"Contingency Constrained Optimal Power Flow for Deregulated Electricity Markets"
 

Optimal power flow (OPF) is a tool used for both operation and planning of electric power systems. In the classical OPF formulation, certain controls such as generator outputs are adjusted in order to optimize an objective function subject to physical and operational constraints at a certain point in time.  Common objective functions include generation cost, network losses and total transfer capacity between sets of generation and loads.  The classical OPF is a static problem that does not allow for inter-temporal constraints, requiring heuristic adjustments that may increase costs unnecessarily. A dynamic OPF includes inter-temporal constraints to produce an optimal solution with significantly increased dimensionality; therefore requiring specially tailored solution methods.

In addition to economic considerations, the power system operating state must be secure with respect to a defined list of contingencies, such as generator or line outages.  Since the number of possible contingencies in a typical power system is extremely large, the contingency constrained OPF also has extremely large dimensionality.  An OPF that accounts for contingencies and indicates the optimal, secure operating state is essential.  Efficient algorithms for the dynamic OPF as well as the contingency constrained OPF will be presented.

Charles Hadlock, Bentley College

 "Looking at Classical Mathematics Through Smoke and Haze"
 

This is going to be a trashy presentation.  Whoops! I mean I'm going to talk trash, lots of trash.  In fact, for those who are game, I'm going to show you more trash than you ever wanted to see.

Wait, let me try again.  I want to show you that buried in that old dumpster of rotting trash is an exciting path to central concepts in classical mathematics, beginning at the pre-calculus level and leading as far as you want into upper-division courses or seminars.  More important, that dumpster can lead us and our students to an engaging, if somewhat unusual, rationale for studying mathematical modeling and applying it to important societal problems, often in our own communities.  And I hope to show you all this through smoke and haze.

An optional field trip to a trash-to-energy incineration plant in Haverhill and relatively near Bradford College will be available in the afternoon for those who still want to see more trash, more smoke, more haze, and some other interesting environmental issues as they are encountered in the real world of practice.

John R. Jungck, Beloit College

 "Ten Equations that Changed Biology and that Should Change Biology Education"
 

Mathematics has played exceptionally important roles throughout the history of biology. More biology students take Calculus than any other single constituency. Too frequently, textbook authors have unappreciated mathematics in biology curricula because they assume that biology students have an inadequate mathematical preparation. This practice: (1) deskills many biology students, (2) is inconsistent with our requirements, (3) misrepresents contemporary biological research, and, (4) underprepares students to read many articles or to contribute to many areas of biology.  However, the recent calculus and biology reform movements have empowered students to actively investigate the behavior of many famous mathematical models in biology. While numerous recent publications are replete with
numerous models, there is a need to identify a succinct list of achievements that represent the power of mathematics in biology. Hence, "ten equations that changed biology" and a brief description of their historical importance are presented here with BioQUEST software instantiations in order to: first, draw attention to a variety of mathematical models that have been intrinsic to significant discoveries in biology and, second, to illustrate that the tools are currently available for engaging students in active investigation of biological phenomena and the development of systematic strategies for biological problem solving.

David Meeker, University of New Hampshire

 "Mathematics  and an Ice Core Time Machine"

In 1993 scientists of the Greenland Ice Sheet Project 2 (GISP2) finished drilling a 3053-meter ice core (to bedrock) at Summit, Greenland.  The GISP2 ice core contains a record of atmospheric chemistry deposited year-by-year in annual precipitation for over 200,000 years.  The upper 2900 meters provides a well-dated and high resolution view of climate for the last 110,000 years.

Glaciochemical time series from ice cores are both non-stationary and non-uniformly sampled.  These features, in addition to the basic nonlinearity of the underlying climate system, complicate their analysis and interpretation.  Some of the mathematical tools and techniques developed and adapted for the analysis of the GISP2 series -- and the surprising view of climates of the past they reveal -- will be discussed in this talk.

 Charles Vinsonhaler, University of Connecticut,  http://www.math.uconn.edu/~vinson/

"Are Mathematicians Good Problem Solvers?"
 

Some evidence indicates that we mathematicians could improve our understanding and practice of problem solving. This in turn could improve our teaching of problem solving in particular, and mathematics in general.  I will present the evidence along with a number of questions, such as: Can we teach problem solving? Should we?

Paula Russo, Trinity College

"The Challenges and Benefits for Mathematics in Interdisciplinary Courses and Programs"

Many scientists have predicted that the next century will be the century for biology and the life sciences much as physics was the pre-eminent scientific discipline for much of the twentieth century.  Given the complexity of living systems compared to physical ones, it is likely that the much of the new research will be highly interdisciplinary in nature.  What will be the role of mathematics in this setting?  Will it be possible or advantageous to bring some of this interdisciplinary spirit into our own classrooms and courses?

These and related questions will be discussed in this talk.
 
 

David Mazur, Western New England College
Polyhedral Combinatorics

Polyhedral combinatorics is an elegant field which blends the geometry of affine Euclidean spaces (the continuous) with combinatorial optimization problems (the discrete).  We'll introduce the field and provide a flavor of its interesting and exciting results.
 
 

Len Brin, Western New England College
The Fractal Nature of Three Classic Analysis Counterexamples in Analysis

In fractal geometry, "strange" behavior such as an uncountable subset of the real line with zero measure (the Cantor Set), a continuous function with zero derivative almost everywhere that nonetheless increases (the Cantor-Lebesgue function), or a continuous nowhere differentiable function (the saw-tooth construction) abound.  Plus, fractal geometry leads to simple generalizations of each.

James Tanton, Merrimack College
Layered Tilings

A basic class of problems in combinatorics concern themselves with the tilabilty of selected regions in the plane by a given set of tiles. Domino and polyomino tilings in particular have offered sources of much amusement and interest to both the recreational and professional mathematician. In this paper we examine the notion of multiple layered tilings and explore criteria for the non-triviality of such tilings.
 
 

Ed Sandifer, Western Connecticut State University
Euler and the Zeta Function

Euler's proof of the sum-product formula for the Riemann zeta function is elegant and beautiful.  Sit back and enjoy a peek into the workings of the Master's mind.
 
 

Ann Moskol, Rhode Island College
The Mathematically Gifted: Are we doing enough to teach the very best?

In the present climate of "heterogeneous" grouping, special homogeneous classes for the mathematically gifted are often considered "elitist."  Most school systems do not offer advanced mathematics classes until middle or high school.  By that time, mathematically gifted students, bored by repetition of arithmetic algorithms, may be "turned off" to mathematics. Compounding this problem, is the inadequate mathematical preparation of elementary teachers and attitudes that are not compatible with gifted mathematical students.  Unfortunately, many elementary teachers, especially in the lower grades, are not experts in mathematics, and many fear mathematics. I plan to discuss the challenges of educating the mathematically gifted in the elementary and secondary levels, and to describe some programs (such as the Mathematics Olympiads for grades 4 - 6) for the mathematically gifted. In addition, I will offer some suggestions and recommendations.
 
 

Michael Bradley, Merrimack College
"Bites of Pi"

A brief survey of some interesting ideas associated with the number pi.  We will do some simple one dimensional and two dimensional geometrical approximations, discuss some of the history of formulas for calculating the digits of pi, mention some properties of pi as a real number, and conclude with some miscellaneous items of general interest from various web sites. The presentation is intended to entertain and inform, but even more to stimulate and motivate the audience to learn more about this intriguing number.
 
 

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