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| Program Highlights | Program Details | Hotel Information | Driving Directions, Maps, and Parking | Call for Papers | Registration |
Note: The deadline for paper submissions is October 19, 2005.
Deadline for Pre-registration is October 24, 2005.
Invited Speakers:
* Frank Farris, Santa Clara University and Editor of Mathematics Magazine, who will speak on "Equitability and the Gini Index."
* Brigitte Servatius, Worcester Polytechnic Institute and Editor of the Pi Mu Epsilon Journal, who will speak on “Bracing of square grids”
* Catherine Bénéteau, Seton Hall University, who will speak on "The Isoperimetric Problem."
Here is a website with information about how to submit abstracts for this meeting:
http://www.math.vt.edu/people/brown/call4papersf05.html
Frank
FarrisThe rich are indeed getting richer, as measured by the Gini index, a number that economists use to express the degree to which a distribution of resources is equitable. If everyone had a perfectly equal share of the pie, the Gini index would be 0. One person having it all would lead to a Gini of 1. In the United States, the Gini index for family income has been rising steadily since the 1960s, from a low of about 0.34 to a current value of about 0.41. The Gini index for wealth has also been increasing and is now about 0.80. In this talk, I'll develop the Gini index and discuss the problem of computing it from data. The main mathematical tool is a simple one, the definite integral that gives the area between two curves, but more advanced topics, such as moments and order statistics, also appear.
Frank Farris serves as editor of Mathematics Magazine through 2005. He hopes to continue its tradition of inspiring and challenging teachers and students of mathematics at the undergraduate level. A native Californian, Frank did his undergraduate work at Pomona College and received his Ph.D. from M.I.T. in 1981. Awards include a Trevor Evans Award for his article "The Edge of the Universe" in Math Horizons and the David E. Logothetti Teaching Award at Santa Clara University, where he has taught since 1984.
Brigitte ServatiusThe study of complex geometric objects often begins by identifying the basic ingredients, such as points, lines, and planes, and determining the incidences among these objects. The resulting incidence structure is a combinatorial object that only partially captures the original. For example it may have more symmetries than the original geometric object. Under special circumstances it is possible to recover key properties of a geometric object from the combinatorial information alone. As an illustration of a general procedure, we use the characterization of self-dual graphs to classify self-dual polyhedra.
Suppose that you are constructing a rectangular grid out of rigid beams of some fixed unit length. Such a simple grid can be easily deformed. By using beams of length equal to the square root of 2, we can brace the grid by placing a diagonal in each (or just some?) of its squares. The fundamental questions that we wish to explore and ultimately answer are:
1. How many braces are actually necessary to make the grid rigid?
2. How should they be placed?
We will generalize the problem to tension bracings and explain a relatively new type of structures with a wide range of applications, namely tensegrities.
Brigitte Servatius is Professor of Mathematics at Worcester Polytechnic Institute. She received MS degrees in Mathematics and Physics from the University Of Graz, Austria and a PhD in Mathematics from Syracuse University in 1987. Since then she has been teaching at WPI. Her main research interests are matroids, especially rigidity matroids, as well as graph and combinatorial group theory. She enjoys coaching the Putnam Team, directing graduate and undergraduate research and using models puzzles and games in the classroom. She is editor of the Student Research Projects for the College Math Journal and editor of the Pi Mu Epsilon Journal.
Catherine BénéteauThe isoperimetric problem, posed by the Greeks, proposes to find among all simple closed curves the one that surrounds the largest area. The isoperimetric theorem then states that the curve is a circle. It is first mentioned in the writings of Pappus in the third century A.D. and is attributed there to Zenodorus. However, a rigorous proof was only achieved towards the end of the 19 th century! I will discuss the history of the problem and some of its geometric and analytic proofs. Finally, I will talk about some applications to the study of shapes of electrified droplets and small air bubbles in fluid flow.
Catherine Bénéteau has an undergraduate degree and a master’s degree in mathematics from McGill University in Canada, and a Ph.D. in mathematics from the University at Albany. She is a member of Project NExT, a professional development program for young mathematicians. She taught at the program for talented youth run by Johns Hopkins University and is currently an Associate Professor at Seton Hall University in South Orange, New Jersey. She has published papers in the areas of complex analysis, ergodic theory, and mathematics education. She has received grants for her own research, and for her work in curriculum development and undergraduate research. She recently had a daughter and finally found something that she loves at least as much as mathematics!
A full program schedule and abstracts of contributed papers for the meeting will be posted as they become available.
Here are the details for the Fall section meeting:
WHAT? The MAA MD/DC/VA Fall Section Meeting
WHEN? Friday and Saturday, November 4 and 5, 2005
WHERE? Montgomery College, Germantown (MD) Campus. Germantown is located on I-270 about ten miles NW of the Capital Beltway (I-495). Here is a nice map . Details about places to stay and the like will be placed on the Section website as they become available.
WHAT'S HAPPENING? Plenty. Here is a list of activities and happenings:
* A Friday workshop: Brigitte Servatius of Worcester Polytechnic Institute (and Editor of the Pi Mu Epsilon Journal) will give a workshop entitled "Bracing of square grids". Here is a description of Brigitte's workshop:
Suppose that you are constructing a rectangular grid out of rigid beams of some fixed unit length. Such a simple grid can be easily deformed. By using beams of length equal to the square root of 2, we can brace the grid by placing a diagonal in each (or just some?) of its squares.
The fundamental questions that we wish to explore and ultimately answer are:
1. How many braces are actually necessary to make the grid rigid?
2. How should they be placed?
We will generalize the problem to tension bracings and explain a relatively new type of structures with a wide range of applications,
namely tensegrities.
* A Friday banquet: Frank Farris of Santa Clara University (and Editor of Mathematics Magazine), is our banquet speaker. The title of his talk is "Equitability and the Gini Index". Here is an abstract of Frank's talk:
The rich are indeed getting richer, as measured by the Gini index, a number that economists use to express the degree to which a distribution of resources is equitable. If everyone had a perfectly equal share of the pie, the Gini index would be 0. One person having it all would lead to a Gini of 1. In the United States, the Gini index for family income has been rising steadily since the 1960s, from a low of about 0.34 to a current value of about 0.41. The Gini index for wealth has also been increasing and is now about 0.80. In this talk, I'll develop the Gini index and discuss the problem of computing it from data. The main mathematical tool is a simple one, the definite integral that gives the area between two curves, but more advanced topics, such as moments and order statistics, also appear.* A Saturday membership meeting.
* Two Saturday hour speakers. One of these will be Brigitte Servatius (Friday's workshop leader); the title of her talk is "Combinatorics catalogs Geometry - Geometry generates Combinatorics". Here is an abstract:
The study of complex geometric objects often begins by identifying the basic ingredients, such as points, lines, and planes, and determining the incidences among these objects. The resulting incidence structure is a combinatorial object that only partially captures the original. For example it may have more symmetries than the original geometric object. Under special circumstances it is possible to recover key properties of a geometric object from the combinatorial information alone. As an illustration of a general procedure, we use the characterization of self-dual graphs to classify self-dual polyhedra.
The other Saturday hour speaker will be Catherine Bénéteau of Seton Hall University; the title of her talk is "The Isoperimetric Problem". Here is an abstract:
The isoperimetric problem, posed by the Greeks, proposes to find among all simple closed curves the one that surrounds the largest area. The isoperimetric theorem then states that the curve is a circle. It is first mentioned in the writings of Pappus in the third century A.D. and is attributed there to Zenodorus. However, a rigorous proof was only achieved towards the end of the 19th century! I will discuss the history of the problem and some of its geometric and analytic proofs. Finally, I will talk about some applications to the study of shapes of electrified droplets and small air bubbles in fluid flow.* A Saturday lunch.
* A number of contributed talks (probably between 20 and 30 of these) in five or six parallel sessions. (These are yet to be scheduled. You can submit an abstract for a contributed talk at the following website: http://www.math.vt.edu/people/brown/call4papersf05.html
The deadline for submitting abstracts is Wednesday, October 19, 2005.* A book display.
* Activities for Section NeXT.
* A chance to mix and mingle and talk about mathematics and undergraduate research and teaching and like that.
Abstracts (Word)
Abstracts (PDF)
Schedule (Word)
Schedule (PDF)
Participants are encouraged to preregister for the meeting. You MUST preregister if you wish to attend either the dinner on Friday evening or the lunch on Saturday. While on-site registration is available, preregistration simplifies the process. Your name badge, receipt, and any meal or workshop tickets will be waiting for you at the registration desk when you arrive.
DEADLINE: Preregistration forms must be received by October 24, 2005. Unfortunately, we will not be able to receive preregistration forms by email or fax, so please mail your form early. Click here for a printable version of the registration form and a mailing label.
Registrants for the meeting sometimes bring along a GUEST (typically a spouse, parent, son or daughter, etc.) who attends the meeting STRICTLY FOR SOCIAL REASONS, and not out of an interest in the program. For a guest to attend a meal event, a preregistration form must be submitted. Guests are not charged a registration fee for the meeting, only the cost of the meal(s) attended. Note that there is a place on the preregistration form to designate that the attendee is a guest.