In 1988, at the initiative of Dr. Anne Hudson, the then Department of Mathematics and Computer Science at Armstrong State College began a near-weekly luncheon colloquium. Students and faculty would gather in the luxurious confines of Hawes 203 for hot dogs, spaghetti, taco salad, etc., and an enjoyable talk on some topic in mathematics or computer science. In 2003 this luncheon-colloquium series was named in honor of Anne and Sigmund Hudson.
Today, the colloquium is sponsored by the Department of Mathematics and takes place on Wednesdays at 12:15 in University Hall, room 158 (unless otherwise noted). For a donation of a dollar—$2 for faculty and other non-students—you can enjoy a delicious light lunch, invigorating conversation with students and faculty members, and a lecture, demonstration, or other event arranged by faculty, students and/or visitors. Please come.
Please contact Dr. Jim Brawner if you are interested in giving a presentation. Also, please send your email address to Dr. Brawner if you would like to be added to the mailing list. If you're interested in helping with lunch preparation, please contact Dr. Brawner. His email is James.Brawner@armstrong.edu
Fall 2009
November 11
Dr. Mark Budden with Scott King and Alex Moisant
Permutations of Rational Residues II
Abstract: Reciprocity laws in number theory relate the residue symbols of distinct primes with one another. Mathematicians' attempts to extend such laws have guided the direction of algebraic number theory for hundreds of years and their results have implications throughout mathematics. In this talk, we will provide an overview of the natural setting for proving rational reciprocity laws and will explain how an extension of Zolotarev's 1872 proof of the Law of Quadratic Reciprocity may be generalized to proving more recent generalized rational laws.
October 28
Dr. Jared Schlieper
Financial Mathematics
Abstract: Dr. Schlieper will take a brief excursion into financial math from the simple (interest) to the random. Financial mathematics has many topics that everyone will encounter at some point in their life (e.g., auto loans or mortgages). The area also includes stochastic models of interest rates and financial derivatives. Dr. Schlieper will go over a few examples to give an idea of the mathematics and statistics involved. (Disclaimer: The presenter takes no responsibility for your financial losses after the talk, but expects to be compensated for your gains.)
October 7
Dr. Sungkon Chang
The Equal Circle Packing Problem
Abstract: For a closed convex region S in the Euclidean plane and a positive integer k, the equal circle packing problem is to find the largest radius a for which k open disks of radius a can be inscribed in S such that the disks do not intersect each other. This problem, which was introduced in the 1960's, is an interesting NP-hard optimization problem. With the aid of computer technology, the literature on computational results and algorithmic developments has been recently rich and active. This talk will introduce the theoretical aspects of the problem and will also introduce results for the six circle case. All students are invited, and especially those who are interested in research experience are encouraged to come and learn about the opportunity.
September 2
Dr. Sean Eastman
Using Numerical Analysis to Re-Visit Calculus
Abstract: A standard undergraduate course in numerical methods assumes that students are very familiar with a number of theoretical ideas from calculus, such as the Intermediate Value Theorem, the Mean Value Theorem, and Taylor's Theorem. All too often, these ideas get short shrift in beginning calculus, as students generally tend to focus most of their effort on learning techniques of symbol manipulation. This talk will give an overview of a new approach to teaching numerical analysis that utilizes a constructive approach to mathematics, which allows the student to take a new look at these calculus ideas in the context of algorithm construction. The talk will also include a constructive proof of the Mean Value Theorem.
Spring 2009
April 15
Dr. Sungkon Chang and William Nathan Hack
Maximizing the Minimum Mutual Distance (Preliminary Report)
Abstract: In this talk we shall introduce the problem of maximizing the minimum mutual distance. This problem is in fact in the heart of coding theory, but its obvious analogue to Euclidean space is also very interesting. We began to investigate some cases, and the main part of the talk will be a preliminary report on our investigation.
April 1
The Armstrong Putnam Team
Reflections on the 69th Annual Putnam Mathematical Competition
Abstract: On December 6, 2008, an intrepid team of Armstrong students spent most of their Saturday working on a dozen frighteningly challenging mathematical problems. Why? Just another installment of the notoriously difficult William Lowell Putnam Mathematical Competition. Members of the team will discuss solutions of their favorite problems from the most recent competition.
March 11
Dr. Jared Schlieper, Mathematics
An Introduction to Convex Bodies
Abstract: If we slice the cube through its center, in which direction will the slice have greatest area? We will begin by answering the classic problem of slicing a cube in R3 and then move on to Rn. We then see how the problem led to the recent use of the Fourier transform in solving some classic problems with volumes of convex bodies. Finally, we will examine some recent research efforts related to the cube slicing problem.
THURSDAY February 19
Jeanette Olli, University of North Carolina at Chapel Hill
An Introduction to Dynamical Systems
Abstract: There are many things that are unpredictable that people try to predict, such as the weather. Dynamical systems involve studying a system's long term behavior. After providing a definition of what a dynamical system is, we will look at several examples of dynamical systems and properties of them that we can study. One type of dynamical system is a substitution system, which is defined by a particular substitution in either one or two dimensions. A 2-dimensional example of this is a tiling system, which is a covering of the plane by particular tiles that fit together with no overlap. We'll also look at several examples of those and some of their properties.
February 4
Nova Films
Hunting the Hidden Dimension: A NOVA film about fractals.
Abstract: You may not know it, but fractals, like the air you breathe, are all around you. Their irregular, repeating shapes are found in cloud formations and tree limbs, in stalks of broccoli and craggy mountain ranges, even in the rhythm of the human heart. In this film, NOVA takes viewers on a fascinating quest with a group of maverick mathematicians determined to decipher the rules that govern fractal geometry.
Fall 2008
November 12
Dr. Sungkon Chang
The Birch and Swinnerton Dyer Conjecture and Quadratic Twists of an Elliptic Curve.
Abstract: Solving an equation is a fundamental problem in mathematics, and in number theory, solving a polynomial equation of two variables for rational solutions is a well-known difficulty problem. In this presentation Dr. Chang will introduce the basic theory of cubic equations of two variables known as elliptic curves, and present his research results in this area.
The immensity of the arithmetic of elliptic curves was revealed to the mathematics community when the proof of Fermat's Last Theorem was completed in 1995 by Sir Andrew Wiles et al proving a conjecture about elliptic curves, called the Taniyama-Shimura-Weil Conjecture. One of the most prominent problems to solve in the theory of elliptic curves today is the Birch-and-Swinnerton-Dyer Conjecture. This conjecture asserts that some analytic complex-valued generating function L(s), called an L-function, associated with an elliptic curve reveals a pack of arithmetic information about the elliptic curve in its Taylor expansion at s=1. Many number theorists in this area are interested in proving a probabilistic implication of this conjecture on a certain family of elliptic curves, called the quadratic twists of elliptic curves, and Dr. Chang will introduce the literature and his work in this area.
October 29
Dr. Paul Hadavas
Operations Research: The Time of Your Life
Abstract: Operations Research(OR) has officially been a field of study in mathematics for almost 60 years. But what is it and how does it affect your daily life? In this talk, we'll dig a little deeper into Operations Research, recently dubbed "the science of better", and look at four examples from every day life where OR techniques can be applied. These examples include:
- brewing beer
- electing a president
- getting home the quickest
- spending $700 billion in the most efficient way
In addition, we'll examine how different mathematical formulations for these problems can lead to optimal solutions within seconds instead of hours.
October 8
Dr. Selwyn Hollis
Turing Instability and the Leopard's Spots
Abstract: In a 1952 paper, The Chemical Basis of Morphogenesis, Alan Turing explained that spatial patterns of chemical concentration can be generated by simultaneous reaction and diffusion processes, suggesting that this behavior may account for the development of some animal pigmentation patterns such as a leopard's spots. In this talk, Dr Hollis will present an introduction to reaction-diffusion equations and outline the mathematical basis for Turing's theory of pattern formation, which has become known as Turing (or diffusion-driven) instability. Several Mathematica-generated animations will provide illustration.
September 17
Dr. Jim Brawner
Playing with Polyhedra
Abstract: What do Plato, Archimedes, Johannes Kepler, and Norman Johnson have in common? They each have a class of polyhedra named after them. We will survey a variety of polyhedra, some better known than others, and explore some interesting properties and relationships among them.