Michigan MAA & MichMATYC

2006 Annual Meeting

Calvin College, Grand Rapids, MI
May 5-6, 2006

Plenary Speakers

Friday luncheon

The Project SEED Socratic Method of Instruction Daniel Mulligan Project SEED

Project SEED is a dynamic nonprofit organization that works in partnership with school districts, universities and corporations. Founded in 1963 with the goal of using mathematics to increase the educational options of urban youth, the program is still on the cutting edge. Project SEED employs highly trained mathematicians and master teachers who use a unique Socratic method of instruction to teach higher mathematics to entire classes of low-achieving students. Simultaneously, they provide teachers with state-of the-art professional development based on modeling and coaching. Similar methods have proven successful in training for adults in corporations, universities and community settings. Because of its four-decade history of success, Project SEED is recognized nationally as a standard of excellence. It has been featured in research based books and over 600 articles (Newsweek, New York Times, etc.) as well as in national TV coverage. Project SEED has also been recognized by numerous local, state and federal agencies, universities and other organizations. Longitudinal evaluations of Project SEED's work with elementary school students show, without exception, that students' mathematics scores increase significantly. There is also an increase in the number of students taking algebra and higher mathematics courses when they reach high school and beyond. In this talk, I will present an introduction to the Project SEED Socratic Method of Instruction.

Friday afternoon plenary

Permutations, the Braid Group and Garside Groups Joan Birman Barnard College

Frank Garside was the headmaster in a boy's school in Oxford when he began the work that became his 1968 Oxford PhD thesis (F.A.Garside, "The braid groups and other groups", Quart. J. Math Oxford Ser. (2), 20. 1969, 235-254.) Having a full-time job, he knew he would be working slowly, so he chose a topic which was outside the then-mainstream of fashionable mathematics: he set out to solve the conjugacy problem in the braid groups. In his thesis, he uncovered hitherto unknown structure, which has since had wide applications and generalizations that reach far beyond his thesis topic. For example there are ongoing applications to public key cryptography, and there is a large class of infinite groups which are called "Garside groups". In this talk we will describe Garside's discoveries and some of their subsequent generalizations. We remark that while Garside's 1969 contributions started an area of research which remains active in 2006, he never published another paper!

Friday Dinner

An ODE to Toys: Motivating Mathematics with Physical Models and Demonstrations Michael Moody Franklin W. Olin College of Engineering

A number of concepts and applications of differential equations can be illustrated or motivated using physical models. We will explore some interesting examples using ropes, chains, tuning forks, chemical reactions, pendulums, and other objects. These toys will motivate a discussion of problems from physics, chemistry and engineering and their mathematical analysis.

Saturday morning plenary

Multiscale Modeling of Klesiella pneumonia Aggregation in Flowing Blood David Bortz University of Michigan

Klebsiella pneumoniae is an opportunistic gram-negative bacteria which is a major cause of nosocomial pneumonia, sepsis, and other infections. Of particular interest is the behavior of the pathogen under bacteremic conditions. In our collaboration with a physician in emergency medicine, we have been studying murine bacteremia, focusing on the pathogenesis within the blood stream. In nutrient conditions similar to those encountered in the blood stream, recent experiments have shown that the bacteria aggregate together in clumps akin to a suspended biofilm. Our overall strategy in studying murine bacteremia employs a model selection methodology, which will be discussed. Within this context, to study the dynamics in the blood, we have developed a size-structured model based on the Smoluchowski coagulation equations. We have employed our model to identify dominant mechanisms and investigate limitations in the current data, suggesting novel experimental directions. Numerical computations and analysis results as well as future directions will be presented.

Saturaday luncheon

Rearranging the Alternating Harmonic Series Carl Cowen IUPUI

The commutative property of addition is so familiar to all of us as school children that it comes as a shock to those studying college level mathematics that NOT all 'natural extensions' of the law are true! One of the first instances that we see the failure of an extended commutative law of addition is in infinite series. Often in the introduction to infinite series in calculus, one sees Riemann's Theorem: A conditionally convergent series can be rearranged to sum to any number. Unfortunately, the usual proof of this theorem does not indicate what the sum of a given rearrangement is. In this talk, we will examine the best known conditionally convergent series, the alternating harmonic series, and show how to find the sum of any rearrangement in which the positive terms and the negative terms are each in their usual order. Results from this talk can be used as the basis of exercises and examples for calculus, advanced calculus, and real analysis.

Other Invited Speakers

The Mathematics of Referendum Elections and Separable Preferences Jon Hodge Grand Valley State University
In recent years, referendum elections have become an increasingly popular way to give voters a direct say in certain state and local issues. In spite of this fact, referendum elections can sometimes produce outcomes that are undesirable and even paradoxical. Many of these undesirable outcomes are directly related to the existence of interdependence within voter preferences. This connection, known as the separability problem, has been studied in recent years by economists, political scientists, and mathematicians. In this talk, we will explore some of the mathematics pertaining to referendum elections and separability. We'll see how mathematics can give us insights into the behavior of separable preferences and shed light on potential solutions to the separability problem. This talk assumes only minimal mathematical prerequisites and should be accessible to general audiences.
	Mathematical Neuroscience: Building the Brain Melinda Koelling Western Michigan University
As biology has become more quantitative, mathematicians have found an increasing number of interesting problems modeling biology. With over 100 billion neurons in the human brain, neuroscience provides mathematicians opportunities to model on many different scales and to appreciate the overall complexity of the biological system which is the brain. In this talk, we will compare some models that explain phenomena observable at different scales. The talk is intended for a general mathematical audience that is familiar with the idea of a differential equation.
The Collapse of The Tacoma Narrows Bridge Kristen Moore University of Michigan
For decades, scientists in many disciplines have worked to explain the dramatic torsional oscillations that preceded the collapse of the Tacoma Narrows Bridge in 1940, as well as the puzzling behavior of suspension bridges such as the Golden Gate, the Bronx-Whitestone, and Deer Isle. The forty-year effort to control the behavior of the Deer Isle Bridge in Maine, and the recent closing of London's Millennium Bridge testify to the fact that the problem of controlling suspension bridge oscillations remains unsolved. I will discuss some popular explanations for the collapse of the Tacoma Narrows Bridge. In addition, I will describe models for the motion of suspension bridges that yield rich and surprising numerical and theoretical results that explain the phenomena observed at Tacoma Narrows on the day of its collapse.
	College Geometry with Sketchpad: Following in the steps of Apollonious Nathalie Sinclair Michigan State University
Mathematics majors taking a mandatory geometry course frequently arrive with little relevant visualization ability, an overly algebraic disposition, and a brittle model of proof. In this talk, I will describe how dynamic geometry software and a ladder of tangency configurations leading to the problem of Apollonius, played pivotal roles in an advanced course responding to these students. I highlight the mathematical and pedagogical opportunities for developing geometric reasoningdescribing, organizing, visualizing and constructing geometric objects and relationships from basic ideas such as perpendicular bisectors to more advanced ones such as inversion transformationsprovided by this structure.
High Order Compact Finite Difference Schemes Jennifer Zhao University of Michigan--Dearborn
In this talk, I will talk about high order compact finite difference schemes: their advantages over regular finite difference schemes, their constructions and applications to different types of PDEs. Numerical examples will also be presented for comparison purpose and to verify the theoretical results.