Program Schedule

This is the program to date -- please check back for updates. (Last update: 6/10/2010)

Friday, June 11, 2010
Time	Speaker & Topic	Location
11:30AM - 5:30PM	Registration	O'Hare, lobby
Noon - 3:00PM	Section NExT (with lunch)	O'Hare 106
2:00PM - 3:00PM	Executive Committee Meeting	Jazzman, Faculty Dining room, O'Hare
3:00PM - 3:50PM	Engaging Liberal Arts Mathematics Students Through Examples From Statistics, David Abrahamson & Rebecca Sparks, Rhode Island College. Beginning with 19th-century records of hits, runs, and errors, statistical measures from the world of sports have always appealed to fans. Recently, the number of measurements available to the fan has exploded, ranging from surprisingly useful things like some of baseball's sabermetrics to silly numbers like pro football's passer rating. Several examples from the mushrooming collection of statistical commentary on sports will be discussed, with an eye to how they can fit in general education mathematics courses.	O'Hare 160
4:00PM - 4:50PM	Green Operations Research at the US Coast Guard Academy and Beyond, Ian Frommer, US Coast Guard Academy. The use of quantitative methods as an aid in decision-making, has long been applied to energy and environmental areas. It is playing an increasingly important role in the challenges of sustainability such as green-house gas reduction, renewable energy, and waste flow and is particularly well suited for undergraduate research projects of a practical and local nature. In this talk I give an overview of work undertaken in "Green OR" and then discuss undergraduate projects I have advised on waste flow optimization, hazardous material reduction, and sustainable lighting. These projects combined OR techniques such as multi-objective linear programming and mixed-integer programming with some common-sense human considerations. I close with suggestions for similar projects that can be undertaken by others at their own institutions.	O'Hare 160

Student Paper Sessions
	O'Hare 106	O'Hare 107
Time (PM)	Speaker & Topic	Speaker & Topic
5:00 - 5:12	Synchronization of Two Pendulums on a Moving Support, Kevin M. Tichy, Western Connecticut State University. A three hundred year old observation made about two pendulum clocks fixed on the same wooden beam would tend to synchronize. This observation was explored by James Pantaleone using two mechanical metronomes on a free floating platform in his 2002 paper "Synchronization of metronomes." We use Lagrangian Mechanics to construct a mathematical model of system that consists of two pendulums with a common free moving support, producing a system of three ODEs that models the motion and dynamics of the system. The behavior of the model is explored using Maple. We investigate the effects of a driving force and friction on the pendula motion.	Fibonacci Nim: How number theory allows you to always be a winner, Nancy Wang, Williams College. Using a beautiful theorem about Fibonacci numbers found by Zeckendorf, we reveal a strategy that will allow us always to win at a neat version of the famous "Nim" game. Behind these fun puzzles are some subtle notions from number theory. We will demonstrate these ideas with a couple of rounds of play.
5:15 - 5:27	Hybrid Trigonometric Polynomial Approximations, Zachary Grant and Sidafa Conde, UMass Dartmouth. Fourier Series approximations are well known for their spectral convergence of data reconstructions on smooth and periodic functions. However, they fail to produce similar convergence when faced with discontinuous problems due to peculiar behavior near the discontinuities. Our work remedies this problem by using a hybrid method. In this method, we use a combination of more flexible polynomial approximations and the classical Fourier reconstructions. We present numerical differences between our methods and other previous methods applied to similar popular problems.	Writing natural numbers in a really cool way: How many terms do we need on average? David Clyde, Williams College. Using a divide & conquer algorithm, we can easily see that every natural number is the sum of distinct, non-adjacent Fibonacci numbers. But how many terms in such a sum do we expect on average? Here we will offer some intuition and answer this interesting question and a recent generalization.
5:30 - 5:42	Exploration of Robust Rumor Spreading Protocols, Charles Drake Poole, UMass Dartmouth. Randomized rumor spreading protocols are classically used to spread information across a network. We start with the model proposed by Doerr-Huber-Levavi where each node must follow certain rules to maintain the robustness of a random protocol to insure against transmission failure. We will explore the wastefulness of algorithms with regard to the topology of the network. Also looked at is rumor spreading on a grid, on a torus, and on various hypertorii.	Finding your own neat Fibonacci identities: Moving from multiples to sums, Cory Colbert, Williams College. Using sums of powers of the golden ratio, we are able to find ways of expressing certain multiples of nearly any Fibonacci number as an explicit sum of distinct, non-adjacent Fibonacci numbers---thus giving an explicit form of Zeckendorf's decomposition in these special classes of numbers. The idea of the proof is a new notion named the "Golden ratio division algorithm."
5:45 - 5:57	Time Series Analysis of Keyboarding Dynamics Using Normal Inverse Gaussian with Generalized Auto-Regression, Sidafa Conde & Charles Drake Poole, UMass Dartmouth. Keyboarding text can be thought of as a process of making transitions from one state to another. Associated with each transition is a real number, time. Similarly, written text gives rise to a discrete time series of keyboard distances between successive symbols. We will discuss how correlating the above time series assists us in building a model of what is being typed from the time intervals between successive symbol pairs. This model is useful in security issues, such as to decipher text through recorded time between successive key strokes, as in Secure Shell (SSH) data. We examine whether the state transition times for keyboarding form a Markov chain.	Continued fractions: How their denominators generate all natural numbers, Gea Shin, Williams College. Every real number can be written as a repeated fraction-within-fraction. This expansion is called a continued fraction. Here we will describe how to find a continued fraction and share an amazing theorem by Ostrowski from the 1930s about the denominators associated with infinitely long continued fractions.

Time	Speaker & Topic	Location
6:00PM - 6:30PM	Reception	Ochre Court, first floor
6:30PM - 7:30PM	Dinner & Teaching Award Presentation	Ochre Court, first floor
7:45PM - 8:45PM	A Mathematician at the Grammies? Kevin Short, University of New Hampshire. This talk will look at the mathematics underlying the analysis of music signals, and how ideas like the uncertainty principle, convolution, partitions of unity, and the (fast) Fourier transform naturally arise in the analysis. Applications to music decomposition, compression and repair will be considered. Some examples will be shown of the work on restoring a 1949 Woody Guthrie wire recording that resulted in a Grammy award in 2008. Other examples may include real-time playback of layered decompositions of music, tracks from a compressed chaotic music synthesizer, and image and video compression. Some related mathematical concepts will be presented if time allows.	O'Hare 160

Saturday, June 12, 2010
Time	Speaker & Topic	Location
8:30AM - 11:00AM	Registration	O'Hare, lobby
9:00AM - 9:50AM	An Introduction to Design Theory, Stephanie Costa, Rhode Island College. We are all familiar with the famous Bridges of Kvnigsberg problem, introduced by Leonhard Euler, which led to the development of the branch of mathematics known as graph theory. Closely related to graph theory is a branch of mathematics known as design theory. We will look at some famous problems in recreational mathematics that can be solved using design theory, such as Kirkmans schoolgirl problem and a variation of Euler's 36 officer problem. We will see how designs can be used to construct balanced statistical experiments and tournaments. Finally, we will talk about some recent results and current research in design theory.	O'Hare 160
10:00AM - 10:30AM	Break
10:30AM - 11:20AM	Check Digits, Keith Conrad, University of Connecticut. Numerical codes, such as credit card numbers, ISBNs on books, and VINs on cars, are ubiquitous. Nearly all of these codes come with a special number, called the check digit, whose purpose is to prevent the codes from being incorrectly processed. We will explain the mathematics behind the design of some of these check digit protocols and see how they are capable of detecting (or not detecting) certain kinds of errors.	O'Hare 160
11:20AM - 11:45AM	Business Meeting	O'Hare 160
Noon - 1:15PM	Lunch	Jazzman, O'Hare
1:15PM - 2:05PM	Battles Lecture: How Always to Win at Limbo, Ed Burger, Williams College. Remember in your days of first-love how you would dream about that special someone and wonder to yourself: "How close are we?" This presentation will answer that question by answering: What does it mean for two things to be close to one another? We'll take a strange look at infinite series and dare to mention a calculus student's fantasy. We'll even attempt to build a series that can be used if you ever have to flee the country in a hurry: we'll either succeed or fail... Will you be at the edge of your seats? Perhaps; but if not, then you'll probably fall asleep and either way, after the talk, you'll feel refreshed. No matter what, you'll learn a sneaky way to always win at Limbo.	O'Hare 160

Contributed Paper Sessions
	O'Hare 106	O'Hare 107	O'Hare 121
Time (PM)	Speaker & Topic	Speaker & Topic	Speaker & Topic
2:15 - 2:30	The Pythagorean Theorem, Peter Ash, Math for the Rest of Us. What could be new and interesting about the Pythagorean Theorem? I will present a few tidbits. There is a beautiful 3-d version of the Pythagorean Theorem that is too little known. It states that the sum of the squares of the areas of three faces of a right tetrahedron is equal to the square of the area of the fourth face. I'll sketch a messy proof using Heron's formula and an easy one using linear algebra. In computer graphics it's often necessary to find the distance between two points in the plane as quickly as possible, that is without taking a square root or multiplying real numbers. Fortunately, only an approximation to the distance is necessary. I'll show how this is done and how accurate the approximation is. You can think of the result as an "approximate Pythagorean Theorem." If time permits, I'll show a couple of non-routine problems for students based on the Pythagorean Theorem.	Quadrature Methods for Multilevel Data Analysis, Jacob Gagnon, University of Massachusetts Amherst. Longitudinal and cluster data appear in a wide variety of disciplines: education, epidemiology, biology, medicine, and sociology. Unfortunately, likelihood based analysis of these data structures requires integration of very high dimensional integrals (>100 dimensions). Many numerical methods have been proposed to perform high dimensional integrations such as second order Laplace approximation, high order Laplace approximation, adaptive Gaussian quadrature, Markov Chain Monte Carlo, and spherical radial integration. In this talk we propose a new integration technique, Hierarchical Spherical Radial Quadrature, which is applicable to high dimensional integrals involving hierarchical data. We discuss the time complexity of our algorithm and compare our approach with other integration techniques.	Teaching Undergraduate Number Theory Using the Moore Method, Hema Gopalakrishnan, Sacred Heart University. A first course in undergraduate Number Theory requires little prerequisite knowledge of students other than some level of mathematical maturity to write proofs. It is therefore a good course to enable mathematics majors to become more independent in learning mathematics by conjecturing theorems through concrete examples before attempting a formal proof. In this talk, I will describe how my course was structured and my experience in teaching it without lectures using a form of the Moore method.
2:35 - 2:50	What I Learned about Using Online Homeworks from Student Feedback, Laura McSweeney, Fairfield University. There are many reasons why instructors choose to use an online homework system in their mathematics courses. A variety of online systems exist and an extensive literature search finds that online homework systems "do no harm" and can, in fact, help students to learn. In this presentation, we examine how students' feedback can be used to judge the impact and effectiveness of online homework systems on their learning.	Logistic Curves in the Mandelbrot Set: Analyzing the Tilt of Julia Sets, Lynette Boos and Daniel J. Ford, Providence College. We focus on the effects of the complex seed c on the "tilt'' of the filled Julia set defined by fc(z) = z2 +c , an iterative map in the complex plane. We define tilt as the slope from the origin to the Julia set's largest modulus (except for real c > 0, where it is defined as 90 degrees, and for c = 0, where it is indeterminate). We attempt to analyze the tilt for any c within the bounds of the Mandelbrot set, since otherwise K(fc) is not connected and called Fatou dust.	Summands of the normal bundle of a rational curve in a hypersurface, Bin Wang, Rhode Island College. Rational curves are the simplest curves in algebraic geometry. Topologically they are just 2 dimensional spheres. Their intrinsic properties are simple and all understood. But how a variety X contains them is a big mystery. Evidently this containment gives invariants of the variety X. This phenomenon does not only appear in the mathematics but also in the theoretical physics (String Theory). Their normal bundles in X determine their moving properties in X. In our paper we give a bound (6-h)d-2 to the summands of a normal bundle of a rational curve in a hypersurface, where h and d are degrees of the rational curve and the hypersurface. This bound in the quintic (h = 5) case is a new result and in other cases gives a different proof to many known results. For instance it reproves Clemens' result: there are no smooth rational curves in a general hypersurface of degree larger than 6.
2:55 - 3:10	Group Quizzes in Calculus, Fei Xue, University of Hartford. In this talk I will describe how I use group quizzes in Calculus. Group quizzes allow students to work collaboratively to better understand the content of the course. Additional benefits and some challenges of group quizzes will also be discussed.	Hamiltonian Decomposition of Hypercubes, Joseph E. Fields, Southern Connecticut State University. Even-dimensional hypercubes may be decomposed into edge-disjoint Hamiltonian circuits. This fact has consequences for fault tolerant communication schemes between computing elements that correspond to the nodes of a hypercube - a fairly popular topology in supercomputer architectures. Until recent work by Bae and Bose, only a non-constructive proof was known. We will present an alternate approach.

---

Mathematical Association of America Spring NES Meeting - June 11-12, 2010 - Salve Regina University, Newport, RI.