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is a list of the talks that they can give.
1. The Linear Algebra Bound in Combinatorics and Geometry.
This talk uses the notion of dimension in a vector space to
provide elegant upper bound proofs for various problems
in combinatorics and geometry. The talk is probably
appropriate for advanced undergraduates.
Surreal Numbers were created by John Conway
and named by Donald Knuth. The purpose of this
presentation is to introduce Surreal Numbers
through an activity workshop. Previous knowledge
of Surreal Numbers would probably hinder the
effectiveness of the workshop, however those with
previous knowledge of Surreal Numbers are still
strongly invited to attend.
One of the most spectacular of all theorems, Gauss-
Bonnet relates the total curvature of a closed surface
to the number of holes in the surface. Accessible
to students.
2. Differential Forms in Advanced Calculus
Differential forms give a unified approach to div, grad,
curl and other imponderables of advanced calculus.
Accessible to students.
Our experience with implementing the Purdue Project
is that students resist the program that includes
working with computers in small groups, but that those
who stick with it learn to think mathematically.
4. Teaching College Algebra from an Environmental Text
Students come to class and stay awake when college
algebra is taught using the text Earth Algebra by
Schaufele and Zumoff. The students work in small
groups using graphing calculators to model the
factors contributing to global warming.
One can consider dynamical systems as symbolic
processes. We will introduce the notion of entropy
and compute it for some simple examples of
symbolic systems and discuss the relationship
to Shannon's approach to language and information
. 2. Pre-Image Entropy of Symbolic Systems
We introduce a notion of entropy for non-invertible
dynamical systems. The class of objects which we
consider are one-sided symbolic dynamical systems.
We define the pre-image entropy of such a system,
which measures in a sense the exponential growth
rate of the ''past.'' We will provide examples of such
systems (mathematical in nature) and give an indication
of how one would compute the pre-image entropy of
such systems.
1. Putting a Rather Plain Tiling Into Perspective.
Renaissance ideas of Viator, Leonardo (the Construzione
Legittima), Alberti and de Vries on perspective will be
developed in order to give an informal and conceptual
proof of the Fundamental Theorem of Plane Projective
Geometry (all quadrilaterals are perspectively equivalent).
There is an interesting analogy between the Renaissance
ideas behind this proof and the more modern Circle Limits of
Coxeter and Escher.
2. Emulating the RSA Public-Key Cryptosystem with a Spreadsheet.
Spreadsheet software provides a very practical way
to integrate computers into an elementary number theory
classroom. Spreadsheets which students can design as a
typical course in elementary number theory progress and
which culminate in the entire class jointly designing a
spreadsheet which emulates an RSA network will be described.
This talk will use a computer to create simulations of
vibrating strings, of the evolution of temperature in a thin
wire, and of electron diffraction. Computer simulations
bring to life many of the classical topics of Fourier analysis.
2. Wavelet Analysis vs. Fourier Analysis
This talk will give an introduction to the methods of wavelet
analysis and compare its methods with the classical ones of
Fourier analysis. Applications to noise removal and compression
of signals will be described.