Abstracts - Friday, February 20^th

Abstract:  The Malfatti-Steiner problem is perhaps  the most beautiful problem of the 19th century.  Steiner’s amazing discovery led to the solution even though he did not give the proof.  Based on Julius Peterson's work we give the detailed construction with all the necessary proofs.

Abstract:  The draining of a cylindrical tank through a small aperture is a staple problem in many Calculus and ODE textbooks; yet, a physical justification for the assumed square-root model is rarely given there.  We derive and study a general model for arbitrary aperture size, which includes the bottomless case.

Abstract:  Class Room Performance System (CPS) is a wireless response system that brings interactivity to the class room/lecture hall.  The wireless response pads are remotes that are easy to use and provide immediate feedback to both the instructor and the student.  Math Zone is a complete on-line course management system.

Abstract:  The infamous brown tree snake invasion on Guam motivates our study of population models involving one predator and two prey species.  Starting with the standard (single-prey) Lotka-Volterra model, we add layers of complexity in an attempt to explain the invasion dynamics.

Abstract:  Why are the zero's of Riemann's zeta function important? How did Euler solve the Basel problem? Polynomials can be reconstructed from their zeros and the method generalizes (with a lot of machinery) to the entire functions of complex variables.  We will prove the reconstruction in some special cases including sin x, using just calculus.

Abstract:  We have developed visual representations that complement their algebraic counterparts for sequence and series problems.  We demonstrate these visual approaches and provide a theoretical basis for explaining their potential in promoting conceptual mathematical understanding and creativity.  The development of visual understanding by students for series and sequence problems has implications for mathematics learning and teaching.  Our work is framed by the view that posing and analyzing rich tasks for students provides windows into their thinking with ramifications for curriculum and instruction.

Abstract:  This preliminary result suggests how even relatively print-heavy documents can be transformed into something appropriate for a Distance Learning, or perhaps Hybrid-DL course, providing that some dynamic visuals are included.  The topics -- such as Systems, Modeling, Storages, Energy Diagrams --require only HS algebra and a smattering of science.

Abstract:  We present two computer simulations for draining a tank through an arbitrary-sized hole.  Macroscopically, we derive a nonlinear ODE from simple fluid physics and solve it numerically.  Microscopically, we model the fluid molecules as agents with simple behavior.  Our goal is to observe the macroscopic behavior in the microscopic model.

Abstract:  The geometry of sets of points in projective space can be approached algebraically, via Hilbert Functions and generators of ideals.  This talk will give an overview of these tools for points in the projective plane.

Abstract:  In this talk we study the behavior of walks on infinite planes paved by binary tiles.  Whenever we step on one tile the display on it either change from L (for left turn) to R or from R to L.  We conjecture that all walks are unbounded.  For planes paved by block patterns we conjecture that all walks are eventually directed (along one direction to infinity) and prove the conjecture in many cases.

Abstract:  Magic Squares, or squares formed from placing integers in a "square" pattern in such a manner that the rows and columns all have an identical sum, have been around since 2000 B.C.  Throughout history these squares have fascinated many great and famous people.  Among these are Albrecht Durer, Pierre de Fermat, and Benjamin Franklin.  Magic squares are given names based on their properties, and some mathematicians have spent as much time trying to determine the numbers of certain squares as others have the next largest prime number, or an approximation of pi! In 1973 it was determined that the number of 5^th order squares is 275,305,224.

Abstract:  In this presentation, we will survey the methods of Stochastic Automata Network (SAN).  These are used in the modeling of parallel and distributed computer systems, because of their compact way of representing the state transition matrix.  We will focus on the modeling and analysis of complex systems, the numerical issues and difficulties that are arising from the automata’s interactions.

Abstracts - Saturday, February 21^st

Abstract:  We start by visiting the well-known trigonometry/calculus exercise:  "how far should the observer stand to get the best view of a painting?", then take an excursion to visit a multiplex stadium-seating theater, the Royal Mountain (Regiomontanus), ruler-compass construction, Brocard points, and geometric inequalities, with some journal problems as our tour guides.

Abstract:  This talk will give a brief introduction to the biology of bacterial phage.  A non-linear system of differential equation model for the dynamics of bacterial phages due to Anita et al. will be presented.  We will introduce an improved model by incorporating phage decay and immune efficiency factor in the existing model.  Further, we will analyze our improved model.

Abstract:  This pilot project uses a combination of FrontPage and Blackboard 6 in a two pronged attack on students’ languid mood when it comes to keeping up with their studies.

Abstract:  Journey with zero from its inception to the present day.  Invented by the Babylonians around 300 BC and in the west by the Mayans around 300 AD.  Controversial, zero threatened the foundations of Greek Philosophy, Calculus and the Big Bang theory.  Eventually zero amassed defined properties and took its place among the other numbers.

Abstract:  From the beginning C(2n, n) knew it was destined for greatness because it was the central binomial coefficient.  Hence, it was not surprised when a multiple of itself appeared in an answer to a problem posed and solved by Euler.  Unfortunately, it received no formal recognition as Euler’s answer until about 60 years later when that same multiple was called a Catalan Number.  From there C(2n, n) went on to star in Erdös's proof that there is always a prime number between the positive integers m and 2m whenever m exceeds 1, and in Apéry’s astonishing proof that ς(3) is irrational.  We’ll talk about these results and several others.

Abstract:  This year is the 18^th birthday of the “Tulane Conference” which sparked “calculus reform”.   “Reform” has been implemented to a greater or lesser extent at all levels of mathematics instruction.  The panel, representing secondary and post-secondary teaching, will discuss the meaning of reform, the extent of implementation, and student learning.

Abstract:  This presentation will focus on several tricks to help re-entrant students limit their math anxiety.  It will cover dressed-up numbers, the "Journal of Hidden Stuff", SAD, near-sighted exponents, monte and bias.  It will also introduce teaching-everything-at-once, managing democratic and "wild card" tests.

Abstract:  Membrane systems are new models of computation inspired by basic properties of living cells.  A membrane system (P system) consists of hierarchical arrangement of regions equipped with multisets of objects and evolution rules.  We present the computation process in some variants of P systems along with examples and recent results.

Abstract:  In "Measurement of a Circle" Archimedes develops an iterative process for finding rational upper and lower bounds for the value of Pi.  One of the starting points for this process is the nonobvious approximation 265/153 < √3 < 1351/780, which he states without further comment or explanation.  We will present several of the proposed methods that have been given over the years that Archimedes may have used to arrive at these bounds, along with an additional possibility that appears to be new.

Abstract:  The search for an appropriate dynamical framework for a quantum theory of gravity has recently led to interest in a class of Markov chains taking values in the collection of partial orders on the natural numbers.  We discuss a well-studied example of such a chain and, working from this example, we establish a number of new results involving the properties of any chain which occurs as a member of our class.

Abstract:  We have developed applications with Microsoft Excel designed to teach students about prime numbers, truth tables, Normal distributions, Z scores, and other topics.  We propose to demonstrate these applications and provide a theoretical basis for explaining their potential in promoting mathematical understanding and curiosity in a wide range of courses.

Abstract:  The fundamental theorem of arithmetic says that any integer greater than 2 can be written uniquely as a product of primes.  This presentation will examine irreducibility (the analog of primality) in Z[ √-5 ], a ring in which unique factorization fails.