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Spring 2004
UConn Math Club
Speaker:
Time: Wednesday, February 4, 2004 at 4:30 pm
Place: MSB 117 (UConn - Storrs)
Abstract: The UConn Math Club is starting up again, this week.
On Wednesday, there will be an organizational meeting
in MSB 117 at 4:30. In the following weeks, some of the scheduled talks are
K. Conrad: Relativistic Addition and Real Addition
D. Pollack (Wesleyan): An Introduction to Elliptic Curves
W. Wickless: The Impossibility of Trisecting Angles
For general information, see the webpage
http://www.math.uconn.edu/~kconrad/mathclub.
Send email to Prof. Conrad (the address
is at the website) if you are interested in attending, so enough
pizza and soda is ordered.
Comments: Free Refreshments
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UConn Math Club
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, February 11, 2004 at 5:00 pm
Place: MSB 117 (UConn - Storrs)
Abstract: In classical physics, velocities add
like real numbers. For instance,
if you are traveling on an open-air platform moving at
10 mph, and throw a baseball at 50 mph in the direction of motion,
then an observer on the ground sees the ball move at 10+50 = 60 mph.
However, according to the (special) theory of relativity, no
particle travels faster than the speed of light, c.
If your platform is moving at (3/4)c and
you throw the ball at (1/2)c in the direction
of motion, then it appears to an observer on the
ground that the ball's velocity is
not (3/4)c + (1/2)c = (5/4)c,
which exceeds the speed of light, but instead
(10/11)c.
We can think about these two situations
from a mathematical point of view, without
worrying about the physics involved. They describe two
different types of addition, one on R using
ordinary addition, and the other on the interval
(-c,c) using relativistic addition.
It turns out that
there is a "relativistic logarithm,"
that converts relativistic addition on (-c,c)
into ordinary addition on R.
This means relativistic addition is just ordinary addition in
disguise, even though they may seem quite different.
We will explain what it means for any interval (a,b) to
have an "addition law,"
and then prove that all such addition laws are just a disguised form
of ordinary addition on R. The proof involves
an interesting mix of calculus and algebra. No physics will be assumed or
used.
Comments: Free Refreshments
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UConn Math Club
Speaker: Bill Wickless (University of Connecticut)
Time: Wednesday, February 25, 2004 at 5:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Everyone who has been around a math department awhile
has seen an ominous bulging manila envelope
arrive in the department mail. On the outside of the envelope
is written something like "Do you care about the truth?"
Inside is a 256-step procedure for trisecting a general angle,
using only compass and straightedge. The author wants somebody
to spend time to check through this, in order to verify that nothing is
wrong.
I will explain why it's not necessary to check through this. More
precisely, what do we mean when we say one cannot trisect a general
angle with compass and straightedge? This question leads to another
interesting topic, the notion of a constructible number. Everyone
is welcome. No special background is needed for the talk.
Comments: Free Refreshments
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UConn Math Club
Speaker: David Pollack (Wesleyan)
Time: Wednesday, March 3, 2004 at 5:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: What are all rational number
solutions to the equation
y2 = x3 + 17? An easy rational
solution is (x,y) = (2,5).
Other rational solutions are less apparent, such as (-64/25,59/125)
and (5023/3249,-842480/185193)! How were they found?
The graph of an equation like
y2 = x3 + 17 is
called an elliptic curve, and such curves are a central topic in
number theory. In recent years elliptic curves played a crucial role in
the proof of Fermat's Last Theorem, and they are of great use in
cryptography. We'll give an overview of elliptic curves, discussing
some of their main properties and ending with several open questions.
Comments: Free Refreshments
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UConn Math Club
Speaker: Alex Russell (University of Connecticut)
Time: Wednesday, March 17, 2004 at 5:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We will introduce some basic notions of
modern provably secure cryptography, including
one-way functions and pseudorandom generators.
Applications to natural cryptographic problems
such as encryption and secure function computation
will be discussed. No knowledge of cryptography
is assumed.
Comments: Free Refreshments
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UConn Math Club
Speaker: Joe McKenna (University of Connecticut)
Time: Wednesday, March 24, 2004 at 5:00 pm
Place: MSB 311 (UConn - Storrs)
Abstract: This week's talk will use some hi-tech equipment, so it is in MSB 311 instead of
our usual meeting place.
Comments: Free Refreshments
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UConn Math Club
Speaker: Ralph Kaufmann (Oklahoma State Univ.)
Time: Tuesday, March 30, 2004 at 12:30 am
Place: MSB 118 (UConn - Storrs)
Abstract: The branch of mathematics called topology has its origin in the observation that
certain geometric properties of a figure (e.g., whether it is bounded or has a hole)
are unchanged by bending or stretching. Professor Kaufmann will explain some of the basic ideas of this beautiful area of mathematics.
Comments: Free Refreshments
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UConn Math Club
Speaker: Obi Rej (University of Connecticut)
Time: Wednesday, March 31, 2004 at 5:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Quaternions were introduced in 1843 by the Irish mathematician Hamilton.
They are numbers of the form a+bi+cj+dk where a,b,c,d
are real numbers. They generalize complex numbers, with a more
interesting rule of multiplication. Quaternionic multiplication
can be seen as a precursor to the vector cross product in
R3.
In this talk, I will describe the algebra of quaternions and an
application to rotations in three-dimensional space. We will also
see the connection between quaternions and
more familiar algebraic objects such as matrices, as well as
their role in studying spins of elementary particles such as the electron.
En route, we will encounter an extraordinary historical saga of ambition,
obscurity, and resurgence which will exemplify the very human face of
mathematical discovery.
Comments: Free Refreshments
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UConn Math Club
Speaker: Reed Solomon (University of Connecticut)
Time: Wednesday, April 7, 2004 at 5:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The concept of infinity has intrigued and puzzled mathematicians
for centuries. Near the end of the 19-th century,
Cantor made the shocking discover that not all infinite sets have
the same size. Shortly afterwards, Russell found a paradox in Frege's
system of set theory and showed that mathematicians did not understand
the idea of a "set" as well as they thought they did. Together,
these discoveries helped launch the modern study of set theory and
of infinite sets.
In this talk, we will discuss these ideas and examine related
questions. How can we measure the size of a set? How can one
infinite set be bigger than another infinite set? How big is the
set of real numbers? This last question is one that is still debated
today!
Comments: Free Refreshments
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UConn Math Club
Speaker: Davar Khoshnevisan (University of Utah)
Time: Thursday, April 15, 2004 at 5:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Randomness affects all of us every day. So perhaps we should
ask ourselves, "What does it mean to be random?" I will
describe two short stories that might convince you that
the honest answer is "No one really knows." The only formal
prerequisite to this talk is a term of freshman calculus.
Act 1: It may be chaotic, but it's surely not random!
Act 2: Is that a normal number in your hands?
Comments: Free Refreshments
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UConn Math Club
Speaker: Tom Weston (Amherst College)
Time: Wednesday, April 21, 2004 at 5:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The Banach−Tarski paradox is the suprising fact that
any three-dimensional solid object can be "cut" into finitely
many pieces which can be rearranged to form any other
solid object. For example, a pea can be cut up and rearranged
to form the sun. In this talk, we will discuss the proof of the
Banach−Tarski paradox and especially the role of the infamous
"axiom of choice." No specific mathematical background is required.
Comments: Free Refreshments
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University of Connecticut | 
