Northern Michigan University
"A Computerized Puzzle Competition as a Math Club Activity"
I have designed a module that goes with my computerized Permutation Puzzles Package and makes it possible to use the puzzles in a competitive mode. We will demonstrate how one can use the system to set up competitions that will have students learning some math while having fun doing it. If we can work out the logistics, we will set this up for audience participation.
Lake Superior State University
"Homework & the Distance Education Course"
A critical step in for an instructor in developing their students' mathematical abilities involves the distribution and evaluation of homework. Additional challenges exist when the students are not physically on campus. In this talk we will discuss some of the challenges regarding homework distribution and evaluation in the first year Calculus course offered via interactive television and have a brief demonstration of the web based homework server. Conference participants are invited to explore the system on their own after the conference from both the student's and the instructor's perspective.
Saginaw Valley State University
"Increased Voting Incentive by Apportionment Changes"
This talk briefly surveys various apportionment methods that have been used for the U.S. House of Representatives. Several paradoxes and undesirable features of the various methods are illustrated. Possible changes in the current process, which may lead to an increased incentive for voting, are explored along with a consideration of their impact on the Electoral College.
Michigan Technological University
"Modern Financial Mathematics"
Financial mathematics became one of the most exciting fields of modern applied
mathematics. It combines differential equations, computations, statistical
methods, data mining, and modeling. This is a very interesting field for
graduate students. I will give overview of current state-of-the-art, data
acquisition, and interaction with industry, based on my summer work in Chicago
for options-trading company.
Grand Valley State University
"Lines, Lines,
Everywhere Lines"
In the early 20th
century, Felix Hausdorff introduced a function that measures the distance
between compact sets. This function, now known as the Hausdorff metric, has been
extensively studied and has many interesting applications. However, the geometry
imposed by this metric on the space of
,
(ún)
all non-empty compact subsets of
ún
has been given little attention.
We have been studying this geometry as part of the Grand Valley State University
Research Experiences for Undergraduates program. In this session, we will
discuss some of the fascinating properties of circles and lines in the geometry
of ,(ún).
We will see that the behavior of these Hausdorff lines and circles is quite
different from the familiar properties of lines and circles in Euclidean space.
Michigan Technological University
"First and Second Order Optimality Conditions in Set Optimization"
By exploring the ideas around the so-called Dubovitskii-Milyutin approach, first and second order necessary optimality conditions are given for various optimality notions in set optimization. These optimality conditions are given by employing the first and second order contingent derivatives and the generalized contingent epiderivatives of the objective set-valued map and the set-valued maps defining the constraints. The notions of subgradients and scalarized subgradients for set-valued maps are proposed and employed to state some regularity conditions.
Northern Michigan University
"Does Computational Complexity Measure Success in Nature?"
In our mathematical models of multi-species evolution, the system of equations for "niching equilibrium" consists of high-order, high-degree polynomials. When we run the corresponding computer simulations, we find that natural selection is unable to find the global equilibrium distribution. But when we modify the model to simplify (linearize) the equilibrium equations, we find that the corresponding simulations quickly and reliably converge on the (same) global equilibrium. We are than able to apply the modified "speciation algorithm" to hard problems, including real-world applications and NP-complete problems, with excellent initial results. Have we improved on one of "nature's algorithms"?
Northern Michigan University
"Abstract Algebraic Techniques in
Statistics and Probability"
Algebraic methods have been used extensively in the construction of tatistical designs of experiments having certain desirable properties. For example, abstract algebra (group theory) has been used to construct 'balanced' factorial designs with specific 'aliasing' properties, and to deal with the identifiability problem in such designs. Other uses of polynomial algebra and related algebraic methods can be found in probability, Boolean logic, statistical modeling, Monte Carlo sampling, and so forth. Methods based on Grobner bases have proved themselves to be widely useful in this context.
Here we start with the preliminary algebraic groundwork needed for defining Grobner bases, and then go on to define those bases. Next we discuss some of their important properties and conclude with a couple of examples of their usefulness in statistics/probability.