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. Branwer 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

This Semester
Fall 2008

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.

January 30
Dr. Selwyn Hollis
A Tour of Mathematica 6
Wolfram Research's Mathematica has been among the most powerful and widely-used computational software packages for some twenty years now. Mathematica likely came into existence to provide Stephen Wolfram with a laboratory for his cellular automata research, but no one can accuse the man of not thinking big. The Wolfram website touts, "Mathematica is the world's most powerful global computation system." Much of this talk will be an attempt to explain what the heck that means --- as well as what makes Mathematica unique and what good Mathematica code looks like. (Computer scientists familiar with LISP and Prolog will notice similarities.) We will also give the audience a small taste of the staggering array of new features and capabilities of version 6.0 of Mathematica, released last May. Those interested may prepare for the talk by perusing www.wolfram.com .

Recent Colloquia

Fall 2007

November 14
Dr. Felix Hamza-Lup and James LaPlant
Distributed Haptic Virtual Environments
Dr. Hamza-Lup and undergraduate James LaPlant are investigating techniques that will allow an additional human sense, haptic touch, to be sent over the Internet. At present, networks are designed to carry information that stimulates two human senses: the auditory sense (e.g., VoIP) and the visual sense (e.g., video, graphic, text etc). A significant research effort is targeted towards providing different levels of service for different types of traffic through the introduction of Quality of Service levels. The introduction of haptics for training purposes in the medical field has underscored the importance of simulating the sense of touch. We are at the dawn of the widespread use of haptic devices in a multitude of application domains. With the introduction of the Falcon haptic interface (Novint™ Technologies), such devices are not laboratory specimens anymore, but have become “household appliances”. In this presentation, Dr. Hamza-Lup and James LaPlant illustrate a distributed haptic environment for collaborative object manipulation. They will discuss their investigation into the effects of network delay and jitter on visual-haptic task performance.

November 7
Dr. Mark Budden
The Search for Unique Factorization
Shortly after learning about divisibility, students encounter the factorization of integers greater than 1 into products of primes. The Fundamental Theorem of Arithmetic guarantees that such a factorization always exists and is unique (up to reordering).  Unfortunately, this property does not always extend to other integral domains and it has led to many false “proofs” in mathematics. In particular, the assumption of unique factorization in integral domains led to mistakes in the works of Euler and Lame’. The lack of unique factorization is still an unwelcome obstacle in mathematical research. In this talk, Dr. Budden discusses how the works of Kummer, Kronecker, and Dedekind resolved the issue in many settings.

October 31
Dr. Wayne M. Johnson
Solid Freeform Fabrication: An Overview and Applications
Solid Freeform Fabrication (SFF) is a relatively new technology that allows physical (prototype) models to be created from a three-dimensional computer-aided design (CAD) drawing. Use of these physical models is a significant tool in product design and realization. The parts are created by depositing material layer-by-layer in cross-sectional planes until the part is "built-up". Build materials include icing, silicone, starch, and plastic depending on the SFF technology used. The cost of commercial SFF devices is the most prohibitive aspect in the adaptation of this technology by inventors, smaller sized companies, and universities.  This talk will provide an overview of various SFF techniques being used in industry and academia. It will also highlight efforts at AASU to incorporate SFF into the Engineering Studies curricula. This effort includes the use of SFF models in the Engineering Graphics course, and the construction and testing of a low-cost SFF system based on the open-source Fab@Home Personal Desktop Fabricator Kit developed by Cornell University. The Fab@Home system will be used to demonstrate the technology and to build additional SFF models in the Engineering Graphics course.

October 24
Dr. Sungkon Chang
The Arithmetic of Elliptic Curves
In number theory, the rational solutions of quadratic/cubic equations in two variables are classic subjects, and yet, there are many open problems. When the solutions of a cubic equation are not "isomorphic" to the solutions of a quadratic equation, the cubic equation is called an elliptic curve.  It is somewhat harder to study the rational solutions of an elliptic curve, and for the past 100 years, this subject has attracted many number theorists.  In this talk, Dr. Chang introduces the basic theory of elliptic curves, and discusses two conjectures important in the theory of elliptic curves -  the Birch-and-Swinnerton-Dyer Conjecture (one of the millennium problems) and the Taniyama-Shimura Conjecture.  In 1990, Ken Ribet at the UC, Berkeley, published the proof of Serre's epsilon conjecture, which implies that if the Taniyama-Shimura conjecture is true, then so is Fermat's Last Theorem (that  has no positive integer solutions x, y, and z  for an integer n > 2). Dr. Chang will discuss how Sir Andrew Wiles began to realize his childhood dream of proving Fermat's Last Theorem as soon as he heard about Ribet's result and began to work secretly on the Taniyama-Shimura Conjecture to force himself concentrate exclusively on the problem.  Later, collaborating with Richard Taylor, a former student of his, he proved the conjecture for special cases of elliptic curves, which was strong enough to prove Fermat's Last Theorem.

October 10
Dr. Dale Kilhefner
Going from 2 to 3
Life has many situations in which complications arise when we go from two to three (and not just in romantic relationships). A geometry/art example would be the struggle to use a 2-dimensional medium to represent 3-dimensional objects accurately. Mathematics has many situations in which something is fairly simple until one more degree of generality is added.  Dr. Kilhefner will examine two situations mastered by most precalculus students for second degree polynomials, but ignored by most advanced students (and perhaps some faculty) for higher degree polynomials.

October 3
Dr. Tim McMillan
Does “b-2” only make you think of shouting “bingo!”? Not after this talk!
B-2 Sequences are sequences of natural numbers. Their defining property is that no two distinct pairs of terms from the sequence have equal sums. The sequence of squares {1,4,9,16, …} is not a B-2 sequence. Can you find a counterexample?  Dr. McMillan will feature the utility of B-2 sequences in this talk, along with some of their interesting properties and unsolved problems.

September 19
Dr. Omar Zeidan, MD Anderson Cancer
The Latest Technology in Medicine: The Field of Radiation Oncology
We are currently experiencing an avalanche of new technologies in medicine, particularly in a relatively new field of medicine - radiation oncology. The purpose of this presentation is to highlight the state of the art treatment modalities and their application for various cancer treatments. Dr. Zeidan will introduce two new treatment concepts: 4D treatments and image-guided radiation therapy (IGRT). He will start with an introduction to medical physics, including the chronological evolution of treatments from the turn of the 20th century to the current state of the art. Dr. Zeidan will also discuss some of the current challenges with planning and delivery of patient treatments, along with potential improvements. Finally, Dr. Zeidan will point out how advances in medicine are benefiting from interdisciplinary research.

September 12
Dr. Jim Brawner
Weighing the Evidence: A Sampling of Counterfeit Coin Problems
Suppose you have twelve coins, one of which may be counterfeit, weighing slightly less or slightly more than the real coins.  Equipped with only a balance scale, devise a strategy to detect the counterfeit coin and its defect (too light or too heavy) with a minimum number of weighings.  For over sixty years problems such as this one have delighted and frustrated mathematicians both professional and amateur.  This talk will give a survey of weighty problems from the realm of recreational mathematics involving both balance scales (with two pans) and spring scales (like the one in your bathroom).

September 5
Dr. Daniel Liang
An Experimental Automatic Grading System
In this talk, we introduce an experimental automatic grading system for Java/C++/C programs developed here at AASU. The system allows:
Students to compile, run and submit the exercises online, letting them know if they answered correctly or not. (Students can continue to test and run the exercise before submitting.) Instructors to create their own exercises, to sort and filter all exercises and check grades (by time frame, student, date, and/or exercise), to review incorrect submissions; to correct them online; and to provide feedback to students online.

August 29
Dr. Lorrie Hoffman
Fostering the Rare Event (the Student-Scientist)
Pressure to produce more and better scientists is ubiquitous.  Let us say it begins with NSF (e.g. PRISM, STEM), filters down through our Georgia BOR (e.g. mandated graduation quotas for 2013) and into the academic management here at AASU (e.g. student-faculty collaborative grants), and thus ultimately steers our faculty toward certain pre-determined goals.  This talk covers a brief look at some Chronicle of Higher Education articles, information from NSF websites, reports by independent reviewers of NSF programs, and opinions offered by the professional scientific societies relating to NSF budgeting in this area.  Proof of the influence of the goal to educate the student-scientist will become evident from the discussion of some AASU departmental summary statistics, internal AASU grant execution, and recent research and publications being produced, particularly by the Mathematics Department, but numbers from all AASU science and technology disciplines will be shown.

Spring 2007

April 11
Dr. Sungkon Chang
Antiderivatives as Elementary Functions
In calculus, we learn how to find the derivative of a function y=f(x), which provides us with a way to intelligently study the geometry of the curve formed by this function in the rectangular coordinate plane. The area of the region formed by these curves is a natural geometric concept, and it is the Fundamental Theorem of Calculus that formulates the answer to the problem of finding the area, in terms of the antiderivative, F(x), of f(x) [i.e., a function F(x) whose derivative is f(x)]. Then we learn how to find the antiderivative of a function y=f(x). It turns out that it is not always possible to write F(x) in terms of so-called elementary functions such as sin(x) and exp(x), which are a class of functions considered in the usual calculus course. It was Louiville who first gave a description of f(x) for which the antiderivative is elementary, and Ostrowski generalized it to wider classes of meromorphic functions. In spite of the essentially algebraic nature of the problem, all proofs had been analytic. In 1968, Rosenlicht gave an algebraic proof.  Dr. Chang will present Rosenlicht's proof in this talk, and will address further questions in this topic.

April 4
Dr. Felix Hamza-Lup, Michele Adams, Eric Freeman
Haptic Feedback Applications for Education and Training - HaptEK16
"I hear and I forget. I see and I remember. I do (touch) and I understand."-- Confucius.
Research in Multimodal Interfaces is undergoing a shift towards the haptic paradigm. Such interfaces, combining 3D graphics, sound and haptics (touch sensation) have the potential to advance our understanding of concepts and phenomena, as well as to promote new methods for teaching and learning. Involving students in the learning process has been a challenge for educators for many years.   In this presentation we describe our multimodal haptic simulator, HapteK16, designed to assist students in understanding difficult concepts underlying hydraulics and the Pascal’s Principle. The simulator includes three different components: pressure measurements, hydraulic machines simulation, and hydraulic car lifting. HaptEK16 has the potential to augment or replace traditional laboratory instruction with an approach offering enhanced motivation, retention and intellectual stimulation. (Website: http://www.cs.armstrong.edu/felix/projects/HapteK16/index.html)

March 28
The Armstrong Putnam Team
Refections on the 67th Annual Putname Mathematical Competition
On December 2 2006, 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 21
Dr. Priya Goeser and Dr. Cameron Coates
Real Time Flight Load Identification: Methods and Applications
Structural health monitoring is becoming increasingly important in military and civilian aerospace applications.  The identification of real time flight loads is advantageous in several ways.  For example, the information may be used to improve fatigue or critical load damage modeling, to improve aircraft handling or pilot response to unusual loads. Autonomous vehicles may use this information to make flight adjustments or to detect and quantify damage while in flight.  This type of flight load information will also provide reliable databases, which may be used in a condition-based maintenance program.  The measurement of real time flight loads, displacements and stresses are typically very difficult due to the complexity of load measurement instrumentation.  This work seeks to identify in-flight loads based on real time data provided by strain gages.

March 7
Dr. Ashraf Saad
The Application of Hybrid Soft Computing Techniques to Classifier Design
Research on classifier design, both theoretical and applied, has been ongoing since computers were first put to use to solve pattern classification problems. Numerous computational techniques have been developed over the years to build binary and multi-class classifiers. These techniques include Bayesian and neural net based classifiers. There are two main challenges that must be addressed in order to design a pattern classifier for any given application. The first is determining the structure of the classifier itself. The second is extracting a set of features from the input space and determining a subset of those features to use in order to obtain the desired classification output. In this talk, Dr. Saad presents the results of a multi-year investigation into the use of soft computing techniques to design binary classifiers. The methodology is based on using evolutionary computation for classifier design and feature selection. Dr Saad presents the methodology, as well as the results of applying it to three real world problems. He will conclude the talk with insights and directions for further research. Additional research results that are related to this talk have been presented in the 11th Online World Conference on Soft Computing. They are posted at http://www.cs.armstrong.edu/wsc11.

February 21
Amanda Beecher, SUNY, Albany
Introduction to Matroids  and their role in  Free Resolutions of Multigraded Modules
Given a matrix with entries in a field, we will define a matroid. We will discuss properties of matroids and their relationship with matrices, lattice theory, and simplicial topology. Ultimately, we will descibe simplicial complexes called the broken circuit complex and the reduced broken circuit complex. In the remaining time, we will describe how these simplicial complexes help us to understand the connection between multigraded modules and matroids.

February 14
Dr. Farrokh Mistree, Systems Realization Laboratory, Georgia Institute of Technology
Strategic Engineering - A Response to Globalization
Are you interested in:
1. Issues confronting educational and manufacturing enterprises in the near future?
2. Learning how to increase agility and decrease time to market in response to changing markets through:  Leveraging of existing technology and infusion of new technology? Linking market and design capability forecasts to plan product portfolios? Using computing, information, and decision frameworks for coordinating distributed decision makers?
3. Learning career sustaining skills to be effective in today’s marketplace?
4. Becoming insane?
If the answer to any of the preceding questions is "yes", please join Dr. Mistree in exploring Strategic Engineering - a contemporary paradigm to forecast and respond with agility to the needs of a rapidly changing world.

February 7
Dr. Raymond Greenlaw
Parallel Complexity of Hierarchical Clustering and CC-Complete Problems
Complex data sets are often unmanageable unless they can be subdivided and simplified in an intelligent manner. Clustering is a technique that is used in data mining and scientific analysis for partitioning a data set into groups of similar or nearby items.  Hierarchical clustering is an important and well-studied clustering method involving both top-down and bottom-up subdivisions of data.  In this presentation, Dr. Greenlaw addresses the parallel complexity of hierarchical clustering and describes known sequential algorithms for top-down and bottom-up hierarchical clustering. He defines a natural decision problem based on bottom-up hierarchical clustering, and adds this Hierarchical Clustering Problem (HCP) to the slowly growing list of CC-complete problems (problems reducible to comparator circuit evaluation), thereby showing that HCP is one of the computationally most-difficult problems in the Comparator Circuit Value Problem (CCVP) class. By proving that HCP is CC-complete, he demonstrates that HCP is very unlikely to have an NC algorithm (a parallel [polylogarithmic] algorithm that uses a polynomial number of processing elements).  This result surprisingly shows that the parallel complexities of the top-down and bottom-up approaches are different, unless CC equals NC.  This work is joint research with Sanpawat Kantabutra of Chiang Mai University.

Fall 2006

September 13
Jeremy Dyal and Jeremiah Eisenmenger
Outcomes of the 2006 Student-Faculty Summer Collaborative Research Program
Abstract: This past summer, two AASU mathematics majors participated in the first Student-Faculty Collaborative Research Program offered by the College of Arts and Sciences. Each student will present an overview of the topics they studied and outcomes of their work. Jeremy Dyal will present the bus driver sanity problem, which is a graph theoretical instance of a scheduling/routing problem. He will discuss the background of the problem, the scenarios that were posed, and the solutions to the scenarios.  Jeremiah Eisenmenger will examine the reciprocity laws proved by Gauss, Scholz, and Buell and Williams in order to provide the motivation for a generalization of Scholz's law. The generalization depends upon the residuacity of carefully chosen units in field extensions of the rational numbers.  

September 6
Dr. Lorrie L. Hoffman
Exploring Applications of Missing Data Algorithms
The problem of handling missing data began to be extensively studied in the late 1970’s. The mechanism of solution is inherently a multivariate one with at least four popular approaches: 1) Listwise Deletion, 2) Mean Imputation, 3) EM algorithm, 4) Direct Maximum Likelihood. Just a decade ago, journals targeted at quality assessment wrote of future innovations in multivariate applications. Thus in a quality engineering environment, the act of addressing “missingness” in data collection and analysis is a rather new endeavor. Dr. Hoffman will explore the application of these four approaches via an example dealing with SPAM filters. She will also illustrate the importance of the concept of “missing at random” and its effect on proper convergence to the maximum likelihood estimates.

August 30
Dr. Felix Hamza-Lup, Students: Iyatiti Mokube and Ivan Sopin
Visual and Haptic Interfaces in Medical Applications for Simulation and Training
High-power computing, real-time graphics and haptics (the science of applying touch (tactile) sensation and control to interaction with computer applications) have spawned revolutionary human-computer interfaces in multiple domains. Such multimodal interfaces (combining 3D graphics, sound and haptics) have the potential to advance our understanding of concepts and phenomena as well as promote new methods for training/teaching. In this presentation, Dr. Felix Hamza-Lup focuses on the use of visual and haptic interfaces in medical applications designed specifically for simulation and training. He provides a review of the available haptic technologies and associated hardware/software characteristics. While virtual reality is just emerging as an accepted scientific discipline for medicine, the majority of applications are in the area of planning, inter-operative navigation and training. As an example, Dr. Hamza-Lup presents a 3D visual simulator aimed at saving time and resources in generating the optimal treatment plan for radiation therapy by allowing physicians to visualize potential collisions in the system.

April 5
Elijah Allen
Prime Constellations
Consider a k-tuple of prime numbers in ascending order. Such a k-tuple is considered inadmissible if there are no other k-tuples of prime numbers that match its intervals between successive primes exactly. Thus, admissible k-tuples of primes establish a pattern that is repeatable with other k-tuples of primes. An admissible k-tuple with the smallest possible difference between the last and the first terms is defined to be a prime constellation with k terms. The prime k -tuple conjecture states that every admissible pattern for a prime constellation occurs infinitely often. This research looks into this still-open question and gives results so far.

March 22
Dr. Robert L. Taylor, Clemson University
Fun and Opportunities in Probability and Statistics
Probability and statistics problems have intrigued and puzzled people for many years. Dr. Taylor will analyze some of these problems to determine logical solutions and to illustrate facetious approaches to solutions. He will present Monty Hall's "Let's Make a Deal" puzzler as one example of illogical and logical solutions. In addition, Dr. Taylor will discuss career opportunities for students in the mathematical sciences, especially probability and statistics.

March 8
Dr. Jim Brawner, Jeremiah Eisenmenger, Duc Huynh
Reflections on the 2005 Putnam Exam
The Armstrong student team for the 2005 Putman Exam in Mathematics will present a synopsis of their experiences in taking this challenging national examination. Each of the three team members will discuss a solution for one of the problems on the examination.

March 1
Dr. Ray R. Hashemi
A Signature-Based Predictive System for Liver Cancer
Dr. Hashemi will present a hybrid predictive system that improves the prediction of liver cancer caused by a group of chemical agents. The system employs both SOM net and Hopfield net. The SOM net performs the clustering of the training set and delivers a signature for each cluster. Hopfield net treats each signature as an exemplar made up of 2,717 × 2,717 digits and then learns the exemplars. Each record of the test set is also converted into a vector of 2,717 elements and is considered a corrupted signature. The Hopfield net tries to un-corrupt the test record through several iterations using its associative memory property and then attempts to map it to one of the signatures and consequently to the prediction value associated with the mapped signature.

February 22
Amy Chambers, University of Colorado at Boulder
Cuntz Algebras
If E is a directed graph, the graph C*-algebra C*(E) is the universal C*-algebra generated by families of partial isometries and projections corresponding to the edges and vertices of the graph E satisfying certain relations that form a Cuntz-Krieger E-system. Graph C*-algebras have been much studied in the last ten years by D. Pask, A. Kumjian, and I. Raeburn and have proved useful in the general structure theory of C*-algebras. In this talk we will examine the question of the existence of a conditional expectation from the tensor product of two graph C*-algebras, C*(E₁) ⊗ C*(E₂ ), to the subalgebra B = span{S_mS_v* ⊗ S_a S_b* : m and v are paths in E₁ with the same source, a and b are paths in E₂ with the same source, and |m| - |v| = |a| - |b|}. Using an action of the unit circle T on C*(E₁) ⊗ C*(E ₂), we will show that there always exists a conditional expectation from C*(E₁) ⊗ C*(E₂) onto B. We will then define a directed graph e derived from the graphs E₁ and E₂ and examine two examples. In our first example, the conditional expectation maps O _d1 ⊗ O_d2 , the tensor product of two Cuntz algebras, onto B = C*(e) = O_d1d2. The second example we give exhibits a case in which C*(E) does not equal B. Finally, with these two examples in mind, we will make precise the requirements necessary for C*(E) to be equal to our subalgebra B.

February 15
Dr. Charles W. Champ, Georgia Southern University
Using Multiple Characteristics In Quality Assessments -Properties of Multivariate Control Charts with Estimated Parameters.
In this presentation, Dr. Champ will discuss his and co-author L. Allison Jones-Farmer’s research into Hotelling's T², multivariate exponentially weighted moving average (MEWMA), and several multivariate cumulative sum (MCUSUM) charts. Traditionally, these types of charts track varying attributes of a product or service over time. He will present two descriptions of each chart, with estimated parameters for monitoring the mean of a vector of quality measurements. For each chart, one description explains how the chart can be applied with estimated parameters in practice and the other description is useful for analyzing the run length performance of the chart. Run lengths are important in quality control because they offer information about the expected time until a “false alarm” (i.e., a stop-the-manufacturing-line signal that is erroneous). Dr. Champ demonstrates that, if the covariance matrix is “in control”, the run length distribution of most of these charts depends only on the distributional parameters through the size of the process shift in terms of statistical distance. Simulation is used to provide performance analyses and comparisons of these charts. Dr. Champ presents an example to illustrate the MCUSUM and MEWMA charts when parameters are estimated.

February 8
Jim Brawner
The Marriage Problem
As Valentine’s Day approaches, you may be wondering about a strategy for finding the spouse of your dreams. (Then again, you may consider advice on dating from a mathematician to be about as helpful as an ethics seminar conducted by Jack Abramoff. ) In this talk, Dr. Brawner will discuss the problem of finding an optimal strategy for pairing men and women into stable marriages based on their preferences for the members of the opposite sex. In addition to offering at least one genuine piece of advice for marriage seekers, Dr. Brawner will discuss why this problem might be of particular interest to pre-med, pre-law, and economics majors.

February 1
Tim Ellis
The Complete Dummy's Guide to the Greatest Unsolved Problem in Mathematics
In 1859, Bernhard Riemann was appointed a corresponding member of the Berlin Academy, based on his 1851 doctoral dissertation and his 1857 work on abelian functions. In response to this honor, he submitted a paper entitled "On the Number of Prime Numbers Less Than a Given Quantity". In this paper, he presented an educated guess (since known as the Riemann Hypothesis), which is arguably the greatest unsolved problem in all of mathematics. The purpose of this presentation is to explore the background of the Riemann Hypothesis, to shed some light on its meaning, to delve into the history of attempts to prove or disprove it, and to describe the current prognosis of a solution. This presentation will be fully understandable by anyone possessing a passing familiarity with complex numbers and Calculus I.

January 18
Selwyn Hollis
Nuts and Bolts of Nonlinear Optimization
In the latter half of the 20th century, advances in computing technology spurred numerous scientific and mathematical fields. Among them is the field of optimization, which in its broadest sense overlaps significantly with operations research, numerical analysis, the calculus of variations, and optimal control theory. However, the field known to today's applied mathematics community as optimization is essentially a subfield of numerical analysis that deals with algorithms for optimization (minimization or maximization) of functions, with emphasis on efficiency and applicability to large-scale problems, i.e., problems involving a large number of variables. While linear programming is a fairly common topic in a variety of settings, nonlinear optimization/programming is a relatively small discipline that seems oddly obscure within the broader mathematics community, even though multivariable calculus, linear algebra, and basic real analysis provide sufficient background for its study. In this talk, Dr. Hollis describes some of the fundamental problems and algorithms in nonlinear optimization and gives a brief outline of its history.

November 9
Jatin Patel
Algorithm Animation and Visualization
The primary goals of this presentation are two-fold: 1. To provide a basic knowledge about three sorting algorithms (Bubble Sort, Insertion Sort, and Selection Sort) and two searching algorithms (Binary Search and Linear Search). 2. To provide a visual tool for beginning computer science students to understand these algorithms and for professors to use as a teaching tool to supplement the textbooks. The demonstrated application will be readily available. The application will be in Java, and hence will be platform-independent. Consequently, students will be able to use it anytime with their own inputted values, and thus will be able to understand the concepts of these algorithms much more easily.

November 2
Joe Fu, University of Georgia
Convex Valuations
A convex valuation is a finitely additive measure on the family of all compact, convex subsets of a euclidean space. Φ is a valuation if it assigns a number Φ(A) to every compact convex set in such a way that if A and B are convex sets, and their union happens to also be convex, then Φ(A ∪ B) = Φ(A) + Φ(B) - Φ(A ∩ B). Three common and foundational examples of convex valuations are volume, perimeter, and the constant valuation χ(A) = 1 for all convex sets A. Hadwiger's classical (1957) theorem states that these three valuations, and a few others very much like them, span the vector space of all valuations that are continuous in a certain inevitable sense, and invariant under the euclidean group (i.e., the numerical value assigned by the valuation to a convex body is the same as that assigned to any rotation or translation of A). Over the past five years or so, mathematicians have produced some amazing and beautiful results concerning the structures on the space of all convex valuations. Dr. Fu will discuss the new understanding that these results have produced, along with some of the new puzzles they have posed.

October 19
Lorrie Hoffman and Jaree Hudson
Famous Women Mathematicians
A journey from the work of one 18th century mathematician, Sophie Germain, to the research of a present-day mathematician, Nan Laird. This talk discusses the link between these women, their findings, and their fame. The presentation will address mathematical topics ranging from prime numbers to missing numbers. In addition, the talk will include information on research inquiry tools, including those used to trace academic genealogy and to track journal article citations.

October 5
Dr. Lewis VanBrackle, Kennesaw State University
An Alternative to the Least Squares Estimator in Statistics
The slope mean is defined as the tangent of the mean of the angles between the x- axis and the lines from the origin through statistical data points. Examining the statistical properties of the slope mean is an excellent exercise for undergraduate mathematics and statistics majors. In the process of evaluating the statistical properties of the slope mean and comparing them to the properties of the ordinary least squares estimator, students can apply techniques they have learned in a variety of mathematics and statistics courses. In this presentation, Dr. VanBrackle will show how the Fundamental Theorem of Calculus, the Central Limit Theorem, the Gauss-Markov Theorem, Taylor's series approximations, and calculation of probabilities by numerical integration and simulation can all be applied in deriving the statistical properties of the slope mean.

January 19
Cynthia Y. Young
Mathematical Modeling of Atmospheric Effects on Laser Beams
Scientists and engineers are interested in using optical (laser) systems as opposed to conventional radio frequency systems. The two main types of systems that are of special interest are laser communications and laser radar systems. The advantages of laser communications systems is that they enable 1000 times higher data rates and require less space and power which makes them ideal for satellite systems. The advantages of laser radar systems is that they provide secure channels for military target identification applications. Of course, with advantages also come disadvantages. The disadvantage is that the Earth's atmosphere has deleterious effects on optical waves that it does not have on radio waves. Star twinkle is an example of intensity (or brightness) fluctuations which correspond to a fade in a communication system. In order to take advantage of laser systems we must first have a solid understanding of the magnitude of the disadvantages such as amplitude and phase fluctuations, power loss, error rates, etc. The Earth's atmospheric effects are random and therefore statistical quantities are investigated. In this talk, mathematical models of atmospheric effects on laser beams and their corresponding engineering consequences will be discussed.

January 26
Ed Wheeler
Weighted Voting Systems
Following a series of weighty talks on topics such as The Geometry of Gaussian Elimination and the Rook's Pivoting Strategy and Mathematical Modeling of Atmospheric Effects on Laser Beams, Wheeler will deliver a real creampuff showing how a little arithmetic can shed light on a potentially important issue related to political processes. Though the mathematics will be light, Wheeler might manage to say a word or so at the end indicating some of the important contributions that persons trained in mathematics can make in lots of different work environments. Comments might be useful to students currently undecided about whether a major in mathematics might contribute to their career goals.

February 2
Jim Brown, University of Michigan
L-functions and Arithmetic
Abstract A large number of very beautiful theorems in number theory arise from the study of L-functions, in particular, their special values. It is a general philosophy that one can get arithmetic information about a "motivic" object by studying the L-function that is associated to it. I will illustrate this concept through several examples. We will start with the basic Riemann zeta function and work our way to elliptic curves and modular forms. I will assume a basic knowledge of complex analysis (i.e., what it means to be holomorphic) and some basic abstract algebra (i.e., what a field extension is) and work from there to develop the theory.

February 9
Farrah Jackson, North Carolina State University
P-adic Symmetric Spaces
This presentation we will introduce p-adic Symmetric Spaces, which are a generalization of the real symmetric spaces. Before we discuss these we will first introduce the concept of a p-adic absolute value and a metric. Then we will discuss the construction of the p-adic numbers and how arithmetic is performed in the p-adic field. Next we briefly describe the connection between involutions and symmetric spaces. Finally, we will discuss the classification of involutions and the corresponding symmetric spaces of SL(2,k) for various fields k.

February 23
Sean Eastman: Colorado State University
Linearization Error for Computational Error Estimates, and the Perturbed Power Method
A-posteriori error estimates for nonlinear equations based on residuals and variational analysis are subject to an error of linearization. It is not well understood what effect the linearization has on the estimate, and in this talk I will present some ideas for ways in which to bound the effect of linearization. The primary computational tool is very closely related to the Power Method for finding the dominant eigenvalue and eigenvector of a square matrix.

March 23
Ram N. Mohapatra, University of Central Florida
Power and Frontiers of Mathematics
In this lecture, we shall consider how mathematics is used to model physical systems. We shall also take a brief tour of some of the emerging areas of mathematics viz. Fractals, Wavelets and Neural Nets. Some application of each of these will also be mentioned. As much as possible the talk will be self contained.

March 30
Wayne Johnson & Priya Thamburaj
Vibrations: A Couple of Applications
The principles of vibration analysis can be applied to numerous situations based on a simple spring-mass-damper-system model. First, we present the underlying principles of vibrations associated with rotating tire imbalances and discuss how they can be eliminated. The system will be modeled as a single degree of freedom system subject to harmonic force excitation. Next, we look at a large-scale application ~V the response of structures to earthquakes. This ground motion during an earthquake is measured and represented by a set of accelerations, which serve as the input for vibration analysis of the structure. This talk will present the response of simple structures to such excitations. The basic concepts behind design considerations of such structures will also be discussed.

April 20
Jonathan Kish
Cyclotomic Fields and Reciprocity

August 25
Dr. Lorrie Hoffman
Mathematical Modeling and Its Role in Computer Performance Analysis
Variously trained mathematicians, computer scientists, engineers, and statisticians are employed by a large cross-section of industry to maintain, enhance and create computer networks that are performance-optimized. Speedy response times are necessary on United Airlines travel reservation systems. Quick data retrieval is mandatory on mini-computers built by companies like AT&T. The Army issues RFPs (request for proposals) to fund researchers who can find mechanisms for synchronizing performance-mismatched simulators. Mathematical modeling is one tool used to study problems in this area of Computer Performance Analysis. Both analytical and simulation techniques are used to understand the behavior of these business environments. Many of the analytical solutions are derived by using knowledge from the area of Stochastic Processes and in particular the sub-field referred to as Markov Chains and Queueing. These academic concentrations provide powerful mechanisms to investigate industrial problems of this type. We will examine the contribution of the Chapman-Kolmogorov equation and apply the results to producing a cost effective selection of a disk subsystem for a computing network.

September 15
Dr. Jim Brawner
Color My World
How many colors does it take to color a map? It was conjectured over 150 years ago that four colors suffice (for a sufficiently nice map) and the problem has attracted the attention of amateurs as well as professional mathematicians ever since. An incorrect proof was published in 1879 and went unchallenged for the next ten years. In 1978 Appel and Haken published a proof that was somewhat controversial because it used a computer to check a large (but finite) number of special cases. In this talk we will give a brief history of the problem and discuss related colorings of all sorts of objects: maps, graphs, polyhedra, doughnuts, and more.

September 22
Dr. Mark Burge
Pervasive Computing
How do we prepare our students today to develop applications for tomorrow's most widely available computing platforms? In fact, pervasive computing devices like cell phones and personal digital assistants (PDAs) are now more numerous then PCs. Cheap and ubiquitous, these compact mobile devices are the computing platforms of tomorrow. During the last four years, with the support of IBM, Motorola, and the NSF, we have started to address the unique software engineering challenges (e. g. , small memory models, cross-platform development, and wireless networking) of these platforms in our curriculum. Topics to include: secure computing using Java Card smartcards, wireless Personal Area Networks (PANs) using Bluetooth, and advanced J2ME application development using real hardware.

October 13
Dr. Paulius Micikevicius
Protein Structure Prediction from Inter-atomic Distances
Determining the three-dimensional structure of a protein molecule (or any other large biomolecule) is an extremely important and computationally challenging problem. One of the most widely used approaches relies on NMR (nuclear magnetic resonance) spectroscopy, through which a small subset of the inter-atomic distances in an n-atom- molecule is determined. Furthermore, these distance measurements are not exact, but each lies within an upper and a lower bound. In this talk we will review the computational problems and approximate solutions employed to solve them when distance-bounds are used to predict atom coordinates in the 3D Euclidean space.

October 27
Dr. Ray Greenlaw
The Fastest Hike: A Lesson in Leadership
The Pacific Crest Trail (PCT) is a 2,659-mile-long national scenic trail that winds over mountains from the Mexican border at Campo to the Canadian border near Manning Park. Completing such a hike tests and develops one's leadership skills. We examine perspective, creative thinking, problem solving, and other leadership issues in the this context. Schedule building equipment selection, logistics, and stories from the trail will be presented.

November 3
Dr. Mark Budden
A Brief History of Reciprocity
Euler and Legendre were the first to consider the problem of determining when an integer is a square modulo an odd prime. Although Legendre gave an explicit description of what we now refer to as the Law of Quadratic Reciprocity, Gauss was the first to provide a complete proof. During his lifetime, he provided eight different proofs of the law and stated several generalizations of it. The development of algebraic number theory can be traced through the attempts of mathematicians to provide an all-encompassing generalization of the Law of Quadratic Reciprocity. Among the mathematicians whose names have been attached to Reciprocity laws since Gauss are Kummer, Eisenstein, Hilbert, and Artin. In this talk, we will discuss the criteria for determining what can be classified as a Reciprocity law and look at some of the developments in Reciprocity since the time of Gauss.

November 10
Dr. Andi Kivinukk, Talin University, Estonia
Fast Computation of π
In the nineteenth century, Karl Friedrich Gauss developed an elementary iterative technique for computing π. This method influenced many new and modern methods which can be shown briefly.

November 17
Dr. George Poole
The Geometry of Gaussian Elimination and the Rook's Pivoting Strategy
A geometric analysis of Gaussian elimination is presented to better understand several difficulties encountered when this algorithm is applied in a finite-precision environment (computers). Based on this geometric analysis, a better understanding of Gaussian elimination (GE) is achieved which leads to a better understanding of the subject of scaling. These new insights also lead to a new pivoting strategy, Rook's Pivoting (RP), which encourages stability in the back-substitution phase of GE while controlling the growth of round-off error during the sweep-out. In fact, Foster has already shown that RP, as with Complete Pivoting, cannot have exponential growth error. Empirical evidence will be presented to show that RP produces computed solutions with consistently greater accuracy than Partial Pivoting, but with comparable costs. That is, Rook's Pivoting is, on average, more accurate than Partial Pivoting, and the cost of implementing Rook's Pivoting in a scalar or serial environment is only about three times the cost of Partial Pivoting.