2004 Southern Regional

 Weekend Algebra Conference

Program for Students

 

Friday, 5 November 2004

Fayard Hall, Room 205

1:00-1:20        Dr. Tammy Bourg                  Welcome

Dean, College of Arts and Sciences, Southeastern Louisiana University

 

The rest of the talks for undergraduate students will take place in

Fayard Hall, Room 214

 

1:30-2:00        Dr. Kirby Smith                      On a problem relating to integer valued

polynomials

Abstract:        An integer valued polynomial is a polynomial p(x) such that p(n) is an integer for every integer n. The problem that I will present arose from a student's question on writing infinite series.

 

2:15-2:45       Dr. Shane Redmond                Facility Location: An application of graph

theory

Abstract:        Imagine you have to choose the optimal location for a hospital or a shopping mall. How will you make your choice?  We will discuss how to use the idea of distance in a simple graph to guide our decision.  (Attend the speaker’s other talk to see an application of centrality in graphs to commutative ring theory.)

 

3:00-3:45      After  Math, Career discussion
 
4:00-4:30      Dr. Julie C. Jones                         When Modular Arithmetic Met The Dot 
                                                                                                           Product

Abstract:    Modular arithmetic and the dot product are two topics in the study of mathematics that have been around for centuries.  Euler studied modular arithmetic in 1761.  Gauss used the dot product to solve problems in the 1830's.  Until recently, these two topics in mathematics seemed to have little in common.  Currently, modular arithmetic and the dot product are used together for some important

applications.  Applications include UPC numbers, ISBN's, driver's license numbers, check routing numbers.  In this talk, we will discuss modular arithmetic, the dot product, and some current applications.

 

4:40-5:10        Audrey Cabezuela                  Automorphism Groups

Abstract:  Given a finite group G we are interested in finding, up to isomorphism, all finite groups X for which Aut(X) = G.  In particular, we discuss this equation for several classes of groups.

Saturday, 6 November 2004

9:00-9:30          Dr. Kent Neuerburg             Implementing Newton's Method

Abstract:       Newton's Method is a standard topic in every introductory Calculus course.  However, even though Newton's Method generally converges quickly to a root, we are generally left with the questions of "How should one choose an initial approximation?" and "How many iterations will provide a good (meaning to within some predetermined accuracy) approximation to the root?"

 

9:45-10:30   Graduate School Panel Discussion

 

10:45-11:15  Dr. Laurie Edler                       Problem solving techniques

Abstract:       Problem solving sessions are an invigorating avenue for meaningful interaction between students and faculty in a mathematics department.  This talk addresses an initial solution proposed at a weekly departmental session to the following problem:  For a set A, define  A+A={x+y : x,y є A}.  Also define Sn={0,1,2, … ,n-1,n} for a natural number n.  Find a set A, of non-negative integers, with

smallest cardinality such that S100 is a subset of A+A.  Subsequent attempts to generalize the problem, with emphasis on techniques using mathematics accessible to undergraduates, will also be discussed. 

 

11:30-12:00    Dr. Bruce Olberding              Paradoxes

Abstract:          Paradoxes are, roughly speaking, surprising conclusions reached by seemingly sound arguments.  The most disturbing paradoxes are those that consist of two seemingly contradictory conclusions resulting from sound arguments.  We discuss certain paradoxes that had a profound influence on the development of mathematics in the 20th century.  We also discuss some lesser-known paradoxes,

some of which can be explained away, and some of which are still the subject of much debate.       

 

12:00-2:00      Lunch

 

1:45-2:15        Dr. Jason Huffman                Making Heaviside Rigorous:  the story

behind operational calculus

Abstract:  Oliver Heaviside was a brilliant, self-trained thinker in late 19th-century England whose unorthodox, but practical, approach to mathematics won him fame with engineers and ignominy with professional mathematicians.  His innovative techniques in the theory of electric circuits and telegraphy marked the dawn of a new era in analysis and set the stage for the theory of generalized functions. 

However, the lack of mathematical rigor in his work led to frequent troubles for Heaviside.  This talk will explore Heaviside's personal and professional history, and that of Polish mathematician Jan Mikusinski, who finally justified many of Heaviside's techniques in a rigorous mathematical setting.

 

2:30-3:00    Dr. Greg Boudreaux                  Off on a Tangent

Abstract: The modern definition of tangent is the limit definition we learn in Calculus. But mathematicians were finding tangents before Newton’s way of calculating them was discovered and long before it became the definition. So what was the definition before Newton and Leibniz came along? In this talk we will consider some classic definitions of tangents. In particular, we will see that the definition of

tangent used by Euclid and Apollonius worked well for conic sections, but was inadequate for dealing with more general curves. Also, we will see how the popular definition of tangent in the time of Descartes was stolen from a property of Euclid's tangent, but still was a bit "off" from hitting the mark. Inspired by Euclid's Propostion 16, Book III, and the clumsiness of the tangent concept of Descartes' time, a new

definition will be given that turns out to be equivalent to the modern definition, yet has the benefits of being geometric in nature and free from the limit concept.

 
4:30 Picnic at the Alumni Center