|
|
Fall 2004
UConn Math Club
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, September 15, 2004 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: A number is called irrational when it can't be expressed as
a ratio of integers (equivalently, the decimal expansion is not
periodic). The ancient Greeks proved, for instance, that
the square root of 2 is irrational. The Greek geometers also
were familiar with the number
π = 3.14159265358979323846264338327950288419716939937510582...,
but they never found a proof that π is irrational.
Of course, you might think it is obvious
π should be irrational. But how do you really prove it?
Come to the first meeting of the UConn math club this year
and find out!
To prove π is irrational, it turns out that
the main tool is not geometry, but calculus.
The method we use, which involves some
definite integrals, will look very mysterious. To put the
idea of that proof in perspective, we will also
use definite integrals to prove
the irrationality of
e and its fractional powers (such as e1/2 and
e7/3,
but excluding the single case of e0=1).
If time permits, we will see how the irrationality proof for
powers of e is
related to the irrationality proof
for π through the use of complex numbers.
Comments: Free Refreshments
|
UConn Math Club
Speaker: Sasha Teplyaev (University of Connecticut)
Time: Wednesday, September 22, 2004 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: I will explain in very basic terms how one can develop analysis
on some relatively simple fractals such as the Sierpinski gasket (triangle).
It is related to such diverse topics as probability and electrical networks,
and the exact self-similarity of the fractal plays an important role.
In particular, I will highlight similarities and differences of
such analysis and the familiar one-dimensional Calculus.
Comments: Free Refreshments
|
UConn Math Club
Speaker: Steve Conrad (Math Leagues)
Time: Wednesday, September 29, 2004 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: When you test convergence or divergence of an infinite series (with
positive terms), are you unsure which convergence test is
the right one to apply? I'll show you how to use the
highly intuitive concept of rates of growth to do all the hard work!
After that, it's easy to use one test, the comparison test, to check
convergence or divergence of most series of positive terms.
This approach is fast, fun, easy, elementary,
and the most mathematically satisfying way to
do most convergence testing of series in calculus.
Comments: Free Refreshments
|
UConn Math Club
Speaker: Reed Solomon (University of Connecticut)
Time: Wednesday, October 6, 2004 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Does mathematics contain contradictions?
That is, might there be a result that could be
proved true by one mathematician
and could be proved false by another?
If so, mathematics would be in deep trouble!
Hoping to show this situation was impossible,
Hilbert asked (in the early 20-th century) whether there is a formal system
strong enough to encompass all of mathematics
and which could be proved to contain no contradictions.
Around 1930, Goedel showed Hilbert's goal could not be realized.
We will discuss Goedel's "Incompleteness" theorems
and explain how they relate to Hilbert's program.
Comments: Free Refreshments
|
UConn Math Club
Speaker: Chuck Vinsonhaler (University of Connecticut)
Time: Wednesday, October 13, 2004 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: SET is a card game invented by a population
geneticist, Marsha Jean Falco, in 1974.
Though simple to learn and play, the game has a rich
mathematical structure linking it to combinatorics,
geometry and the theory of error-correcting codes.
After learning the game, we will examine some of the
mathematics. No background is necessary, although
familiarity with addition and multiplication modulo
3 will be helpful.
Comments: Free Refreshments
|
UConn Math Club
Speaker: Michael Korman (University of Connecticut)
Time: Wednesday, October 20, 2004 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: As we approach this year's presidential election,
interest in electronic voting methods has risen.
Although they will not be used in this year's
elections, voting systems based on elegant
cryptography foretell the future of e-voting. Still,
electronic systems pose many problems:
How do we ensure that votes are tallied properly?
How can we guarantee that the privacy of each voter is maintained?
In this talk, we will discuss how simple mathematical
devices can be used to provide such services.
Comments: Free Refreshments
|
UConn Math Club
Speaker: Jim Carlson (Clay Math Institute)
Time: Wednesday, October 27, 2004 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Two Stanford graduate students, Sergei Brin and Larry Page,
developed a way of searching the World Wide Web that
was far more effective than the methods used by other
search engines. Thus Google was born. Their method
was based on an elegant piece of mathematics which we
will explain.
Comments: Free Refreshments
Additional Comments: USG Funded
|
UConn Math Club
Speaker: Farshid Hajir (University of Massachusetts, Amherst)
Time: Wednesday, November 3, 2004 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Number theory is rampant with easily stated conjectures
that remain elusive for hundreds of years. A conjecture
of this flavor was formulated comparatively recently, based on
a circle of ideas of several mathematicians
(Stothers, Mason, Szpiro, Masser, Oesterlé):
Suppose A and B are any positive integers with
no common factor, and let C = A + B. Let N
be the product of the prime factors of ABC. Then
C < N2.
This is, more or less,
the ABC conjecture.
For instance,
if A = 5 and B = 27, then C = 32 and
N = 30. We have C < N2.
Look at it another way: find an equation A + B = C
with A and B having no common factors and
log(C)/log(N) as large as possible.
When A = 5 and B = 27,
log(C)/log(N) ≈ 1.02.
Try to find
an example where, say, log(C)/log(N) > 1.6. Have fun!
Because of its links to certain other topics,
this simple-sounding conjecture
quickly became a central problem in modern number theory.
If there is time, for instance,
I'll describe how the ABC conjecture
is related to the problem of finding integer solutions
to certain equations, such as in Fermat's Last Theorem.
Comments: Free Refreshments
Additional Comments: USG Funded
|
UConn Math Club
Speaker: Steve Miller (Brown University)
Time: Wednesday, November 10, 2004 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: How can you tell if a sequence of numbers is random (and, of course,
what does random mean here)? We discuss a variety of
real-world problems where the behavior of the leading digits of a 'random'
sequence is not what you would expect. This phenomenon was
first noticed by observing which pages of log tables were most worn with age.
Nowadays it is used by the IRS to catch tax cheaters.
For most of the talk, all that is needed is basic algebra, though
we will quote one or two needed results from number theory.
Comments: Free Refreshments
Additional Comments: USG Funded
|
UConn Math Club
Speaker: Lance Miller (University of Connecticut)
Time: Wednesday, November 17, 2004 at 5:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Suppose we have a method of sending information,
but the message which is received could have corrupted data.
There is no way to recover the missing information, right?
Well, mathematicians have found ways to
make even unreliable methods of transporting information
reliable. These methods are currently used in many
aspects of life, from NASA probes sending data through
unstable environments to CDs where
errors in transmission are introduced by skipping. In this
talk, we will discuss the mathematics of error-correcting codes, and
see how linear algebra plays a large role in solving this problem.
Comments: Free Refreshments
Additional Comments: USG Funded. Note the time!
|
UConn Math Club
Speaker: Joe McKenna (University of Connecticut)
Time: Wednesday, December 1, 2004 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The calculus of variations is an important topic in
non-linear analysis, numerical analysis, and
mechanics. I will try to give an accessible description,
including both what I understand, and what I don't understand,
in this area.
Comments: Free Refreshments
Additional Comments: USG Funded
|
UConn Math Club
Speaker: Ron Blei (University of Connecticut)
Time: Wednesday, December 8, 2004 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We will discuss the concept of independence, focusing on its meaning
and on ways we model it. The discussion will be in part philosophical
(very simple-minded), as well as mathematical (very elementary).
And all should be very accessible...
Comments: Free Refreshments
Additional Comments: USG Funded
|
|
|
University of Connecticut | 
