James Smith (San Francisco State University)
The Use of Symmetry by Western Composers
The talk draws an analogy between the symmetries studied in 2D Euclidean geometry and devices used by composers: augmentation, diminution, imitation, fugue, and so on. I do more music than geometry. I play musical passages with displayed moving-bar scores, and analyze the symmetries used. The examples range from Bach to Schoenberg. This talk is understandable by a general audience.
Declan Quinn (Syracuse University)
Representation of the Symmetric Group
The Symmetric group is one of most elementary finite groups. It has received a lot of attention and there is a tremendous amount of information known about it, including its representations. On the other hand surprisingly little is known about the Kronecker product of its representations. We will introduce the group and its representations and survey what is known, as well as presenting a recent result. Prerequisites will be kept to a minimum. (A first course in abstract algebra will be sufficient for most of the talk.)
Chi-Lung Chang (CSUDH)
Teaching Probability using Event Grids
10/24/07
Event Grids are the result of partitioning the sample space by events
represented as rectangles. More specifically, we think of the creation
of an event as the result of bisecting the sample space or bisecting
the existing grids by means of horizontal or vertical lines. For the
sake of simplicity, we will confine ourselves to finite sample spaces
even though the technique is applicable to any sample space with no
significant modifications. Data grids are used frequently in
statistics but grids are only used in a limited fashion in probability
if at all, which is unfortunate. Indeed, if Event Grids are used as a
starting point of Probability Theory then, as we plan to show, all the
information about the axioms, definitions, rules or theorems of
probability emerges out of these Grids naturally and
effortlessly. Once they learn how to construct and work with Event
Grids, students find probability fun and easy to learn without having
to memorize a large body of rules and formulae. This technique has
generated good results in both elementary and advanced
probability/statistics courses that I have taught in recent years,
although the advanced students need to be reminded and shown that all
rules and theorems can be proven from the axioms and definitions
independent of the grid diagrams.
The talk is accessible to anyone at the level of finite
mathematics/elementary probability or above.
Chadwick Sprouse (CSU Northridge)
Inequalities and rigidity theorems for the first Dirichlet
eigenvalue
10/10/07
Let R be a connected open set in the plane with compact closure, which we will call a domain. Then the Dirichlet problem on R has a sequence of positive eigenvalues, which can be thought of as the vibrational frequencies of a thin membrane stretched across R and fixed at the boundary. There is a large body of work devoted determining the relationship between the eigenvalues of R and the geometry of R. This subject was initiated by Lord Rayleigh, who conjectured that among all domains of a fixed area, the disc has the lowest possible (first) eigenvalue. This result was proven by Faber and Krahn in the early 20th century, and one can compare it to the well-known fact that among all domains of fixed area, the circle minimizes the length of the boundary. In fact, the two results are equivalent! Moreover, any domain which achieves the lowest eigenvalue must be isometric to the disc, which is referred to as a rigidity theorem. I will discuss some of these ideas, and in particular how they relate to similar results for domains in curved surfaces and Riemannian manifolds.
Gretchen Davis (UCLA)
Implementing the Guidelines from the American Statistical Association in Introductory Statistics
Courses at UCLA
09/27/07
We will illustrate each of the six recommendations with specific examples and activities.
Silvia Heubach (CSULA)
Do you Sudoku?
05/09/07
Are you a Sudoku addict or novice who wants to learn about the game that has become the hottest puzzle? I will give a brief history of the game, talk about strategies to solve a puzzle, and discuss some mathematical questions related to Sudoku puzzles, such as the minimal number of given values needed have a unique solution. We also will look at fun variations from the Sudoku championship.
Nicole Kersting (Lessonlab Research Institute)
Using Video Clips of Mathematics Classroom Instruction
as Item Prompts to measure Teachers
04/25/07
Responding to the scarcity of suitable measures to assess teacher knowledge, this paper reports on a novel assessment approach to measure teacher knowledge of teaching mathematics. Building on findings from research on expertise in cognitive psychology and education, the new approach uses teachers' ability to analyze episodes of teaching as a proxy for their knowledge of teaching. Video clips of classroom instruction, which respondents' were asked to view and then analyze in writing, were used as stimuli (item prompts) to elicit their knowledge of teaching. Teachers' responses to the video-clips were coded and scored according to four dimensions. It was judged whether (1) alternative teaching strategies, (2) an analysis of student thinking, and (3) an analysis of the mathematical content were included in the response, and (4) the overall level of interpretation. A proto-type video-analysis assessment consisting of 10 video clips of eighth grade mathematics instruction was developed and its reliability and criterion-related validity were examined. Respondents' scores were found to be sufficiently reliable ($>.8$). Positive moderate correlations between respondents' scores on the video-analysis assessment with a criterion measure of teachers' mathematical content knowledge for teaching and with expert ratings of their knowledge of teaching, provided initial evidence for the criterion-related validity of the video-analysis assessment. These promising results suggest that teachers access their pedagogical content knowledge when interpreting/analyzing teaching.
Jesse Elliott (CSU Channel Islands)
Integer-Valued Polynomial Rings
04/11/07
A polynomial is integer-valued if it assumes integer values at all of the integers. For example, the polynomial x(x+1)/2 is integer-valued. The set of all integer-valued polynomials forms a ring under addition and multiplication of polynomials. In this talk we will investigate properties of the ring of integer-valued polynomials and various generalizations.
Gizem Karaali (Pomona College)
Algebra for the Quantum World
3/21/07
The term "quantum group" itself is only very loosely defined. However, the theory involving the relevant algebraic (and geometric) objects is fascinating. The main purpose of this talk is to provide a comprehensible exposition of the algebraic theory of quantum groups, though towards the end, a few fuzzy and vague words will be used to explain what I do in my research. Along the way I expect to mention representation theory, Lie algebras, and Hopf algebras, although no previous knowledge of these terms will be necessary to follow the talk. If you know how to multiply matrices, then you have the right prerequisites.
Gary Brookfield (CSULA)
Bubble Math
3/14/07
Bubbles can do really hard math! Soap films always try to minimize their surface areas. In doing so, they can "solve" some really interesting geometry problems - problems that are too hard for mathematicians. In this talk, I will demonstrate what bubbles can do and discuss what mathematicians have been able to prove about bubbles so far. Also on the agenda are square bubbles, bubbles-inside-bubbles, double bubbles, weird foam, and more.
Daniel Kern (University of Nevada, Las Vegas)
Optimal control applied to native-invasive population dynamics
2/28/07
In this talk I will present a two-species competition model with ecological disturbance as the control variable. The original inspiration for this problem came from observing cottonwood-tamarisk population dynamics in the American southwest. Periodic disturbance, such as flooding or fire, can be critical to the life cycle of native species (especially plants); without it, invasive non-native species have an opportunity to displace established ones. A question, then, is whether the restoration of disturbance can restore a native plant as the dominant species - preferably without excessive economic damage to human development.
The model here is a system of differential equations where some of the parameters are control dependent. The cost funcitonal balances economic impact against the desire to maximize the native population. The control is constrained in time so that disturbance can not exist outside of limited time frames that occur periodically. The optimal control is found using Pontryagin's Maximum Principle. Numerical results are presented for several different combinations of parameters.
Rod Freed (CSUDH)
A New Approach to the Solution of Integral Equations
2/14/07
When solving integral equations (such as (1)) we use known k(x,t) and known f(x) to solve for \varphi(x). However, in many situations we seek a solution to an integral equation when k(x,t) is unknown, but when we have observations on \varphip(x): see Corduneanu (1991), Porter and Sterling (1981),
f(x) = \varphi(x) + \int_a^b k(x,t) \varphi(t) dt (1)
Moiseiwitsch (2005), or Tricomi (1985) among many. In this paper we present a method which can be applied, when k(x, t) and f(x) are unknown functions but when we have observations on \varphip(x). Our procedure produces an approximation to \varphi(x) which converges almost everywhere to the actual \varphi(x) as the number of observations on \varphi(x) approaches infinity.
Attila Maroti (University of Southern California)
Covering and (pairwise) generating finite groups
1/31/07
For a finite group G that can be generated by two elements let \mu(G) be the largest positive integer m so that there exists a subset X of G of size m so that every pair of elements in X generates G.
The motivation of this talk comes partially from the following beautiful theorem of Blackburn. For all sufficiently large odd integers n we have \mu(S_n) = 2^(n-1) where S_n is the symmetric group of degree n. The exact value of \mu(S_n) for n even is not known.
Since every finite simple group can be generated by two elements, one may study \mu(G) for finite non-Abelian simple groups G.
In this talk we will investigate \mu(G) and its relationship with the (so-called) covering number of G for G an alternating group, a projective special linear group, or a sporadic simple group.
Alex Stanoyevitch (CSUDH)
A Brief Survey of Genetic
Algorithms
11/15/06
Since antiquity, mathematics has been used to model and better understand biological processes. Evolutionary computation is a field of artificial intelligence that has turned this around: Natural biological processes, centered around Darwin's "survival of the fittest" theory are used to motivate and develop algorithms for finding solutions to difficult mathematical problems. When used in tandem with the ever powerful computing resources that continue to be available, evolutionary computation has proved to be a powerful tool that is poised to play a role of continued importance in the many scientific fields. This talk will focus on the mechanics, implementation, and applications of genetic algorithms, which are prototypes for evolutionary algorithms.
William Murray (CSULB)
Nakayama Automorphisms of Frobenius Algebras
11/01/06
Frobenius algebras were first studied by Frobenius himself a century ago in the context of group representations. Since then, they have been the focus of a rich theory with surprisingly diverse applications to many fields of mathematics and physics, including, most recently, coding theory.
I will introduce Frobenius algebras and symmetric algebras and sketch a few of their key features. I will then connect these properties to the Nakayama automorphism, a distinguished automorphism on the algebra. By showing that the automorphism is independent of the ground field, I will make a case that many of these features are not consequences of linear algebra; instead, they are the result of deeper ring-theoretic properties.
A graduate course in algebra should be enough background to understand this talk.
Matthew Jones (CSUDH)
First-Year Impact of Mathematics
Professional Development on the Teaching of Urban Middle Grades
Students
10/25/06
Professional development for grades 5-8 teachers, comprised of
intensive summer and extensive follow-up work, focused on developing
classrooms that implement the principles of How People Learn
(Bransford, Brown, & Cocking, 2000). Evidence of teacher change was
gathered through observations and interviews. In the first year of
the program, most teachers developed classroom norms that increased
student-student interaction through cooperative groups. Some teachers
went further and developed classroom social and sociomathematical
norms (Yackel & Cobb, 1996) in which teachers shared the mathematical
authority with their students, and students learned to justify their
answers, while others incorporated a few new ideas into traditional
practice. Possible sources of these differences and adjustments made
based on this data in the second year of the program are
discussed.
Serban Raianu (CSUDH)
Does the Jordan Form of a Matrix
have the Maximum Number of Zeros?
10/18/06
The talk is based on joint work with F. Brulois and G. Jennings. We
give an answer to the question in the title and comment on the origin
of the problem, as well as on possible new developments. The talk
should be accessible to upper division Math majors.
Raymond Killgrove (retired from CSULA)
Some Configurations
10/12/06
A paper entitled Self-dual confined configuration with 10
points is briefly summarized. So we begin with definitions. One
finds the definition of configuration as expected. One exposed to
projective planes finds self-dual as expected. Confinement
seldom occurs in the geometric literature; nevertheless, it is a
simple idea. Then we explore a few of these 45 configurations. Related
material includes a favorite theorem of the late Professor Erdö
s. If time permits, we talk about an invariant to separate these 45
configurations. Proofs are presented only in the handout given before
the talk.
Wai Yan Pong (CSUDH)
Sum of Consecutive Integers
09/27/06
What can one say about them?
Gwen Brockman (University of Southern California)
What factors influence achievement in remedial mathematics classes?
05/03/06
This study examined the predictive qualities that cognitive and
motivational variables have on remedial mathematics students at an
urban four-year university in southern California. Specifically, this
study measured the motivational variables of mathematics
self-efficacy, math anxiety, task value, intrinsic and utility values
of an undergraduate education, and the self-regulation of study and
learning strategies: rehearsal, elaboration, metacognition, effort
regulation, time and study environment, and help-seeking, with respect
for the whole sample, as well as for gender and ethnicity. This study
also measured the predictive value of the Entry Level Mathematics exam
score and previous number of high school courses had on achievement. A
sample of 242 first-time freshmen students enrolled in remedial
mathematics participated in the study. The study found self-efficacy,
task value, effort regulation, test anxiety, and utility value to be
statistically significant predictors of achievement in remedial math
courses. Approximately twenty-four percent of the variance can be
accounted for by these five variables. It also found that women
outscored the men and the Latino American ethnic group outscored the
other ethnic subgroups on the final exam.
Chi-Lung Chang (CSUDH)
A Unified View of Number-theoretic Sums
04/26/05
Two types of sums of arithmetic functions seem to dominate the
landscape of number theory, namely, the divisor sums and partial
sums. Our first order of business is to generalize the classical
definitions of arithmetic functions, divisor sums and partial
sums. Indeed, by selecting suitable entry points to these two types of
sums, an interesting kinship emerges between them and they seem to
share a highly common genealogy. We will continue to explore the power
of iteration initiated in our 11/09/05 talk, which in turn, as we have
seen, leads to inversion. As is the case elsewhere in mathematics,
inversion is fundamental to number theory. Actually, inversion, dare I
say, is the heart and soul of analytic number theory. These ideas will
be incorporated into the CSUDH Number Theory Initiative, a new
partnership formed by Wai Yan Pong and myself. The talk is suitable
for 'motivated' upper level students.
Brian Evans (DeVry University)
Student Attitudes, Conceptions, and Achievement in Introductory
Undergraduate College Statistics
04/17/06
The purpose of this study was to measure student attitudes and
conceptions, as well as misconceptions, in introductory undergraduate
college statistics, and to determine the relationship between those
attitudes and conceptions, as well as achievement. This study informs
the practice of teaching statistics by giving insight to statistics
instructors as to what student attitudes exist, as well as what
conceptions and misconceptions students possess. Also, this study
provides a catalyst for changing recognized attitudes and correcting
misconceptions, which in turn will consequently lead to higher student
achievement and a better overall understanding of statistics.
Janet C. Vassilev (UC Riverside)
Can you win the Hat Game?
03/20/06
We will discuss how to play the Hat Game. Without knowing some
discrete math, your chances of winning are not too high. The three
person game gives a good starting point to discuss the probability of
winning with students in the middle grades or higher. To win the n
person game, we will learn the basics about vector spaces over Z2 and
error correcting codes, in particular Hamming Codes, to win the game
with a very high probability.
Martin Flashman (Humboldt State University)
Dynamic Visualization of Calculus I-III
03/01/06
Professor Flashman will explain and use free graphing technology
(Winplot) to illustrate how to visualize concepts related to functions
and derivatives in calculus of one and several variables without
graphs. The treatment is suitable for any introductory treatment of
the concepts. Based on mapping (transformation) figures, this approach
allows students to understand the concepts in an n-dimensional context
without any change in presentation from that given for the ordinary
derivative.
Margaret Beattie (Mount Allison University)
Points on Hyperboloids and Units in an Integral Group Ring
02/22/06
There is a correspondence between the group of units in Z[D4] and
integer points on hyperboloids of the form X2 + Y2 = Z2 + n where n is
a positive integer of the form c(c-1). In this talk, we will discuss
methods for finding integer points on such hyperboloids and discuss
the relationship to units in the integral group ring of the dihedral
group of order 8. This project was the work of third year
undergraduate research student Chester Weatherby at Mount Allison
University in the summer of 2003 building on projects done by Paul
Moore in 1991 and Elizabeth Jenkins in 1993, as well as research
papers by Jespers, Goodaire, Parmenter, Leal on integral group
rings. This talk should be accessible to undergraduate students.
Sean Sather-Wagstaff (CSUDH)
Resolutions of modules over commutative rings
11/30/05
A vector space over the real numbers is a set V equipped with an
addition and scalar multiplication that satisfies certain natural
axioms. Given a ring R, an R-module is defined similarly, except that
the set of scalars is R instead of the real numbers. The R-modules
have become central objects of study in abstract algebra, but they are
usually less simple than vector spaces. For instance, an R-module in
general does not possess a basis. In some situations, this new level
of complexity can be demystified by "resolving" the module, a process
intimately related to the fundamental theorem of finitely generated
abelian groups. In this talk I will give an overview of these ideas,
culminating in David Hilbert's famous Syzygy Theorem, describing the
structure of modules over a polynomial ring. This talk will be
accessible to students and faculty who have taken an undergraduate
course in abstract algebra.
Chi-Lung Chang (CSUDH)
The Power of Iteration
11/09/05
In elementary mathematics, the technique of iteration has been applied
to multiple integration and to summation to good and, sometimes,
surprising advantage. In Analytic Number Theory, however, iteration is
not just a useful side show but serves as the backbone of the entire
body of theory. The purpose of this talk is to take a 'fresh' look at
this very important technique in the context of ANT. The talk will
start with an overview of some examples from elementary
mathematics. The talk should also pave the way for future talks in
ANT. The material should be accessible to our upper level students.
Wai Yan Pong (CSUDH)
Playing games using Cryptography
10/12/05
Ever wonder how those online casinos work? We will go over some simple
examples of how to play games over the internet using
cryptography. The materials are taken from a short course that I gave
to a group of high school students last year so the mathematics
involved is very elementary.
George Jennings (CSUDH)
WeBWorK
09/28/05
WeBWorK is a computer package that serves up homework problems to
students over the web, and grades students' answers so they get
immediate feedback. Problems are already written for several courses:
precalculus, three semesters of calculus, statistics, some linear
algebra, and statistics. It's possible to write your own
problems. WeBWorK was written by math faculty and grad students at the
University of Rochester. It was funded by an NSF grant and is
available for free. I have installed it on our math department server.
It is used at several other places e.g. Ohio State, Arizona State, and
CSU Long Beach. I will demonstrate some of its capabilities & will
invite people who are interested to play with it. You don't need
special equipment, just an internet connection and an ordinary web
browser.
Toukaiddine Petit (University of Antwerp)
Strong rigidity of Lie algebras
08/04/05
We call a finite-dimensional complex Lie algebra L strongly rigid if
its universal enveloping algebra U(L) is rigid as an associative
algebra, i.e. every formal associative deformation is equivalent to
the trivial deformation. In quantum group theory this phenomenon is
well-known to be the case for all complex semisimple Lie algebras. We
show that a strongly rigid Lie algebra has to be rigid as Lie algebra,
and that in addition its second scalar cohomology group has to vanish
(which excludes nilpotent Lie algebras of dimension greater or equal
than two). Moreover, using Kontsevitch's theory of deformation
quantization we show that every polynomial deformation of the linear
Poisson structure on L* which induces a nonzero cohomology class of L
leads to a nontrivial deformation of U(L). Hence every Poisson
structure on a vector space which is zero at some point and whose
linear part is a strongly rigid Lie algebra is therefore formally
linearizable in the sense of A. Weinstein. Finally we provide examples
of rigid Lie algebras which are not strongly rigid, and give a
classification of all strongly rigid Lie algebras up to dimension 6.
Amber Rosin (Cal Poly Pomona)
The Mathematics of Peg Solitaire
04/27/05
We will consider the game peg solitaire, more commonly known as
Hi-Q. The instructions for the game claim that if you can end up with
one peg in the center of the board, you are a perfect Hi-Q genius, but
if you end up with one peg anywhere else on the board, you are merely
outstanding. We will use the context of peg solitaire to introduce
the concept of a group. We will then use two group homomorphisms and
the Klein-4 group, to show that the Hi-Q instructions might be more
accurate if they replaced the word "outstanding" by "oblivious." We
will also investigate different versions of the game on different
boards. Most importantly, there will be M&M's.
Davida Fischman (Cal State University San Bernardino)
The Socratic Method Adapted to the Mathematics Classroom
04/13/05
Zeno (apparently) invented and Socrates developed the dialectic method
of teaching: that is, teaching through questioning. The Socratic
method involves skepticism, discussion, a search for precise
definitions of terms, and follows ideas to their logical conclusion
through rigorous thinking and focused questioning. Can we - and should
we - use this method in our classes today? If not in its entirety, can
we use it partially? Which parts? When? How? In what types of classes?
We will discuss these issues in the context of courses that many of us
teach.
Alex Stanoyevitch (University of Guam)
Logistics of Air Travel
03/23/05
In this talk, we will show how to model a network of airline routes
using a directed graph and the so-called incidence matrix. Many
interesting questions about the network can be answered by performing
appropriate computations with this incidence matrix and other related
matrices. We will show how to answer questions like: What is the most
number of separate flights one would need in order to get from any one
city in the network to a different city? If we call this number the
worst case scenario number for the network, another useful question
would be: If the manger of the network is interested in reducing the
worst case scenario number, could this be done by adding a single new
route to the network? If so, by how much, and which would be the best
route(s) to add to accomplish this reduction? Same question with two
new flights? Although some of the concepts that we touch upon will be
rather sophisticated, the formal prerequisites for this talk will be
quite minimal, and everyone will be able to learn some things from it.
Laura Wallace (Cal State University San Bernardino)
Multiplicative Lattices and Generalizations of Properties in
Commutative Algebra
03/16/05
The set of ideals in a commutative ring is a partially ordered set
ordered by inclusion. The basic properties satisfied by this
structure of the set of ideals lead to the abstract idea of a
multiplicative lattice. This more general concept can be used to
obtain results that can then be applied to structures in other parts
of mathematics. We will consider generalizing the notions of a
principal ideal, a Noetherian ring, and the integral closure of a ring
and look at current research in this area.
Min-Lin Lo (Cal State University San Bernardino)
The Bargmann Transform and Windowed Fourier Localization
03/02/05
Operators which localize in both time and frequency are of interest
for applications in signal analysis. I consider the Gabor-Daubechies
windowed Fourier localization operators L£pw, with ``symbol" (or
``weight function") £p and ``window" w. There is an interesting
connection between these operators and Berezin-Toeplitz operators, via
the Bargmann isometry £]. For ``window'' w a finite linear combination
of Hermite functions and some interesting classes of ``symbols'' £p,
L. A. Coburn conjectured an equivalence of the form
£] L£pw £]-1=C*M£p C=T(I+D)£p,
where T(I+D)£p is a Berezin-Toeplitz operator with symbol (I+D)£p, M£p
is the operator of ``multiplication by £p, C=C(w) is a precisely
determined operator, and D=D(w) is a constant-coefficient linear
differential operator with constant term 0. I settled Coburn's
conjecture affirmatively by obtaining the exact formulas for C and the
linear differential operator D. Calculation for a simple window
function will be demonstrated, and the formulas of C and D for the
conjectured result outlined above will be discussed.
Bogdana Georgieva (Pacific University)
Calculus of Variations - The Mathematics of Optimization
02/18/05
Everything we do, we want to do it as efficiently as possible. For
example, a student strives to get the highest possible grades for
her/his efforts, a company endeavors to maximize its profits, ... We
all optimize our efforts sometimes consciously, sometimes
subconsciously. No one is surprised by such observations. However, not
everyone knows that, in a sense, Nature acts in the same way. Many of
the fundamental laws of physics and geometry follow from a principle
of minimization / maximization of a certain quantity. The branch of
mathematics which studies this principle and its applications is
called the Calculus of Variations. In this talk I will attempt to give
you some idea of the problems which can be solved with the methods of
the Calculus of Variations. I will also talk about some examples for
applications to nonconservative processes, to the nonlinear damped
Klein-Gordon equation, and to the propagation of electromagnetic waves
in conductive medium.
Fairly recently, Gustav Herglotz formulated a variational principle
which is more general than the classical variational principle and
contains the classical variational principle as a special case. This
variational principle is important for a number of reasons. Notably,
it is closely related to contact transformations and it can give a
variational description of nonconservative processes.
Sean Sather-Wagstaff (University of Nebraska)
Vanishing of functions on intersections of algebraic varieties
02/17/05
Let X,Y be subvarieties of the affine space of dimension n over a
field k, and fix a polynomial f in n variables over k. We will
discuss the question of finding bounds on the order of vanishing of f
along the intersection X ¡ä Y in terms of the orders of vanishing of f
along X and Y.
Kurano and Roberts' work on Serre's Positivity Conjecture for
intersection multiplicities provides one such bound as well as our
motivation for investigating this question. We will describe a
sharper, more symmetric bound that follows from our generalization of
Serre's dimension inequality. We will introduce the relevant tools
and ideas from commutative algebra used to understand this problem,
illustrating each one with concrete examples.
Alex Kugushev (CyberGnostics, Inc.)
Presentation of CyberStats, a Web-driven Introduction to Statistics
02/16/05
CyberStats is a "living" electronic textbook. Students internalize
statistical concepts by interacting with hundreds of simulations and
calculations and immediate-feedback practice items. CyberStats is
conceptual, not computational software (though it incorporates a
computational component). It provides a learning opportunity that
cannot be delivered in print and is equally effective for on-campus as
for distance learning courses. The presentation will consist of an
online demonstration of elements comprising CyberStats. The presenter
will cover both instructional and learning elements. The learning
elements will be presented by showing how a typical CyberStats Unit
causes a student to interact with concepts and achieve mastery
thereof. It will also cover tutorial aspects of CyberStats. The
instructional elements will show the assistance available to the
instructor: an integrated course management system, testing
facilities, with a test bank and grade book allowing automatic test
grading, full reports on all students' activities, a variety of
communication devices, tips on how to teach successfully with the Web,
and other useful items.
Sergei Chmutov (Ohio State University)
The Kontsevich Integral
02/11/05
The Kontsevich integral is an invariant of knots in 3-space. Sometimes
it is also called universal finite type invariant because it contains
the information of all finite type (Vassiliev) knot invariants. The
Kontsevich integral is represented as an infinite series of terms
whose coefficients are multidimensional integrals. In the simplest
situation the first nontrivial coefficient is a very special double
integral that can be understood by undergraduate students taking
multivariable calculus. I will start the talk with this example and
try to keep the level accessible for undergraduate students for as
long as possible. At the end I am going to explain the Hopf algebra
structure on chord diagrams which is highly important for finite type
invariants.
Deborah Koslover (UC Irvine)
Bloch Electron in a Perpendicular Magnetic Field
02/08/05
We study a model of an electron on a two dimensional crystal lattice
subjected to a perpendicular magnetic field. We determine how the
structure and spacing of the lattice as well as the strength of the
magnetic field affect the motion and allowed energy levels of the
electron.
Miriam Nuno (Cornell University)
A Mathematical Model of Influenza: The Role of Cross-Immunity and
Host-Isolation
02/03/05
Influenza virus infects 5% to 20% of the US population
yearly. Approximately 36,000 individuals succumb to the disease each
year. Understanding the mechanisms that support the periodic outbreaks
(sustained oscillations) of multiple strains has been a topic of great
interest to researchers. Herd-immunity, cross-immunity and
age-structure are among the factors that have been shown to support
strain coexistence and/or disease oscillations. In this study, we put
two influenza strains under various levels of (interference)
competition. We establish that cross-immunity and host isolation lead
to periodic epidemic outbreaks (sustained oscillations) in this
multi-strain system. We compute the basic reproductive number for each
strain independently, as well as for the full system and show that
when the basic reproductive number of both strains is less than 1, the
disease dies out. Sub-threshold coexistence driven by cross-immunity
is possible even when the basic reproductive number of one strain is
below one. Conditions that guarantee a winning type or coexistence are
established in general. Oscillatory coexistence is established via
Hopf-bifurcation theory and numerical simulations using realistic
parameter values.
Freddy Van Oystaeyen (University of Antwerp)
Introduction to Non-commutative Geometry
02/02/05
Stefaan Cenepeel (Free University Brussels ¡V VUB)
The Brauer Group and Corings
02/02/05