Math Colloquia

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The Department of Mathematics hosts a colloquium on topics of interest 3 to 4 times each semester.  Previous topics are listed below.  Click on the title to view the colloquium. Titles with a are viewable with RealPlayer.

October 11, 2005
Really Learning Mathematical Concepts 
(video will be available after 10/11)
Dr. Ruben Schweiger

A mathematical concept is an abstract idea, like the idea of zero or the idea of division. It is hard to think of a mathematical process or approach which is not dependent on one or several mathematical concepts. However in teaching and learning mathematics, little attention is given to specifically teaching concepts. This talk will explore what is involved in constructing mathematical concepts. In the process, Dr. Schwieger will accept the Double Dog Dare to 'teach' a NEW concept in 10 minutes with the further claim that the audience will not forget this concept for the rest of the semester even though it is not mentioned again during the rest of the semester. 

September 13, 2005
An Easy Introduction to Continued Fractions
Dr. Tom Pickett

Continued fractions, in spite of their basic simplicity, provide insight into many mathematical problems and are related to many other areas of mathematics. For example, everyone knows that π is a non-terminating, non-repeating decimal, π = 3.1415926..., and hence cannot be expressed exactly as a fraction. However, a good approximation for π is given by the fraction 22/7. This rational approximation can be obtained using continued fractions. Our seminar will be a simple introduction to continued fractions, using only elementary algebra. So, what is a continued fraction? Watch the colloquium and find out! 

April 20, 2005
The Actuarial Profession: Questions and Answers
Brooke Wilke and Jenny Wilke

Being an actuary is consistently rated one of the best jobs by sources such as Jobs Rated Alamnac for being high paying and low stress with a good work environment and career outlook. Most people, however, don't even know what an actuary does. This Colloquium will be an informal question-and-answer session with two practicing actuaries.  What does an actuary do? How much does an actuary earn? What are actuarial exams? How do you get an actuarial job? Watch this colloquium and find out!

March 29, 2005  
Bigger Than Infinity?!? 
Mr. David Ritterskamp

You are the owner/operator of the Infinite Hotel, where presently all rooms are rented.  Suddenly, your best friend pulls up, needing a place for the night.  Can you somehow make space?  Of course you can!  Adding a single element to an infinite set does not change its size.  In fact, you can accommodate as many new guests as your Infinite Hotel currently holds.  In other words, doubling an infinite set does not change its size.  Yet there exist some sets that are bigger, "more infinite", than others.  This talk will explore some familiar infinite sets using elementary concepts of set theory.   

January 25, 2005 
Using Mathematics in No-Limit Poker 
Dr. Bill Wilding

There are many opportunities to use mathematics in refining poker strategies.  In no-limit poker, situations often arise in which decisions to fold, call or raise can be reduced to a pure math problem.  This talk consists of several examples illustrating the calculation of pot odds and expected values of all-in calls, identifying semibluffing opportunities and demonstrating why they are so effective and determining optimal game theoretic bluffing frequencies.   

December 7, 2004
Numerical Methods and its Analysis for Stochastic ODE  
Dr. Henri Schurz

Systems of ordinary stochastic differential equations (SDEs) play an essential role in dynamic modeling in sciences, engineering, biology and economy due to Heisenberg's uncertainty principle. Most of those equations cannot be solved analytically, and hence one has to resort to numerical methods. After some standard existence and uniqueness results on analytic solutions of SDEs we start with the well-known Ito-formula and present stochastic Taylor expansions along functions of strong solutions of SDEs, known as Wagner-Platen expansions. This leads to the construction of an incredibly rich pool of numerical methods for SDEs which we are going to indicate in a condensed form. Eventually, consistency, convergence, order bounds, contractivity, stability and nonnegativity are discussed as the key concepts of numerical approximations. If time permits, some applications to dynamic pricing theory in economics and random population ecology are presented.

 

The talk focused on key concepts and tools of stochastic numerics rather than all technical details. The audience is supposed to be familiar with some essential facts from ODEs and probability, hence it is also appropriate for those who want to grasp elements of modern stochastic-numerical analysis in a concise introduction.

November 17, 2004 
Electronic Voting: Mathematics and Electronic Security
Algorithms that might be useful in election systems that try to achieve public auditability
Mike Amling

October 27, 2004
Mathematics on the High Seas: Mathematical Models and the Battle of Trafalgar  
Dr. Adrian Gentle

In October 1805 Admiral Horatio Nelson led an outnumbered British fleet to a decisive victory over Napoleon's forces at the Battle of Trafalgar, resulting in a century of British naval supremacy.  In this talk we will construct a simple mathematical model of the battle and use it to show that without Nelson's brilliant and unorthodox tactics the British faced almost certain defeat.  We will also show how calculus can be used  to improve the model and provide deeper insights into military tactics and planning.

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