Spring 2014
Tuesday, February 18 2:45 - 3:35p
Newton 202
Alden Edson, Western Michigan University
Problem-Based Instruction in a Digital World: Technology
Affordances for Task Design and Enactment
Digital instructional resources are rapidly replacing print
materials offering a promising direction for education at all
levels. In this interactive session, we will examine pedagogical and
tool features of a highly interactive digital instructional unit
focusing on binomial distributions and statistical inference. This
experience will be connected to a summary of how tasks originating
in print curriculum materials can be adapted for highly interactive
digital instructional materials and their affordances for student
learning. We will next examine more closely the additional
affordances of the tool features of the digital materials.
Thursday, February 20 2:30 - 3:20p
Newton 202
Michael Pawlikowski, Depew High School and University at Buffalo
Promoting Mathematical Discourse
This presentation includes key ideas from my doctoral research and how
I use this research to enhance my mathematics instruction. These
key ideas engage how small groups of students can work together to
solve problems. Using a topic from calculus I will demonstrate
how math educators can create a lesson designed to promote
mathematical talk, argumentation, and reasoning. This
demonstration will also provide mathematics majors an opportunity to
see how innovative problem posing can lead to an increased conceptual
understanding of mathematics.
Wednesday, April 16 2:30-3:20p
Newton 203
Kristin Camenga, Houghton College
The Numerical Range of a Matrix: Theme and Variations
The numerical range of a matrix is a set of numbers defined by how
the matrix acts on the unit sphere. Most frequently, we work
with matrices with complex numbers as entries and the resulting
numerical range is a set of complex numbers, which can be visually
represented on the complex plane. The resulting numerical
range is convex and contains the eigenvalues of the matrix.
Based on this foundation, we can ask many different questions.
Given a specific type of matrix, what shapes of numerical range
result? Which transformations of the matrix leave the
numerical range the same? What happens if we use different
fields for the matrix entries? What if we associate a set of numbers
to a pair of matrices instead of just one? In this talk we
will define numerical range precisely and look at some of the
different questions that can be explored. Previous experience
with linear algebra is recommended, but all definitions will be
reviewed.
For a taste of the type of talks to expect, here are quite a few
previous talks.
Kaitlyn Gayvert, Cornell University
Mathematical Applications in Biomedicine
The past two decades have been an exciting time in biomedicine,
with the completion of the human genome project and the beginning of
the "big data" era. This has made collaborations between medical
professionals, biologists, computer scientists and mathematicians
both commonplace and necessary. These interdisciplinary efforts have
resulted in scientific breakthroughs in our understanding of
fundamental biological principles, such as the role of DNA and how
it is regulated, as well as increased our understanding of disease
mechanisms. A wide variety of mathematics and other computational
techniques have played important roles in driving these biomedical
advancements, ranging from differential equation models to data
processing and compression methods (such as wavelet transforms) to
optimization methods and statistical analysis. I will give a broad
overview of the exciting and active areas of computational
biomedical research, as well as go more in depth into my particular
area of research in cancer genomics.
Nathan Reff, Alfred University
Polytopes, Pick's Theorem and Ehrhart Theorem
Suppose P is a convex polygon with integer points. Pick's
Theorem says that the area of P can be computed by counting integer
points on the interior and the boundary of P. I will discuss
Pick's theorem as well as a generalization to higher dimensions via
Ehrhart polynomials. If time permits, I will also discuss some
applications.
Kevin Palmowski, Iowa State University, 麻豆传媒团队 Class of 2011
Comparison of Compressed Sensing Techniques with Partial Support
Knowledge
Suppose
that y
=
Ax,
with A
∈
Rn�m,
y
∈
Rn,
x
∈
Rm,
and n
< m.
The problem of reconstructing x
given
y
and
A
is
generally ill-posed. In the case where x
has
sparse support (|supp(x)|
≪ m),
compressed sensing literature provides algorithms, many of
which use l1
minimization,
by which we can accurately reconstruct x
under
certain sufficient conditions. In the case where supp(x)
is partially known, the Modified-CS algorithm can be used to
reconstruct x,
and the sufficient conditions for reconstruction can be
relaxed. Weighted-l1
minimization
uses a combination of standard CS and Modified-CS. We
present new sufficient conditions for exact reconstruction
by weighted-l1
minimization,
compare these to known bounds, and report results of
simulations. An application to image processing is included
as a motivating example.
Elizabeth Cherry, RIT (as part of The Community Health Alliance Speaker
Series)
Cardiac arrhythmias: Improving understanding through mathematical
modeling and computer simulation
Dangerous heart conditions can arise from disturbances in the
electrical signals that trigger the heart to contract. Substantial
experimental evidence links these serious electrical disruptions,
called arrhythmias, with spiral waves of electrical activity in
cardiac tissue. After a single spiral wave has formed, a number of
known mechanisms can destabilize it and generate additional spirals
that complicate restoration of cardiac function. These waves
repetitively excite the tissue at fast rates and alter the sequence
of activation, both of which compromise the heart抯 ability to pump
effectively. This talk will describe the current understanding of
the spatiotemporal organization of electrical waves in the heart
during normal rhythm and arrhythmias using state-of-the-art
experiments, theory, and simulations. The electrophysiology of
cardiac cells and tissue, mathematical modeling approaches, physical
principles, numerical methods, and high-performance computing issues
will be discussed.
Ernest Fokoue, RIT
Taming Big Data with Old and New Mathematical and Statistical
Tools
The technological advances of the recent decades have made it
possible for huge amounts of data to be collected in all walks
of life. In fact, it抯 quite common these days to hear people
say that we live in an era of the so-called 揃ig Data�.
Interestingly, large complex data come in various shapes,
sizes and characteristics. In this lecture, I will present a simple
taxonomy of large/massive data sets, and I will briefly
highlight some of the mathematical and statistical tools that
are commonly used in data mining and machine learning to
extract meaningful information from different forms of complex
data. I intend to touch on data from fields such as
image processing, speech/audio recognition, DNA micro-array
analysis, classification of text documents, intrusion
detection and consumer statistics, just to name a few. My
focus throughout the lecture will be to show and possibly
demonstrate computationally that while some of the
mathematical/statistical tools needed to tackle these complex
data structures are very novel and cutting edge, some are just
straightforward applications or gentle extensions of the
traditional statistical arsenal.
Jeff Johannes & Gary Towsley, 麻豆传媒团队
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.
Yusuf Bilgic, 麻豆传媒团队
The Marriage of Theory with Simulation: Some Data Analysis Stories
Since computationally intensive techniques have been easily available,
have traditional methods for conducting data analysis been losing
confidence? Are developing curricula in teaching statistics making
errors with randomization- and bootstrapping-based techniques? Did we
reject the logic of conventional inference and statistical thinking as
data becomes
ginormous? Let抯 make a decision at 5% level using simulation studies.
Students are encouraged to bring devices with internet access (laptop,
smart phone etc).
Arnulfo Perez, Indiana University
Functions Matter: Using Performance on NAEP to Describe Hispanic
Students� Achievement in Mathematics
This talk discusses my study in progress, which centers on Hispanic
students� math achievement using data from the Grade 12 National
Assessment of Educational Progress (NAEP). I explain the rationale
for focusing on functions as a representation of math achievement
and highlight methods I use to create a profile of achievement for
first-generation college-bound Hispanic students using their
performance on function items. In addition, I discuss the
implications my findings have for policymakers and others interested
in addressing achievement gaps in mathematics.
Dana Dodson, Indiana University Northwest
Square Roots Go Rational
Students recall and model the square root as the length of one side
of a square. But what if the square is not a perfect square? This
collection of activities explores the square roots of not-so-perfect
squares and develops an algorithm to express the not-so-perfect
square root as a rational value.
Christian Northrup, East Henderson High School
Writing in a Statistics Classroom in the 21st Century
In an era of technology, students benefit from instant feedback
enabling them to focus more on analysis and drawing
conclusions. When utilized properly, technology can be a
useful tool for helping students learn new statistical
concepts. What are other methods that teachers can employ in a
classroom that will aid and support students as they learn
statistics? How can statistics teachers be confident that
students are truly grasping concepts? Writing is one answer to these
questions. Join me as we examine the benefits of
writing. In addition, we will discuss the hurdles that will
need to be overcome by students and teachers to successfully
implement writing in a statistics classroom. Please bring your
Smartphone, iPad, or an equivalent device.
Salam Khan, Alabama A&M University
Probability and Social Conflict Model
Probability theory is a very important tool for mathematical and
statistical analysis. The aim of this talk is to discuss basic
concepts of probability and a probabilistic social conflict model
for non-annihilating multi-opponent. In this probabilistic model
opponents have no strategic priority with respect to each other. The
conflict interaction among the opponents only produces a certain
redistribution of common areas of interests. The limiting
distribution of the conflicting areas, as a result of infinite
conflict interaction for existence space is investigated.
Lucia Tabacu, Pennsylvania State University
Ordering in Nonparametric Statistics
Ranking is a commonly used procedure to evaluate daily life
situations, for example in medicine, business, sports, and many
other fields. This method is also used in nonparametric statistics,
the basic idea here being the ordering of the observations on a more
abstract level. The talk will explain the usefulness of this concept
in testing procedures, the famous two-sample problem being an
important example. A more advanced idea of ordering is used to
analyze the ``shoulder tip pain� data set that appears in Brunner,
Domhof and Langer, 2002. This is a clinical study with 41 patients
who had undergone a laparoscopic cholecystectomy and developed
shoulder pain after the surgery. The main question here is to test
the effectiveness of the treatment for shoulder pain.
Xiaohui Chang, University of Miami
Wavelet Analysis in Spatial Interpolation of High-Frequency
Monitoring Data
To get a better understanding of the weather systems, atmospheric
scientists and meteorologists are generally interested in having
available data spatially interpolated to much finer spatial and
temporal grids. Many physical or deterministic models that are
used to generate regional or global climate models are able to
provide accurate point predictions, but it is very difficult for
them to give realistic uncertainty estimates. This calls for the
development of statistical models that can produce uncertainty
estimates through conditional simulations. In this project, we look
at the minute-by-minute atmospheric pressure space-time data
obtained from the Atmospheric Radiation Measurement program. We
explain how spatial statistics can be used to model such data that
are sparse in space but high frequency in time. Due to the
interesting local features of the data, we also take advantage of
the localization properties of wavelets to capture the local
dynamics of the high-frequency data. This method of modeling
space-time processes using wavelets produces accurate point
predictions with high precision, allows for fast computation, and
eases the production of meteorological maps on large spatial and
temporal scales.
Gillian Galle, University of New Hampshire
The Trouble with Trigonometry
Students that enroll in algebra-based physics courses for life science
may be less prepared mathematically than their counterparts in the
engineering, physical science, or mathematics majors. This means
it can be especially difficult for them to develop conceptual
understandings of equations that possess both physical and
mathematical interpretations within the same context. Based on
such students� answers to a particular question on simple harmonic
motion equations, this study undertook to systematically probe the
following questions: What is the range of students� initial knowledge
with respect to trigonometry? Is reviewing trigonometric concepts
valuable and/or necessary? Can students see the trigonometric
equations describing oscillations as conveying an idea, in addition to
being a tool to get 搕he answer?� In this talk I focus on the
efforts of my colleague and I to answer this last question through the
design and timely implementation of a trigonometric intervention and
motivational activity meant to help these students reason through the
underlying connections between trigonometry and modeling simple
harmonic motion. In addition to discussing the research the
intervention was based on, I will address the development of our
motivational activity, our finding that students can learn to see
trigonometric equations describing oscillations as conveying an idea,
and what implications this may have for the way we address this topic
in both high school and undergraduate physics courses.
Valentina Postelnicu, Arizona State University
The Functional Thinking in Mathematics Education: A Cultural
Perspective
One of the most important ideas that influenced the mathematics
education of the last century is the idea of educating functional
thinking, particularly a kinematic-functional thinking. Bringing
students up to functional thinking has proved to be a difficult task
for mathematics educators. We examine the current state of
mathematics education with respect to functional thinking by
considering different curricular approaches to functions in the
United States and other parts of the world. We closely look to one
problem and the way it may appear in different cultural settings. We
focus on issues related to the covariational approach to functions,
the rise of digital technologies, and the need for symbolic
representations
Amanda Beeson, University of Rochester
Title: Did Escher know what an elliptic curve is?
We will give a na飗e introduction to elliptic curves. Then we will
discuss whether the 20th century Dutch artist M.C. Escher knew what an
elliptic curve is. Along the way, we will discover many wonderful
things about his piece called "Print Gallery". This talk will be
enjoyable if you remember how to add and multiply, but some
paper-folding skills never hurt. This talk is based on work of H.
Lenstra.
Carlos Castillo-Garsow, Kansas State University
Chunky and smooth images of change
Students have well documented difficulties with graphs. In this
talk, I discuss recent and current research that investigates
connections between these difficulties and student difficulties in
forming images of change, the impact that these student difficulties
have on more advanced mathematical reasoning at the secondary and
undergraduate level, the damage that developing these difficulties
can do to the preparation of teachers, and the potential role of
technology in developing solutions to these systemic and persistent
problems.
May Mei, University of California, Irvine
Attack of the Fractals!
You may not know it, but you're
surrounded by fractals! They are all around you and even inside
of you. In this talk, we will explore the prevalence of fractal
structure in the natural world and in mathematics. Then we will
construct the standard Cantor set and show you how you can construct
your own fractals.
Emma Norbrothen, North Carolina State University
Number Systems Base p
Rational numbers can construct the real
numbers by using the absolute value norm. Under different norms,
rationals can construct different types of numbers. In
particular, the p-norm
evaluates how much a prime, p,
is a factor in a given rational. We will explore some
consequences of the p-norm
and what kind of numbers it creates from the rationals.
Sue McMilllen, Buffalo State
President, Association of Mathematics Teachers of New York State
(AMTNYS)
Fibonacci Fun
Explore interesting properties of the
Fibonacci sequence. Look for patterns and make
conjectures. Learn about connections between matrices and the
Fibonacci sequence. Bring your calculator.
If you would like to know more about graduate studies at Buffalo State
or about AMTNYS, please stay around after the talk to converse
with Dr. McMillen.
Arunima Ray, Rice University, 麻豆传媒团队 class of 2009
A friendly introduction to knots in three and four dimensions
If you've ever worn sneakers or a necktie, or ever been a boy scout,
you know a lot about knots. Knot theory is also an exciting (and
young) field of mathematics. We will start from scratch to define and
discuss some basic concepts about knots in three dimensions, such as
how to quantify the 'knottedness' of a knot and how to tell if two
knots which look different are secretly the same. We will also see how
a four dimensional equivalence relation reveals a simple and elegant
algebraic structure within the set of knots.
This talk will be very visual with lots of pictures and will be
accessible to students at all levels.
Xiao Xiao, Utica College
The Frobenius Problem
Let a, b, . . . , c be positive integers greater than 1 with
no common factors. The Frobenius problem studies the largest
non-negative integer g(a, b, . . . , c) that cannot be
expressed as a non-negative linear combination of a, b, . . . , c.
In this talk, I will review some of the old and not so old results of
solving the Frobenius problem for g(a, b) and g(a, b, c).
If time permits, I will also describe how a closed formula of g(a,
b, c) in a special case can be used to solve problems in the
classification of F-crystals over algebraically closed field. This
talk is accessible to undergraduates.
Katherine Socha
Sea battles, Benjamin Franklin's oil lamp, and jellybellies
"During our passage to Madeira, the weather being warm, and the
cabbin windows constantly open for the benefit of the air, the
candles at night flared and run very much, which was an
inconvenience. At Madeira we got oil to burn, and with a
common glass tumbler or beaker, slung in wire, and suspended to the
ceiling of the cabbin, and a little wire hoop for the wick,
furnish'd with corks to float on the oil, I made an Italian lamp,
that gave us very good light...." (Benjamin Franklin, December 1,
1762 letter to John Pringle)
Observations of real phenomena have led to mathematical modeling of
surface water waves, interfacial waves, and Lagrangian coherent
structures among other examples. This expository talk will
provide a quick tour of the (mostly advanced undergraduate level)
mathematics needed to describe idealized versions of the rings
formed by striking a surface of water with a large object (like a
bomb), the oil-water waves observed by Founding Father Benjamin
Franklin on his voyage to Madeira, and the motion of nutrient laden
water being swept into the underbelly of a swimming jellyfish.
Ron Taylor, Berry College
The Difference Between a Small Infinity and a Big Zero
Can two people have a different answer to the same question and both
be right? Is there room for perspective in mathematics?
Most often we find that any given mathematical question will
have a single answer, though there are usually many different methods
that can be used to find that answer. In this talk we will
discuss the Cantor set, a remarkable object that seems to leave room
for perspective to play a part in mathematics. Given time we
will discuss generalized Cantor sets, a class of sets with interesting
properties of size.
Emilie Weisner, Ithaca College
The mathematics of bead crochet
Creations in the fiber arts are often based in pattern and
symmetry. Because of this, the fiber arts and mathematics are
a natural pair. In this talk, I'll talk about some of the
mathematics related to bead crochet. In particular, I'll
discuss the work of Susan Goldstine and Ellie Baker, who use
wallpaper groups to understand symmetries in bead crochet
patterns. I'll also talk about work on additional mathematical
aspects of bead crochet, being carried out by IC juniors Rachel
Dell'Orto, Sam Reed, and Katie Sheena.
Ryan Gantner, St. John Fisher College
The Stochastic Voter Model
In this talk, the stochastic voter
model will be introduced and we'll see how it works. After
deriving some results about its long-term behavior, we'll turn to some
examples of how it can be applied. Some examples include the
spread of diseases, the evolution of zombie attacks, ... and
elections! The talk will conclude with a simulation to predict
the outcome of the 2016 presidential election.
Prerequisites: The major mathematical proof in this talk should
be accessible to anyone who has had calculus 2. All other
aspects of the talk involve only intuitive aspects of probability, and
should be accessible to all mathematically inclined students.
Kalyani Madhu, SUNY Brockport
Periodic Points in Finite Fields: A Question in Arithmetic
Dynamics
In Arithmetic Dynamics we study dynamical systems from a number
theoretic point of view. This talk will introduce basic ideas in this
relatively new branch of Mathematics that will enable us to understand
an interesting question concerning the dynamics of 铿乶ite 铿乪lds.
Laurel Miller-Sims, Hobart & William Smith Colleges
When Not Knowing is Enough
It's impossible to do mathematics without running into things we don't
know. We will look at logic puzzles where the key to the solution lies
in a lack of knowledge. It's sometimes surprising where not knowing
will get you!
Rebekah Yates, Houghton College
Numerical Range: Counting Necklaces and Looking for Symmetry
The numerical range of a matrix A is the set of all complex numbers
resulting from mapping a vector in the unit sphere to the dot product
of that vector with A. We will consider the question of when, under
certain conditions, this set is symmetric about the origin. Along the
way, we'll see several properties of the numerical range, encounter
many familiar matrix characteristics, and find ourselves counting how
many different necklaces can be made from a fixed number of beads of
two different colors.
Prerequisite: Math 233 (Elementary Linear Algebra).
Elizabeth Wilcox, Colgate University
The Enormous Theorem
Have you ever thought about the work that goes into proving
mathematical theorems? Take, for instance, the Fundamental Theorem of
Calculus - who proved it? How did he (or she?) even come up with the
idea to prove such a thing? And how long did that mathematician spend
thinking before a proof materialized?
During the talk we'll learn about a theorem that was nearly eighty
years in the making, taking mathematicians from 4 continents nearly
15,000 pages to prove - in a time before FaceTime, Skype, or even cell
phones! I will introduce you to mathematical groups and show you that,
even though you've been working with groups since grade school, these
structures are so complex that after hundreds of years we are still
learning new things about groups every day.
Jim Matthews, Siena College
The Twenty Locker Problem
In many games, an important goal is to maximize your chances for
success. This is true for the locker problem where teams of players
attempt to maximize the chances of every team member being successful.
We will describe the locker problem, invite participants to suggest
solution strategies (possibly offering one or two of our own), and
then using some basic probability (along with a bit of calculus and
computer programming), determine the chances of success for each.
This is a version of a search problem for succinct data structures
that appeared in a paper written by Peter Bro Miltersen and Anna
G谩l which won the best paper award at the 30th International
Colloquium on Automata, Languages and Programming in 2003.
The main ideas for this exposition are accessible to the general
public and the solutions that will be discussed can be carried out by
average middle school level students. The applications of the college
level material to this problem are delightful and probably surprising.
Olympia Nicodemi, 麻豆传媒团队
How many real numbers are there?
In this talk we will find out if infinity comes in sizes and we will
find out how many really real numbers there are. We hope that it
will be accessible and interesting to all students, majors or not.
Douglas Haessig, University of Rochester
An introduction to number theory, from a p-adic
point-of-view
Many number theorists are interested in the solution sets of
multivariable polynomial equations. For example, Fermat's last theorem
asks about integer solutions of the polynomial equation x^n
+ y^n = z^n. In this talk, we will see how the solution set
of a conic (quadratic equation) depends on the domain of the
variables. This will lead us into defining "p-adic
numbers." After discussing a few theorems to see how p-adic
analysis works, and how p-adic
geometry
looks, we will employ the p-adics to count the number of (finite
field) solutions to a famous cubic equation using differential
equations.
Jane Cushman, Buffalo State University
Which cup material holds hot water the hottest, the longest?
Using a temperature probe, TI-84, boiling water and various cup
material (Styrofoam, paper and ceramic), data will be collected.
The data will be shared with the participants and everyone will
analyze the data to determine which cup material held the hot water
the hottest and longest. Which do you think will?
This talk is aimed at pre-service teachers and mathematics majors;
there are no pre-requisites.
Jonathan Hoyle, Eastman Kodak
A Mathematician in the Real World
"How much Mathematics is really used out there in the real
world?" The answer to that question of course varies, depending
on your definition of "real world". Obviously, a different level
of Mathematics would be used by a statistician than would be by the
owner of a pizza parlor. My "real world" is one as a software
developer, and I will talk about some of the mathematics with which I
have been involved. These include work at DuPont, Kodak, and
writing forensic DNA software used to identify victims of the World
Trade Center attacks on 9/11.
Ryan Gantner, St. John Fisher College
It's time to play Hackenbush!
Let's play a game. The only things we?ll need are several red
and blue sticks. Oh, and some interesting mathematical
theories. The game is called "Hackenbush", and it is fairly
simple to play. In this presentation, we'll develop some theory
of partisan combinatorial games to help us better understand what is
the best way to play the game. It turns out that the game
positions can be given number values in a meaningful way. Then,
we can ask what happens when randomness is added to the game, which is
an ongoing area of research.
Bonnie Jacob, Rochester Institute of Technology
A discrete challenge based on optical imaging
Diffuse optical imaging is a method of imaging that consists of
reconstructing the optical parameters inside a medium using data
gathered at the boundary. Optical imaging has wide appeal in medical
applications in particular because the light that is used does not
harm the patient. Despite the appeal of optical imaging, however,
difficulty in obtaining high quality images has prevented it from
being widely used in clinics. One way to get a better reconstruction
is to choose the source cleverly.
Motivated by this problem, we consider a discrete version of the
typical optical tomography model: a network in which each node is
designated as either "scattering" or "absorbing." We consider how the
structure of the network, the location of the different classes of
nodes in the network, and the initial location of the signal --- the
"source"--- all influence our ability to recover each node's
classification.
Helpful co-requisites: This talk will relate well to topics from an
elementary linear algebra course.
Matt Koetz, Nazareth College
Coding Theory: Yeah, We've Got That
Coding theory is the study of
transmitting information efficiently across noisy channels. It
aims to reduce the number of transmission errors, detect and correct
errors, and do these things as quickly and cheaply as possible.
In the search for better codes, we use many branches of
mathematics, including linear algebra, combinatorics, graph theory,
geometry, probability, and number theory. We will explore the
ways in which coding theory uses each of these fields, from its basic
definitions to its most beautiful results.
Quincy Loney, Binghamton University
The Octonions: An Alternative (Algebra) To The Reals.
In this talk we will discuss some of the history and the properties of
the octonions, the 8-dimensional normed division algebra, discovered
by John T. Graves in 1843. We will begin with the real number system
and use the Cayley-Dickson process to construct this exciting
alternative algebra.
Candace Schenk, Binghamton University
A brief overview of the conjugacy problem in Thompson's group V.
This is an introductory talk where I will define all terms used! I
will explain Thompson's group V,
what the conjugacy problem is and the solution. There will be
dynamics! There will be functions! There will be trees!
Brandt Kronholm, St. Mary's College of Maryland
Integer Partitions: 1 + 1 = 2 and the
Subtleties Therein.
The partitions of a number are the ways
of writing that number as a sum of positive integers. For example, the
five partitions of 4 are 4, 3+1, 2+2, 2+1+1, and 1+1+1+1 and we write
p(4) = 5. What鈥檚 the
formula? It鈥檚 less than 100 years old and you wouldn鈥檛 believe it
even if you saw it.
Around the same time that the formula for
p(n)
was formulated, it was observed that
p(n)
had unexpected divisibility properties:
p(5n+4)鈮�0
(mod5)
p(7n+5)鈮�0
(mod7)
p(11n
+ 6) 鈮� 0 (mod 11)
Fifty years later one more divisibility property modulo 17 was
discovered. Are there any others?
The restricted partition function
p(n,m)
enumerates the number of partitions of a non negative integer
n
into exactly
m parts. For
example, the two partitions of 4 into exactly 2 parts are 3 + 1 and
2+2 and we write p(4,2) = 2.
p(n, m)
is like a little brother function to the unrestricted partition
function
p(n) in that
p(n)
=
p(n,1) + p(n,2) + ... + p(n,n).
This talk will introduce the theory of partitions from the ground up
and segue into a discussion of recent results on divisibility
properties for
p(n, m).
Time permitting, we will consider future research regarding
p(n,
m) and formulate some formulas!
Jobby Jacob, Rochester Institute of Technology
Towers of Hanoi and Rankings of Graphs
The Towers of Hanoi is a famous puzzle that has been studied for
centuries. In the Towers of Hanoi, the idea is to move a stack of
disks from one pole to another without placing a larger disk on top of
a smaller disk. The goal is to do this in the fewest number of moves
possible. It is known that this puzzle involving k
disks can be solved in 2k 鈭�1
steps. The puzzle鈥檚 optimal solution relates to some interesting
mathematical problems.
An optimal solution to this puzzle is related to rankings of graphs,
which are generalized vertex colorings. In this talk we will look at
the relationship between rankings of graphs and an optimal solution of
the Towers of Hanoi problem, as well as some properties of rankings.
Jeff Johannes, 麻豆传媒团队
Game: SET - Math
SET is a popular game for many student math groups (including
PRISM). In this talk, we will see many good reasons for
this. From a simple game enjoyed (and excelled) by children, we
will find geometry (the fourth dimension), topology (tori), algebra,
probability, and combinatorics. Aside from all of this, there
will be times to play along, and takeaway prizes.
Bogdan Petrenko, SUNY Brockport
Probabilistic Algebra and Number Theory
At the beginning of my talk I plan to give an intuitive explanation of
how to find the probability that 2 integers are relatively prime.
This should be interesting and quite accessible to any student
who has taken Calculus 2. Next I plan discuss some related explicit
examples from my recent joint work with R. Kravchenko and M.Mazur
posted at .
For this part of my talk I will assume that the audience knows
matrix and modular arithmetic.
Aaron B. Luttman, Clarkson University
The Mathematics of Your Lifetime: Mathematical Advances of the
Last and Next 20 Years
Throughout our mathematical training from elementary school through
the first few years of college, we're taught mathematics as facts and
ideas that were invented or discovered by people hundreds or even
thousands of years ago. This makes it easy for us to think of
mathematics as being complete, as if there's nothing left to uncover
or create. The reality is that we live in a wonderfully exciting time
of mathematical innovation and development, and new breakthroughs are
occurring almost daily. In this presentation we will look back at some
of the most exciting mathematical developments of the last 20 years -
from the solutions of centuries-old problems in pure mathematics like
Fermat's Last Theorem and the Poincare Conjecture to mathematical
transformations of applications such as medical imaging and quantum
computing - and we'll look forward to the possible advances that
today's students will have the opportunity to make in the next 20
years.
Level/Background Required: This talk is aimed at any college students
with an interest in mathematics. A first course in calculus will be
helpful, but no prior knowledge of the problems discussed will be
assumed.
Walker White, Cornell University
Scaling Games to Epic Proportions
An important aspect of computer games is the artificial intelligence
(AI) of non-player characters. Currently in games, developers or
players can create complex, dynamic behavior for a very small number
of characters. However, neither the game engines nor the style
of AI programming enables intelligent behavior that scales to a very
large number of non-player characters; the languages that define
character logic are typically very expensive to process.
In this talk, I will show how solve this problem by modeling game AI
as relational queries. Instead of processing characters
independently, we can combine all of their behaviors into a single
logical query which can then be optimized. The talk will
include an overview of the formal framework for specifying character
behavior, as well as highlight some of the mathematics behind the ways
that we optimize this behavior.
Gary Towsley, 麻豆传媒团队
What does Dante have to do with Mathematics?
This talk is an introduction to the rich treasury of Mathematics to be
found in Dante's La Commedia.
Tom Bleier, Syracuse University
Introduction to the Projective Plane
Come see an introduction to one of the most beautiful and fascinating
areas of mathematics, Algebraic Geometry! This talk will be
accessible to students of all backgrounds.
Paul Seeburger, Monroe Community College
Making Multivariable Calculus Come Alive using
Dynamic Visualization Tools
A tour of an NSF-funded project that seeks to develop geometric
intuition in students of multivariable calculus. This
online exploration environment allows students to create and freely
rotate graphs of functions of two variables, contour plots, parametric
surfaces, vectors, space curves generated by vector-valued functions,
regions of integration, vector fields, etc. This tool is
designed to improve student understanding of the geometric nature of
many of the concepts from multivariable calculus. A series of
assessment/exploration activities has also been designed to help
students "play" with the 3D concepts themselves, and to assess
improvements in geometric understanding gained from these
activities. 3D glasses will be provided.
Phong Le, University of California at Irvine
Using Modulo Arithmetic to Find New
Solutions to Old Polynomials
In this talk we will rebuild the
integers using arithmetic modulo prime numbers. This will allow
us to find solutions to polynomial equations such as x2+1=0
in
an entirely new setting: the finite field. This new algebraic
construction will raise many interesting questions with some
surprising answers.
Kristin Comenga, Houghton College
Polytopes: Generalizing Polyhedra to Higher Dimensions
Most people remember working with polyhedra in elementary and high
school: cubes, prisms, tetrahedra, pyramids, etc. Euler's
relation states that if V is
the number of vertices, E
the number of edges and F
the number of faces, V + F =
E + 2. In this talk we will survey variations on
this result for generalizations of polyhedra called polytopes.
The polyhedra most of us have experience with are
three-dimensional. Polytopes can be any non-negative dimension,
with the simplest example beyond polygons and polyhedra being the
four-dimensional hypercube. How can Euler's relation generalize
to polytopes in any dimension? How can we generalize this to
look at angles of polytopes instead of the number of faces? We
will look at a number of examples of polytopes as we explore some of
the answers mathematicians have found to these questions. We
will end with a brief glimpse of open questions about angles in
polytopes. No specific math background will be assumed, but
curiosity is expected!
Emilie Wiesner, Ithaca College
Clever Counting Strategies in Sudoku
Have you ever played Sudoku? Have you wondered what makes one
puzzle harder than another? what the minimum number of clues could be?
how many puzzles there are? So have other mathematicians!
I'll talk about these questions and, in particular, how mathematicians
have tried to count the number of puzzles. This turns out to
be a tough count to make, and mathematicians have used clever
counting strategies from Combinatorics and Abstract Algebra to do it.
Olympia Nicocdemi, 麻豆传媒团队
Wavelets and Elementary Linear Algebra
Wavelets are in use everywhere, from
deep inside a little digital camera to big telescopes that help us
find out what's out there. The name wavelets sounds so user friendly.
And they are, but the theory behind them is not always accessible to
undergraduates in their early studies. In this talk, we will
make that theory a little friendlier by linking what we learn in
elementary linear algebra to the theory and practice of wavelets.
Mark Steinberger, University at Albany
Topological Equivalence of Matrices
Two n
x n real matrices A
and B are said to be
topologically similar if there is a continuous, 1-1, onto function f:
Rn -> Rn
whose inverse is continuous, such that f(Ax)=Bf(x)
for all x in Rn.
If f were the function
induced by a matrix P,
i.e., if f(x)=Px for
all x in Rn,
then P must be
invertible and PAP-1=B,
so A and B
are similar in the usual sense. Similarity of matrices can be thought
of as saying that the transformations induced by A
and B differ by a linear
change of variables. So topological similarity means that A
and B differ by a
topological change of variables.
De Rham, in 1935, conjectured that topological similarity implies
linear similarity. He was
wrong. We discuss the geometry underlying the existence of a
topological similarity between linearly nonsimilar matrices and
connect it to the algebra used in modern topology.
Patrick Rault, 麻豆传媒团队
Arithmetic Geometry
How many rational points are on the unit circle? That is, how
many points on the circle x2+y2=1
have
coordinates which are rational numbers? In answering this
question, we will find an algorithm that gives all Pythagorean
Triples!
More generally, arithmetic geometry is the study of integral and
rational points on curves. In this talk, we will generalize each
of the following concepts: fractions, discriminants of
polynomials, and the aforementioned Pythagorean Triple method.
We will end with several related unsolved problems, and an upcoming
research and travel funding opportunity to participate in a 2009-2010
research course. This small 3-credit course would be ideal for
those who have taken Math 319 or 330 and are planning to attend
graduate school.
Corequisites: Any students who have taken or are taking
Elementary Linear Algebra (Math 233) should enjoy this talk.
Bronlyn Wassink, Utica College (麻豆传媒团队 Alumna)
Functions, Rubber Bands, and Trees
There is a group of special functions, Thompson's Group F, that
can be represented in many different ways. After showing
exactly which functions are in Thompson's Group, we will explore
both the rubber band model and the tree pair model for this
group. This exploration will involve defining these
models, showing how to quickly and easily change from one model
to the next, and how to compose two functions in this group
using only trees. No background knowledge is required to
understand this talk!!
Michael Starbird, University of Texas
To Infinity and Beyond
Infinity is big. For thousands of years, people also thought it was
incomprehensible--an idea so vast that understanding it was beyond the
scope of people's finite minds. But a child's method of sharing "'one
for me, one for you", an Infinite Inn, a barrel containing infinitely
many Ping-Pong balls, and a game called Dodge Ball combine to take us
to infinity. And beyond.
Vijay Sookdeo, University of Rochester
The Exotic World of p-Adic
Numbers
Under the usual notion of an absolute value, we may "complete" the set
of rational numbers (fractions) to obtain all the real numbers. In
1902, Kurt Hensel found different ways of taking absolute values on
the rational numbers, and thereby discovered the "p-adic
numbers".
This talk will introduce some of the bizarre and wonderful properties
in this strange new world. Among them are: all triangles are
isosceles, every point in a disk is the center, and two disks can only
(non-trivially) intersect in one way. We will also sketch the proof of
an important theorem concerning recurrence relations (the
Skolem-Mahler-Lech Theorem) which exploits the exotic features of p-adic
numbers.
Keary Howard and friends, SUNY Fredonia
Teachers' Masters Capstone
Projects in Secondary and College Mathematics
Does cash money motivate in a college math classroom? What鈥檚
the 鈥榬ight鈥� amount of high school geometry homework? Can
your iPod improve math performance? Are ninth graders really
faster than a calculator? Join us as we attempt to explore these
questions in mathematics education from a quantitative perspective.
Scott Russell, 麻豆传媒团队 Computer Science
Beyond Confidentiality: Cryptographic Applications of
Homomorphic Encryption Schemes
Most people are aware that encryption schemes such as RSA and DES
are useful tools for protecting the privacy of confidential
information, e.g. your credit card or bank account number.
Homomorphic encryption schemes provide additional algebraic
properties beyond those necessary for confidentiality.
Consequently, these schemes are oft-used building blocks in
solutions to a variety of other cryptographic problems. We
will briefly explain the exclusive-or-homomorphic Golwasser-Micali
encryption scheme whose security is derived from the
Quadratic Residuosity Assumption. Then we'll demonstrate
how to use Golwasser-Micali encryption to construct solutions to a
couple of cryptographic problems.
Chris Leary, 麻豆传媒团队
Fractals, Average Distance, and the Cantor Set
After briefly introducing fractals and some of their properties,
we introduce the idea of the average distance between points of a
set. We will construct the famous Cantor Set and use it as
an example of a fractal and finish by computing the
average distance between the points of the Cantor Set. The
material of this talk was developed over the summer with Dennis Ruppe,
a math major here at 麻豆传媒团队.
Prerequisites: Calc I would be nice, but not essential. A
trusting personality is both nice and essential.
Daniel Birmajer, Nazareth College
The arithmetic of formal power series over the integers
We study the arithmetic (units, irreducible elements, unique
factorization, etc.) in the ring of formal power series (in one
variable) with integer coefficients, and discuss some irreducibility
criteria. We will examine in some detail whether or not a quadratic
polynomial is irreducible as a power series.
Bob Rogers, SUNY Fredonia
New Tricks for Old Curves
Even though conic sections have been studied for at least 2400 years,
they still prove to be useful in our modern world. This talk
will provide examples of current uses in medicine, global positioning
systems, and optics and explore potential uses in quantum computing.
Claudiu Mihai, Daemen College
Generalization of Some Optimization Problems
In this talk we present several optimization problems from Calculus
books that can be more easily solved by generalizing them. For
example, maximizing the area inside a triangle, or maximizing the area
inside a parabola region. Similar results will be shown for problems
involving volumes. Some surprising results will be presented.
Darwyn Cook, Alfred University
Geometry and Art
We will look at the relationship between geometry and perspective art.
In particular we will show why vanishing points exist and how to
figure out where they occur. We will use that information to create
some simple pictures using Microsoft Excel and we will also develop a
method for viewing art pieces.
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 .
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, 麻豆传媒团队
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鈥擶hat They Didn鈥檛 Teach You in Boy Scouts
Knot theory is a relatively 鈥渘ew鈥�
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 鈥渦ntangling鈥� 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 鈥渁dd two knots together,鈥� 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鈥檚 like.
Olympia Nicodemi, 麻豆传媒团队
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 麻豆传媒团队 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.
Olympia Nicodemi & Melissa Sutherland, 麻豆传媒团队
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.