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Mathematics Awareness Month
Public Lecture Series
In an ongoing effort to increase public appreciation for the importance
of mathematics, Cornell's Department of Mathematics sponsors an annual
public lecture as part of national Mathematics
Awareness Month.
2008 Lecture — What A Difference A Procedure Makes: Scoring
Rules in Politics and Sports, by Michael
A. Jones
See poster for scheduling details.
An election outcome depends not only on how the electorate cast ballots,
but also on the procedure used to tally votes. That is, the same
votes can result in different election outcomes when different procedures
are used. This is true even on the subset of election procedures
known as scoring rules or voting vectors. For a fixed set of ballots,
convexity and linear algebra are used to determine what outcomes are
possible, and whether or not the outcome changes, under all scoring rules,
as well as how the number of outcomes grows in relation to the number
of candidates on the ballot. Further, when complete information
about the electorate’s preferences is unknown, it is still possible
to determine potential election outcomes under different scoring rules. Examples
in the talk will use data from U.S. Presidential elections, coaches’ rankings
of NCAA football teams, journalists’ votes to determine the MVPs
of the American and National Leagues of Major League Baseball, and scorecards
and scoring rules used on the Professional Golfers Association tour.
2007 Lecture — Unraveling
the Knot of our Sensory Experience, by David
Field
In the last 50 years, we have gained remarkable insights into the machinery
of the brain. Recordings from single neurons in different individuals
and different species have demonstrated what appear to be general rules
for representing the natural environment. Is there a general theory of
information processing that applies to biological systems? In this talk
we will look at some of the new approaches to understanding neural processing
by relating the mathematical structure of the natural world with the
mapping of that structure by neural systems. It will be argued that not
only are new mathematical tools (e.g., wavelets etc) providing insights
but that new approaches to information processing can be gained through
the understanding of biological systems.
2006 Lecture —
Keeping and Sharing Secrets, by Graeme Bailey
It's easy to keep a secret if it never needs to be shared, but in the
real world the value of information depends on the ability to control
and authenticate it. Of course, bad guys exist, and shifting allegiances
means that it's hard to know who can be trusted.
This talk will be a quick introduction to some of the mathematical ideas
used in sharing secrets in both good and hostile communities and ways
to authenticate. We'll put all this in a realistic context, and will
also showcase some recent work done by some Cornell undergraduates in
this area. The talk is aimed at a non-technical audience — essentially
the ability to think is the only pre-requisite!
2005 Lecture —
Order and Chaos in the Solar System, by John
Hubbard
In keeping with the 2005
theme, Mathematics and the Cosmos, Professor
Hubbard’s address explored Order and Chaos in the Solar System.
He began with a look at the history of our understanding of the solar system,
marveling at the work of Kepler and Newton before posing the troubling question
of whether the orbits of the planets are stable. He entertained the audience
with a computer simulation of several planetary systems that appeared stable
for a while, before cataclysmic events sent planets careening through space.
Hubbard concluded his address with remarks about the work of Kolmogorov, who
showed that our solar system might be stable, offering comfort to some.
The tendency to synchronize is one of the most mysterious and pervasive
drives in all of nature. Every night along the tidal rivers of Malaysia,
thousands of fireflies flash in silent, hypnotic unison; the moon spins
in perfect resonance with its orbit around the Earth; the intense coherence
of a laser comes from trillions of atoms pulsing together. Steven Strogatz
conveyed the excitement of this new field in a lecture aimed at a general
audience.
2002 Lecture — Using
a Computer to do Rigorous Mathematics, by Warwick Tucker
It is widely understood that mathematics had an important role in the
development of computers, and computers have had an enormous influence
on all areas of life and learning. But the role of computers in mathematics
itself is a much more subtle and controversial issue.
One group of researchers considers all problems to be solvable, given
a sufficiently large and fast computer. The other group claims that computers
are inherently inexact, and that virtually no results produced by machines
are to be trusted.
In this talk, we will show that there is a narrow (but non-empty!) region
that fits in between these two schools of thought. The main underlying
idea is to NOT try to model the real numbers using a computer's floating
point numbers, but rather to enclose entire sets of real numbers in small
intervals with well-defined endpoints. As it turns out, computers handle
this situation rather well, allowing theorems to be proven with mathematical
rigour.
No previous knowledge of computer arithmetic is assumed, nor is any
mathematics beyond pre-calculus needed to understand this talk.
Warwick Tucker received his PhD in 1998 from Uppsala University for a
thesis in which he proved for the first time that the "Lorenz attractor,"
a famous mathematical model in meteorology, one of the first examples
of "chaos," actually exists. He was awarded the Wallenberg Prize
in 2001 by the Swedish Mathematical Society for this work. He introduced
new methods for using a computer in his thesis, and he will explain these
ideas in his talk.
2001 Lecture — How
to Unfold a Carpenter's Rule in the Plane, by
Robert Connelly
The talk considered a planar linkage, a polygon consisting
of rigid bars connected together with hinges at their ends. (This is
the ruler that a carpenter folds up in a pocket.) Connelly and his coauthors
proved that the linkage can be continuously moved so that it becomes
straight and no bars cross, while preserving the bar lengths. Furthermore,
the motion is smooth, does not decrease the distance between any pair
of hinges and preserves any symmetry present in the initial configuration.
The problem has a long history, and several people have worked on this
and related problems. This is joint work with Erik Demaine and Guenter
Rote.
2000 Lecture — Chaos,
Complication and Control, by
John Hubbard
Beginning with the example of the novice skier, who achieves stability
by planting the skis wide but then discovers she has no control, and leading
through more elaborate mathematical systems described by differential
equations, Professor Hubbard showed how control is attainable only by
sacrificing stability and skirting the edges of chaos. The talk was filled
with amusing metaphors (such as the three philanthropists who compete
to bring coffee, tea and wine to the doorstep of all the inhabitants of
an unfortunate island) and beautifully illustrated by the output of computer
simulations.
Last modified:April 1, 2008 |
