JPEG version of the image was stored on
disk using 46KB. The difference between the two images are
inconsequential. So how did the JPEG format produce a file that
so accurately represented the original image but required substantially
less disk space? This is a question that is paramount in the minds of
anyone who wants to make effective use or enjoy fast transfer of
digital images in today's world.
In this talk, we will give a very elementary introduction to a tool
that finds itself at the center of many image processing applications.
We will introduce the Discrete Haar Wavelet Transform
(HWT) and discuss how it can be used to process digital images. While
the HWT is not the best wavelet transform for processing images (that
is the subject of Friday's talk!), it serves as a perfect tool for
introducing the use of wavelets in applications. During the talk,
we will take some digital pictures (audience participation is thus
required!) and use the HWT to compress the images. We will also show
how to use the HWT to search for edges in our digital images.
Patrick van Fleet, University of St. Thomas
Wavelets and Lossless JPEG Compression
The JPEG format, developed in 1992 by
the Joint Photographic Experts Group, is used by over 80% of all images
that appear on the internet. Despite the popularity of the image format
and the impressive compression ratios it attains, there is room for
improvement. In particular, JPEG is capable of only compressing
images in a lossy manner.
That is, the size of the compressed file is significantly smaller than
the raw format, but the savings was gained by discarding portions
(typically deemed insignificant) of the original image. Thus it is
impossible to recover the original image from a compressed JPEG image.
In 1997, JPEG introduced a new format called JPEG2000. This format
corrects several flaws in the original JPEG format and also provides
many enhancements. In particular, JPEG2000 allows the user to
compress a digital image in a lossless
manner. We get the best of both worlds - the size needed to represent
the image is reduced and the compressed version can be used to recover
the original image!
At the heart of the JPEG2000 compression standard are two wavelet
transformations. One transformation is used to perform lossy
compression while the other allows users to compress images in a
lossless manner. In this talk we will consider the wavelet
transformation used by JPEG2000 to perform lossless image compression.
Incredibly, the mathematics behind this transformation is quite
straightforward - the perplexing part of the process is realizing that
the algorithm \undoes" the rounding operator to exactly recover the
original image!
Ding Feng, University of Virginia
General Concepts of Point Estimation
One very important application of statistics is in obtaining point
estimates of population parameters such as a population mean,
population variance, and a population proportion. Given a
parameter of interest, the objective of point estimation is to
determine the plausible approximate value
of the parameter on the basis of a sample statistic. In this talk, we
first introduce the general concepts of a point estimate and a point
estimator for a population parameter. Since we may have several
different choices for the point estimator of a particular parameter, to
decide which point estimator is the “best” one, we need to examine
their statistical properties and develop criteria for comparing
estimators. Two extremely important criteria, the principle of unbiased
estimation and the principle of minimum variance unbiased estimation
(MVUE), will also be introduced.
Lingji Kong, Union College (Kentucky)
Beta-Power Distribution and Applications
A class of generalized power distribution, namely Beta-power
distribution, is proposed. Properties of this distribution including
limits, modes and moments are presented. Graphs of the density
functions are presented to examine shapes of the distribution for
various combinations of parameters. The beta-power distribution is
shown to be four kinds of shapes: increased, decreased, bathtub or
reverse bathtub. Reliability and hazard functions are derived; in the
end parameter estimations and the test for Beta-power distribution are
also discussed.
Shubiao Li, Central Michigan University
Random Walk and the Ruin Problems
The basic conception of random walk process is introduced from several
real life examples. A classic ruin problem is used to illustrate
modeling techniques for a random walk process. Some properties related
to the problem such as expected duration and expected gain are
discussed; the techniques of obtaining solutions of difference
equations are also addressed.
Amy Stornello, Rochester Institute of Technology
Obtain your Master's in Education at RIT/NTID
Why RIT/NTID? Well, some benefits we offer are: small class size,
personal instruction with faculty and dual certification in grades 7-12
(in your topic area) and Teacher of the Deaf. If you have a
bachelor's in Math or Science, we are even offering $10,000
scholarships to encourage more Math and Science teachers in the
teaching profession. If you've ever wanted to work with deaf/hard
of hearing students, this is the perfect opportunity to do so!
Find out how our two-year master's program works, what classes we
offer, internship opportunities and more information about this
fantastic scholarship!
Matthew Rashford, SUNY Geneseo
Exponential Stability of Dynamic Equations on Time Scales
A time scale is an arbitrary nonempty closed subset of the real
numbers. Two of the most common examples of calculus on time
scales include differential calculus and difference calculus.
This talk will look at some of the background regarding time scales,
conditions for exponential stability, and then will show examples of
time scales, including an application on population dynamics.
This talk is strongly recommended for anyone who has taken or is taking
Differential Equations.
Patti Fraser-Lock, St. Lawrence
University
Marijuana Use, Goldfish, and Knee
Injuries
Effective statistical analysis of data
requires, first, that we are able to obtain valid data from a
sample. We will discuss and illustrate some interesting new
sampling methods and give examples of some recent thought-provoking
results obtained using statistical experiments.
Gary Towsley, SUNY Geneseo
What is a Ph.D. dissertation in Mathematics? An Example:
Conformal Deformation of Meromorphic Functions
Have you ever wondered what it would take to get a Ph.D. in
Mathematics? This sequence of talks will share with you personal
experiences. Although they will present sophisticated
mathematics, no background is assumed beyond calculus. In this
example, we explore the question: when are two continuously homotopic
functions from a compact surface to the two sphere joined by a homotopy
that ranges through the meromorphic functions? What does such a
question mean and what kind of an answer can one get?
Jim Conklin, Ithaca College
Sudo Latin Squares
Sudoku puzzles have a rich pre-history in recreational and applied
mathematics as well as presenting some interesting mathematical issues
of their own. Sudoku grids are special cases of Latin Squares, a source
of mathematical puzzles since at least the 1620's. This talk will
look at some of the mathematical prehistory of Sudoku-like puzzles and
the applied mathematics that grew out of them, and then look at some of
the mathematical issues related to the solution and creation of the
puzzles.
Christopher Andrews, University at Buffalo
An Introduction to Opportunities in Biostatistics
Biostatistics, the science of statistics applied to the analysis of
biological or medical data, has a large and growing demand for
qualified researchers. In this talk I will describe, through
examples, what biostatisticians do. This includes methodological
research, collaborative research, consulting, statistical programming,
bioinformatics, and epidemiological research. Finally I will
discuss how you can prepare for a career in this exciting, rewarding
field.
Michael Fisher, CSU Fresno
Iterated Function Systems (How to Grow Your Own Fractal)
In this talk I will introduce the notion of an iterated function system
(IFS) and take a look at common types of fractals which are easily
described by an IFS. Specific examples include the Sierpinski
gasket, the Cantor set, and Barnsley's fern. If time permits, I
will also talk about graph-directed sets (a generalization of a
self-similar set).
Alison Setyadi, Dartmouth College
Can you hear me now?
Suppose you work for a cell phone company, and your job is to determine
where to place cell phone towers in a certain area. Given that
there is a limit to how many calls each tower can handle at once and
that each tower has only a finite range, how do you determine where to
place the towers so that the company's customers stay happy and the
company stays within its operating budget? Once you decide where to
place the towers, is there a way to increase the area of the company's
cell phone service without having to rearrange the existing towers? By
using graphs to model the locations of the towers, we consider ways to
answer both of these questions.
Aaron Heap, University of Rochester
The Fascinating World of Knots
We will discuss some of the basic ideas in knot theory and its history.
We will see how knot theory is used in some other sciences besides
mathematics. We will also discuss a few examples of knot invariants and
how knot theory may be used as a tool in low-dimensional topology.
Sharon Garthwaite, University of Wisconsin
The Sum of the Parts is …
The sum of the parts is... more interesting that the whole! In
this talk we'll see how a seemingly simple idea -- expressing a number
as the sum of smaller numbers -- leads to really interesting
patterns. We'll then discuss various methods for proving our
observations, seeing that this simple idea is accessible at many
different levels.
David Perkins, Houghton College
An immortal monkey may have already given this talk
No one can be sure who first thought of sitting a monkey at a
typewriter, or who would have the patience to sift through the monkey's
output looking for meaningful text. Two things are for sure, however:
(1) references to immortal monkeys abound in novels, plays, short
stories, and television; and (2) the Borel-Cantelli Lemma implies that
if you're immortal, you can be a monkey and still get published. In
this talk, we'll investigate both these two items that are for sure,
and some that are not.
Pedro Teixeira, Union College
Googling with Math
The success of web search engine Google can be attributed to a system
devised to rank the importance of websites, where the importance
of a website is related to the importance of the websites that link to
it. In this talk I'll discuss the system used by Google and the
mathematics behind it, and in particular how it relates to topics one
typically learns in undergraduate courses. We'll see how Google's
ranking system leads to what has been called "the world's largest
matrix calculation," and examine the techniques used to handle such a
monstrous computation.
Joanna Masingila, Syracuse University
Teachers’ Evolving Practices in Supporting Students’ Mathematics
and Literacy Development
Sociocultural research on mathematics and literacy frames this
interdisciplinary investigation of the evolving practices of secondary
mathematics teachers as they seek to understand and support their
students’ mathematics and literacy development. Teachers’
evolving practices included (a) their use of the “Problem of the Day”
to engage students in thinking and communicating mathematically, (b)
their development of “templates” as scaffolding tools for mediating the
literacy demands of the textbook, and (c) their choice to explore
student engagement and mathematical communication in connection with
their classroom practices.
Ryan Grover & Matthias Youngs, SUNY Geneseo
Infinite Levels of Infinity
Do you accept the idea of infinity? If so, in what ways?
Together we will explore the concepts of infinity to the
mathematician. For instance, if there is somethign of infinite
size, is there something else of even more infinite size? If so
what does it mean to be more infinite? What does it mean to be
infinite? How big is infinity?
Joel Foisy, SUNY Potsdam
Knots and Links in Spatially Embedded Graphs: Tangled-Up
Mathematics.
This talk will be about graphs that have knotted and/or linked cycles
in every spatial embedding. Informally, a graph is a set of vertices and a set
of edges. A graph is defined by the number of vertices is has,
and by which vertices are connected by edges. A particular way to
place a graph in space is called an embedding
of a graph. A cycle in a
graph is a sequence of distinct edges in the graph such that any two
consecutive edges share exactly one vertex, and the last edge and the
first edge share exactly one vertex. We will discuss what is
known about graphs that have a pair of linked cycles in every
embedding. (Intuitively speaking, cycles are linked if they can't
be pulled apart, like two looped pieces of string). We will also
discuss what is known about graphs that have two disjoint pairs of
linked cycles in every embedding, as well as graphs that have a knotted
cycle in every spatial embedding.
Katia Noyes, University of Rochester School of Medicine
Certainty Uncertain: performing and interpreting multivariate
cost-effectiveness sensitivity analysis
A healthcare system comprises complex relationships across many levels
of organization focused on providing healthcare services to individuals
and populations. Health Services Research is the
multi-disciplinary field of inquiry that combines approaches of health
economics, mathematics, epidemiology, biostatistics, anthropology and
other disciplines to study healthcare system and examine the use,
costs, quality, accessibility, delivery, organization, financing and
outcomes of health care service.
Cost-effectiveness research is one of many areas that constitute health
services research. Cost-effectiveness analysis is based on the
incremental cost-effectiveness ratio (ICER), i.e., the ratio of
difference in costs to the difference in health effects of two
competing interventions. By its nature, cost-effectiveness research is
applied: the end result of a cost-effectiveness evaluation should be a
black-and-white decision whether to fund or not to fund. In reality,
two main problems make this happy end problematic. One is the lack of
an analytical solution for variance of a ratio which makes formal
hypothesis testing (e.g., ICER < l) impossible. The other problem is
that nobody really knows what the threshold value l should be. In her
presentation, Dr. Noyes takes standard cost-effectiveness methods a
little further and describes approaches to make sense out of
analytically uncertain cost-effectiveness results.
This presentation is a part the Information and Student Recruitment
Efforts of the Division of Health Services Research at the University
of Rochester School of Medicine. For more information please contact
Dr. Katia Noyes at 585-275-8467 or
katia_noyes@urmc.rochester.edu or visit
http://www.urmc.rochester.edu/cpm/education/phd_hsr/index.html.
Daniel Birmajer, Nazareth College
A Gentle Introduction to the Polynomial Identities of Matrices
Abstract: Finding unexpected relations between apparently
unrelated quantities is one of those things that make us,
mathematicians, love our profession. We call these mathematical
relations
identities.
Some identities are well for their beauty, simplicity and usefulness:
- 1 + 2 + . . . + n
= n(n + 1)/2 for all natural
numbers n;
- sin2(x) + cos2(x) = 1 for all real numbers x;
- xy - yx = 0 for all
complex numbers x and y.
Other identities are not so popular and they require a lot of work to
be understood. Of course, many identities still wait to be
discovered by new generations of mathematicians. In this talk we
will discuss some of the relations that have been found among matrices,
and the many questions that are open to explore.
Sergio Fratarcangeli, McMaster University
Model Theory and Real Geometry
Abstract: Model theory was born in the effort to shore up the
foundations of mathematics. Gradually, the field shifted away
from its syntactic origins, toward a more geometric approach.
Consequently, model theory has found applications in diverse branches
of mathematics. The focus of this talk will be on the interaction
between model theory and (generalizations of) real algebraic
geometry. We will see how the use of so-called o-minimal
structures can simplify some otherwise very messy mathematics.
Markus Reitenbach, Syracuse University
Configurations of Subspaces of Euclidean Space
Abstract: The (proper) subspaces of 3-dimensional Euclidean space are
the lines and planes through the origin, and the origin itself. I will
explain what is meant by a configuration of subspaces, and will give a
classification of configurations, including the ones in higher
dimensions.
Eric Gaze, Alfred University
To Infinity and Beyond: An Irrational Tale
Abstract: This talk will explore the history of infinity, going
back to ancient Greece and the deep philosophical problems that arose
from considering the infinite. Aristotle was effectively able to
put to rest the paradoxes of infinity with an argument later championed
by the Church, but the development of the Calculus brought infinity
back from the depths of human consciousness and forced mathematicians
to study it with rigor. Is it possible to go beyond
infinity? And if so just what would that mean?
Gregg Hartvigsen, SUNY Geneseo
Modeling the spread of influenza through a spatially-structured
host population.
Dr. Hartvigsen is going to present the results from a model that
investigates the dynamics and prevention of influenza in
realistically-structured human populations. This should be of interest
to a broad range of folks interested in how computer and mathematical
modeling can be used to better understand a biological system.
Eugene Olmstead, Elmira Free Academy
An Odyssey of Discovery: Vertical Development of Geometric
Thinking in the Secondary School Curriculum
Dynamic geometry systems like Cabri Jr. and Cabri Geometry II Plus
provide all students and teachers with a unique opportunity to
experience the true sense of mathematical discovery usually reserved
for a few elite mathematicians. Through the guidance of a skilled
teacher, students can begin with some basic ideas, investigate and
explore these notions in traditional and non-traditional ways, and
eventually reach levels of discovery never before available to
students. We will begin with a simple triangle and its four basic
centers, stretching students' thinking past this rudimentary level with
historic constructions that lead to the generalizations of geometric
relationships and eventually to new representations of geometric
ideas. Yet, all of this vertical development is accessible to
secondary school students because of the power of visualization
provided by dynamic geometry software.
Rachel Schwell, University of Connecticut
Knot Theory—What They Didn’t Teach You in Boy Scouts
Knot theory is a relatively “new” field
of mathematics; new in that it has only begun to be explored in the
past one hundred or so years. We will examine knots from a more
mathematical angle, including the accepted mathematical procedure of
“untangling” a knot, if it can be so done, and determining whether two
different-looking knots are actually the same. We will then
consider a way to “add two knots together,” and compare this algebraic
operation to addition and multiplication of natural numbers. The
only knowledge that is required is to know what a knot is and how to
multiply integers!
Immediately following the talk there will be extensive time to talk
with Rachel about graduate school in mathematics . . . why to consider
it and what it’s like.
Olympia Nicodemi, SUNY Geneseo
An Invitation to Galileo's World
In this talk, we take an informal tour of the life and work of one of
history's most important scientists. Galileo was a natural philosopher
who thrust us into the mix of mathematics and experimentation that
physics
had become today. He was also a musician, a talented writer,
a wine maker, and a dedicated father. We will look at how many these
facets come together in his work. The invitation is extended for
you to come explore this further.
Brigitte Servatius, Worchester Polytechnic Institute
Student Workshop: Bracing of Grids
A grid of rectangles is only useful as a rigid supporting structure if
it has sufficient diagonal bracing. How to brace the grid is both
a geometric and a combinatorial problem. We will examine
this problem both theoretically, and practically with the help of
models.
Brigitte Servatius, Worchester Polytechnic Institute
Firing Cannons
Euler was the first to prove that the path of a cannon ball is a
parabola, provided that the only acting force is the force of
gravity. It is well known that firing a cannon on a horizontal
plane at an angle of 45 degrees yields the trajectory having the cannon
ball landing at maximum horizontal distance from the cannon.
We will present what Halley knew about twists to this problem, as well
as some new student thoughts on this old result.
Bonnie Gold, Monmouth University
What IS Mathematics?
OK, you've studied calculus, and (at least in high school) geometry and
algebra; and maybe linear algebra or number theory or differential
equations. So you've seen some examples of
mathematics. But just what IS mathematics? Why do we call
all of these topics mathematics? Is computer science
mathematics? What about economics? Why not? In
this talk, we'll look at some answers people have given, and what a
good answer might look like. In the process, we'll also introduce
the more general topic of the philosophy of mathematics, and some of
the questions it considers.
Rudy Rucker, San Jose State University
Seek the Gnarl: Adventures in Computer Science
In 1986 former Geneseo mathematics professor Rudy Rucker retooled and
became a computer science professor and professional programmer.
But he never stopped thinking like a mathematician. This talk
describes
some of the work he's been involved in over the last twenty years in
Silicon Valley. This will include brief discussions of both the
computer culture and of particular topics in chaos, fractals,
artificial life and computer games. In addition, he'll give a
more detailed discussion of his specialty, cellular automata. The
theme of "gnarl" relates to the class four computations described in
Stephen Wolfram's A New Kind of
Science and elaborated upon in Rucker's forthcoming nonfiction
book, The Lifebox, the Seashell and the Soul: What Gnarly
Computation Taught Me About Ultimate Reality, the Meaning of Life, and How to
be Happy.
Heather Lewis, Nazareth College
The Mathematics of Time
Is it true that there was no October 10 in 1582? Was George Washington
born on February 11, 1731 or February 22, 1732, or both? Why was
an hour equal to 144 minutes after the French Revolution? Does
the
13th of the month really fall on a Friday more than any other day of
the week?
These questions will be answered and other tidbits of calendar trivia
revealed as we look at the mathematics of time. And there will
indeed be some mathematics (modular arithmetic plays a natural role),
but the majority of the talk will be accessible to people of all
backgrounds.
Tom Head, Binghamton University
Splicing Systems: The formal generativer power of enzyme
systems
The application of computational mathematics has aided the
understanding of biological systems. A new scientific frontier is
emerging where biology can aid computational mathematics. The
interdisciplinary field of biomolecular computing explores new
biological paradigms to perform calculations and to use biomaterials in
the fabrication and design of computing architectures at the molecular
level. This talk describes one such approach.
The splicing concept models the 'wet' cut & paste operations
performed by genetic engineers on DNA. The abstract 'dry'
version of splicing has contributed a new generative scheme that has
been studied extensively in the theories of formal languages and
computation. The wet (motivational) aspect will be
discussed in detail. The deepest results in the dry aspect
will be discussed briefly without proofs. Suggestions for
further work will be made.
Jeff Johannes & Gary Towsley, SUNY Geneseo
A Concise History of
Calculus
Abstract: A lively overview of
over two thousand years of
calculus history. Not only who-did-what along the way, but the
cultural and sociological causes and effects of the calculus.
Strongly recommended for anyone who has taken or is taking
calculus.
Olympia Nicodemi & Melissa Sutherland, SUNY Geneseo
The Art and Math of Friezes
A frieze is a horizontal decorative strip. Often we see them as a
strip of wallpaper near the ceiling of a room. In this talk, we look
for
the mathematics hidden in these designs. We are looking for your input
too. The math club PRISM hopes to present this topic as a workshop for
high school girls. We hope to spark ideas as to related math activities
and related art activities.
Nancy Boynton, SUNY Fredonia
Modeling a Birth and Death Process and What Does That Have to Do
With Waiting in Line?
We will start with certain assumptions about births in a system, what
we call a pure birth process. We will see what equations and solutions
this leads us to. Next we will add the possibility of deaths to the
system and see what equations this gives us. These are more complex and
so we can simplify the model by considering the long run behavior of
the system. Finally we
will model a waiting line (like at the bank) as a birth and death
process.
We can view the births as customers arriving and joining a waiting
line.
When a customer completes service and leaves the system we will
interpret
that as a death and look at the probabilities for various numbers of
customers in the system.
Cheryl C. Miller, SUNY Potsdam
Logic and the Natural Numbers
How unique are the Natural Numbers? Some of the simplest
properties to express (without naming specific numbers) include the
fact that the set is infinite, there is always a successor or next
natural number, and that only one of them has no previous
element. Does this completely describe the set? Come see
how some logic formulas and theorems can help us find out more about
the natural numbers, and the possibility of other sets that can also
satisfy these statements.
The talk requires only a basic knowledge of logical formulas, the
symbols used will be explained as needed.
Uma Iyer, SUNY Potsdam
An Introduction to Noncommutative Algebras
Polynomials can be added and multiplied; at the same time, real numbers
can be thought of as polynomials in the form of constant
polynomials.
Hence, all the polynomials in variable x with real number
coefficients
form an "algebra". Suppose we look at objects which can be added
and
multiplied, but the multiplication is not commutative. Then we
get
a noncommutative algebra. Matrices are one example of a
noncommutative
algebra.
The study of noncommutative algebras has been of interest for more than
a century because of the study of matrices. In recent decades, as
the interest in noncommutative geometry grew, noncommutative algebras
have become quite important. In the 90s quantum groups were
widely studied, which had relevance to diverse areas like knot theory
and Lie theory.
In this talk, I will introduce noncommutative algebras through examples.
Julia Wilson, SUNY Fredonia
Eine Kleine Mathmusik
Abstract: Math and music have been linked in curious ways for
thousands
of years. In fact, in the Middle Ages music was considered a
mathematical
subject. In Ancient Greece, the Pythagoreans built their theory
of
the universe on some basic observations about the role of number in
music.
We will look at ways in which people have used mathematical ideas to
describe
and understand music over the millennia.
Dave Bock, Ithaca High School
ESP and Derangements (a journey into probability with a couple of
surprising punch lines)
Robert Kantrowitz, Hamilton College
Matrices and Their Square Roots
Abstract: If A and B are square matrices, and B2
= A, then B is called a square root of A. In
this talk, we shall look at several examples of matrices and their
square roots. The examples will serve also to motivate discussion
of some general facts about square roots. Only knowledge of matrix
multiplication is required.
Bob Rogers, SUNY Fredonia
Calculus before Calculus
Abstract: A number of mathematicians used their
ingenuity to solve calculus problems before its invention by Newton
and Leibniz. This talk explores some of these accomplishments and
discusses their place in the invention of the Calculus.
Brad Emmons, Utica College
Rational Points on Curves
The Pythagorean theorem tells us that the sides of a right triangle are
related by the equation a2 + b2
= c2. One of the main goals in classical number theory
is finding all integral solutions to equations, like the Pythagorean
equation. Many of these problems have rather elegant solutions
when viewed graphically. In this talk we will investigate a few
problems related to the Pythagorean theorem, and the graphical
approaches
to the problems. This will lead to a discussion on elliptic
curves and how you can earn an easy million dollars.
Darwyn Cook, Alfred University
Is It Serendipity?
We will look at some results in mathematics that have had a large
impact in other areas of science. In particular we will be looking at
how closely the result in mathematics was followed by the applications
in other fields. The goal is to discuss these results - please
come prepared to participate.
Tom Pfaff, Ithaca College
Mathematical Ideas in Everday Life
Abstract: As the title suggests, this talk will take a look at
mathematical ideas in everyday life. In no particular order some
of the topics will be, measuring spoons and how not to give advice
to a cook; least common multiples; counting numbers, letters and rocks;
Kevin Garnett; geometric and arithmetic means; cookies and chocolate.
Paul Loomis, Bloomsburg University