Ioana Mihaila (Cal Poly Pomona)
The Art of Multiplicative Periodic Functions on C\{0}
12/01/04
Periodic Functions are a common occurrence in mathematics, but on the
punctured complex plane we can actually consider multiplicative
periodic functions. Can these functions be explicitly constructed, and
are they useful?
Jennifer Switkes (Cal Poly Pomona)
On the Means of Deterministic and Stochastic Populations
11/10/04
Familiar results for differential equation
birth-death-immigration-emigration population models are compared with
the expected population sizes predicted by related stochastic
models. Although under standard assumptions the results are not
equivalent, by removing certain restrictive modeling assumptions the
two types of models can be reconciled.
Terry Millar (University of Wisconsin Madison)
Logic and Mathematics
10/28/04
Terry Millar will talk about the role of logic in mathematics and will
give two examples relevant to education. The first example will be
from propositional logic and will be from a 4-5th grade class. The
second example will deal with the definition of continuity and the use
of infinitesimals. For both examples he will mention the complete and
soundness theorems - for propositional and predicate logic,
respectively. He also will mention a useful consequence - the
compactness theorem - that can be used to introduce infinitesimals in
a rigorous manner.
Mona Mocanasu (UCLA)
On the Milnor Conjecture
10/27/04
In 2002 V. Voevodsky was awarded the Fields Medal for his development
of a new homotopy and cohomology theory for algebraic schemes; a
consequence of this construction is the proof of the Milnor
Conjecture, a problem that awaited a solution for twenty-six
years. The aim of this talk is to give a description of the
conjecture, explain how it works in a couple of particular cases, and
give an outline of Voevodsky¡¦s proof.
Patrick Callahan (University of California Office of the President)
Mathematics Teachers: Supply and Demand in California; Looking for
Mathematics in the Classroom
10/13/04
Mathematics Teachers: Supply and Demand in California: Last year
2,668,093 students took 92,639 mathematics courses taught by 24,799
teachers in California. Who is teaching what? Where is the greatest
demand? We will take a quick look at recent data and trends in
California mathematics classes and teachers. Looking for Mathematics
in the Classroom: How do you know what mathematics is actually
happening in the classroom, if any? What is the quality of the
mathematics? What factors are helping and what factors are impeding
student progress? We will look at some short video clips and look
carefully for evidence. We will then discuss the implications for the
content and nature of mathematics courses for pre-service teachers.
Stan Yoshinobu (CSUDH)
Discovery Based Learning: How and Why I teach Math without a
Textbook
9/29/04
Discovery Based Learning is a teaching method that gets students to do
research at their level. The objective of Discovery Based Learning is
to give students experiences that parallel what research
mathematicians do, which is prove theorems. In this talk, I will
discuss how DBL is implemented for different math courses, with the
emphasis on Advanced Analysis. I will also give a survey of some
evidence that shows why DBL is appropriate, and give examples of how
some of the essential elements can be used in almost any math course.
Susan Montgomery (University of Southern California)
On the Classification of Semisimple Hopf Algebras
09/23/04
Hopf algebras appear as invariants in various other parts of
mathematics, such as topology (in knot theory) and mathematical
physics (in conformal field theory). Thus the classification of Hopf
algebras is of some interest outside algebra. At least for
(finite-dimensional) semisimple Hopf algebras over the complex
numbers, many of the basic results resemble classical facts about
finite groups, with the order of the group being replaced by the
dimension of the Hopf algebra. For example, the dimension of a Hopf
subalgebra always divides the dimension of the Hopf algebra, the
analog of Lagrange's theorem. We survey these results, and then
discuss some cases when the Hopf algebras do not behave like groups.
Serban Raianu (CSUDH)
Calculus and planimeters
09/15/04
According to the Merriam-Webster dictionary, a planimeter is ¡§an
instrument for measuring the area of a plane figure by tracing its
boundary line¡¨. Even without knowing how a planimeter works, it is
clear from the definition that the idea behind it is that one can
compute the area of a figure just by ¡§walking¡¨ on the boundary. For
someone who has taken calculus, this immediately suggests Green's
Theorem. The aim of this talk is to clarify why this principle
works. We do this by using points of view from linear algebra to
elementary plane geometry in order to obtain an intuitive
justification for Green's Theorem. The talk is based on joint work
with Paul Davis.
George Jennings (CSUDH)
Introduction to Mathematica
04/28/04
Mathematica is a very elaborate high level programming
package/language with tools that enable users to simplify algebraic
expressions, solve systems of equations, integrate, differentiate,
solve systems of differential equations, create 2D and 3D graphics,
create and play sounds, create and play animations, format documents
using standard mathematical notations, write programs, and a whole
host of other things. I got interested in it when I wanted to create
different kinds of map projections using real geographic data (yes, it
contains that data too). I will introduce you to some Mathematica
basics and we will try out some things on workstations in the WH C155
computer lab. There are plenty of seats so everyone should be able to
run Mathematica for themselves.
Robert Guralnick (University of Southern California)
A Probabilistic Approach to Generation and Properties of Finite Groups
04/14/04
It was finally shown in 1984 that every finite simple group can be
generated by a pair of elements. The initial proof of this result was
obtained by exhibiting such a pair for every simple group. In the
last 20 years, a new approach has been used -- looking at the size of
the set of pairs of elements that do generate. We will also discuss
related questions about determining properties of groups by
considering subgroups generated by pairs of elements.
Arthur Benjamin (Harvey Mudd College)
Counting on Determinants
03/17/04
We demonstrate how determinants solve many interesting combinatorial
problems. Determinants count non-intersecting lattice paths, spanning
trees, and permutations with specified descent points. Elegant proofs
of these results are based on the definition of the determinant and
occasionally the principle of inclusion-exclusion. This talk is based
on joint work with Naiomi Cameron of Occidental College.
David E. Radford (University of Illinois at Chicago)
Knots and Algebras
02/11/04
There are many ways of associating numbers, or other algebraic
objects, to knots in order to distinguish different knots. We will
explore a very intuitive way of doing this based on a "bead sliding"
algorithm due to Kauffman. Plenty of examples will be given to
illustrate how the algorithm works.
Tom Love (CSUDH)
Hidden Symmetries and the Internal Structure of Elementary Particles
11/12/03
Some manifolds have hidden symmetries. Exploring those symmetries
leads to a new mathematical model of elementary particles in terms of
differential operators and the possibility of new conservation laws.
Our results show that matrix methods are inadequate for the study of
elementary particles.
Piotr Kowalski (University of Illinois at Urbana-Champaign)
Algebraic Groups With An Extra Structure
10/29/03
This is joint work with Anand Pillay. We work over a field with some
extra structure, e.g. a derivation. Then we consider a category
expanding the category of algebraic varieties, where an extra
structure on a variety is related to the extra structure on the
field. These categories were used by Anand Pillay to obtain easy
proofs of some diophantine results. We will show that structures
coming from groups in these categories enjoy certain logical property
(quantifier elimination).
Wai Yan Pong (CSUDH)
More Fair Games
09/17/03
Let n >=2 be an integer. The n-color matching game is a 2-person game
in which the players, called M and N, each draw a ball at random from
a bag containing balls of n different colors. M wins the game if the
balls drawn are of the same color, otherwise N wins. A game is fair if
both players have the same chance to win. We are interested in finding
Fn, the set of n-color fair games and the set of numbers. In
particular, we will give a description of F3. This is joint work with
Jacqueline Barab.
Stefaan Caenepeel (Free University Brussels)
A survey of Galois corings
07/17/03
We introduce Galois corings and give a survey of properties that have
been obtained so far. The definition is motivated using descent
theory, and we show that classical Galois theory, Hopf-Galois theory,
and coalgebra Galois theory can be obtained as special cases.
Frank Miles (CSUDH)
Homeomorphisms of Compact Totally Disconnected Metric Spaces
05/07/03
We define the limit index i(x) of a point x in a compact metric
space. (Roughly: Isolated points have index 0, limit points have index
1, limit points of limit points have index 2, and so on.) We then
consider homeomorphisms f of a compact, totally disconnected metric
space into itself in terms of in terms of how i(x) and i(f (x)) are
related. This leads to a theorem that characterizes the uniform
closure of the set of all homeomorphisms of a compact totally
disconnected metric space into itself. The results to be described
appear in Proc. AMS 84 (1982), 264-266. Prerequisites: basic facts
about limit points, compactness, metric spaces, and uniform
convergence.
Yontha Ath (CSUDH)
Another Method on Computing MTBF for a k-out-n: G Repairable System
04/23/03
It is often necessary to calculate MTBF (mean time between failures)
as quickly as possible in order to make timely design decisions. An
important system for which such calculation must be made is a k-out-of
n: G repairable system with unlimited repair and exponential
interfailure and repair times at the unit level. Although a general
formula is known, but it is not easily remembered nor derived. In this
talk, we would like to present a new method for deriving MTBF in this
situation that is easily reproduced quickly by remembering a few
simple concepts.
Michael W. Leonard (UC San Diego)
Limited-Memory Quasi-Newton Methods: Recent Developments
03/26/03
Problems from all areas of science and engineering can be posed as
optimization problems. An optimization problem involves a set of
independent variables, and often includes constraints or restrictions
that define acceptable values of the variables. The solution of an
optimization problem is a set of allowed values of the variables for
which some objective function achieves its maximum or minimum
value. Quasi-Newton methods for optimization define an approximate
Hessian that incorporates curvature information accumulated over a
number of iterations. Characterization of the subspace on which
curvature is known leads to the definition of limited-memory
reduced-Hessian quasi-Newton methods, that require less storage and
work than their conventional counterparts. We will discuss the current
theoretical developments in this area, and present the most recent
numerical results.
Florence Mihaela Singer (Research Visiting Scholar, Harvard University
Graduate School of Education)
03/12/03
Dorin Popescu (MSRI Berkeley and University of Bucharest)
Modules over Hypersurface Rings
02/26/03
It is well known that a finitely generated abelian group is a direct
sum of copies of Z and Z/(pk), for positive integers k and prime
numbers p. It is also well known that given a finite group G we may
describe all the finitely generated modules over the group C-algebra
C[G] using the so called representation theory. Here we present some
descriptions of finitely generated modules over hypersurface rings of
type K[[X_1,...,X_n]]/(f), where K is a field and f is a
non-invertible, non-zero formal power series.
David Marker (University of Illinois at Chicago)
Algebraic Nonstandard Models of Exponentiation
01/23/03
We outline an algebraic construction of nonstandard models of the real
numbers with exponentiation. These nonstandard models provide useful
asymptotic information about real functions. We will show how they can
be used to answer a question of Hardy's.
Serban Raianu (CSUDH)
An (in)equality with a long mathematical history
12/04/02
This inequality, or the equality associated to it, appears in the
classification of Dynkin diagrams (and therefore in the classification
of Coxeter graphs and complex semisimple Lie algebras), but also in
groups acting on spheres and elementary plane geometry. No
prerequisites are necessary.
Jackie Barab (CSUDH)
The Match Game
11/13/02
Seldom has a problem in elementary mathematics led to more beautiful
interconnections. The main result of analyzing this family of simple,
probabilistic games is one pretty theorem and three different proofs.
Stan Yoshinobu (CSUDH)
The Mathematics of Sound and Tuning Musical Instruments
10/30/02
In this talk I will discuss the Mathematics behind tuning musical
instruments by discussing equal temperament and Pythagorean tuning. I
will also explain why one can tell the difference between different
sounds, and why some notes sound better when played together than
others. This talk is intended for a general audience, and no special
mathematical or musical background is required.
Rod Freed (CSUDH)
Inferring Expectations with the Kalman Filters
10/02/02
Behavior is frequently influenced or driven by expectations. In his
talk, Rod would like to demonstrate how Kalman Filters can be used to
infer expectations from observed behavior in Economics.
Wai Yan Pong (CSUDH)
A Cute Application of Model Theory
9/18/02
The talk will be an invitation to Model Theory. I will give a very
brief introduction to the subject and give an interesting proof to the
following theorem of Ax (and later by A. Borel): If a polynomial map
from the complex n-space to itself is injective then it is surjective
as well.
Silvia Heubach (California State University, Los Angeles)
Counting Compositions: Patterns and Combinatorial Proofs
4/24/02
A composition of n is an ordered sequence of
positive integers whose sum is n. A palindromic composition or
palindrome of n is a composition that reads the same from left to
right as from right to left. We will give methods to create all
compositions and palindromes of n and use these methods to derive
properties and count characteristics of the compositions and
palindromes (total number, number of rises, levels and drops, number
of + signs). We will also count how often a particular integer k
occurs among all the compositions and palindromes of n, respectively,
and look at patterns among these values and their combinatorial
proofs. This talk should be accessible to undergraduates who have
taken a course in Discrete Mathematics.