Real Estate in Hyperbolic Space: Investment Opportunities for the Next Millennium
Mel Slugbate, Real Estate Agent, Slugbate and Mossbutter Real Estate, Williamstown, MA (Sponsored by his brother-in-law, Colin Adams, Williams College)
Abstract: The sky-high stock market got you nervous? What goes up must come down? Antsy about stocks, bonds and mutual funds? Afraid of risky investments in Euclidean space? Then real estate in hyperbolic space is for you.
We will discuss the enormous potential of this new investment opportunity and describe the many fascinating properties of hyperbolic space that make it such an attractive place to live. This is the financial equivalent of the 1980’s junk bond. Don’t miss it. Bring your checkbook and credit references! No previous math or real estate background assumed! Recommended for students and faculty alike! Roger Ebert says, “Two fingers up!”
(Mel Slugbate is a real estate agent in Williamstown, MA. His interest in mathematics comes from his brother-in-law, Colin Adams, who is Mark Hopkins Professor and Chair of the Mathematics Department at Williams College. Colin Adams received his Ph.D. from the University of Wisconsin-Madison in 1983. He is particularly interested in the mathematical theory of knots, their applications and their connections with hyperbolic geometry. He is the author of “The Knot Book”, an elementary introduction to the mathematical theory of knots and co-author of “How to Ace Calculus: The Streetwise Guide”, which has been as high as #62 at amazon.com. A recipient of the Deborah and Franklin Tepper Haimo Distinguished Teaching Award from the MAA in 1998, he is also the Polya Lecturer for the MAA for 1998-2000, and a Distinguished Sigma XI Lecturer for 2000-2002.
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What is Constructive Mathematics?
Fred Richman, Florida Atlantic University
Abstract: Constructive mathematics is “the math of least existence”, according to a headline in the Las Cruces Sun News. I like to describe it as ordinary mathematics done without appeal to the law of excluded middle. It is thinking algorithmically without thinking about algorithms.
I will illustrate the ideas involved by considering two theorems: (1) There is a digit that appears infinitely often in the decimal expansion of pi, and (2) The Intermediate Value Theorem
Fred Richman received his AB from Princeton University in 1958 and did his PhD at the University of Chicago with Irving Kaplansky. His main research interests are abelian group theory and constructive mathematics. He was involved in the development of Scientific WorkPlace, a word-processor/computer-algebra system. Professor Richman was a member of the mathematics department, New Mexico State University, 1963-1989 before coming to Florida Atlantic University in 1990.
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Introductory Maple Workshop
Doug Jones, Moana Karsteter, Jerry McBee, Tallahassee Community College
In this “hands on” workshop, you will learn some basic Maple commands and how to use them to solve a variety of problems. Internet interface will also be demonstrated.
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Environmental Mathematics – Visual, Qualitative, and Computational
Ben Fusaro, Florida State University
This Calculus-free approach models the target system with a simple energy diagram. This diagram becomes the basis for a qualitative Energy versus Time solution graph and a Flow Equation (a DE in disguise). The Flow Equation is solved numerically via a calculator, spread sheet or computer program. The results are used to construct an Energy versus Time graph.
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ALEKS (Assessment in LEarning and Knowledge Space) Hands-On Workshop
McGraw Hill
ALEKS (Assessment LEarning in Knowledge Space) is an artificial Intellegence-based system for individualized math learning available over the World Wide Web. The ALEKS system was developed with a multimillion-dollar grant from NSF. ALEKS delivers precise qualitative assessment of students' math knowledge and guides them toward mastery of curricular goals.
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Distance Learning with Demonstration: The Global Classroom Project
Marcelle Bessman, Jacksonville University, and Douglas Quinney, Keele University
The overriding goal of this project was to develop a model for distance learning instruction using the World Wide Web that incorporates cooperative learning techniques and team teaching with a distant instructor, and stresses written, oral, and technological communication skills. We will discuss (1) the project from our respective perspectives as local and “visiting” instructor; (2) the reaction of students to the project; (3) plans for extending the scope of the project.
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Beauty of Mathematical Patterns
Shiv Aggarwal, Embry-Riddle Aeronautical University
Abstract: In addition to historical anecdotes, some beautiful number patterns, starting with Pythagorean triplets, will be presented. References will be made to the works of Fermat, Euler, Ramanujum and Jacobi.
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So You Want to Go Online! Issues and Strategies
Marcelle Bessman, Ph. D., Jacksonville University
Abstract: This presentation will look at the why and how of going online on an Intranet or the Internet. Among the issues to be discussed are determining the target population, setting goals, format, and synchronicity.
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Emphasizing a Mathematics Course for Prospective Teachers of Grades K-6: Motivated Reasoning and Computer Use
Steven Blumsack, Mathematics Department, Janice Flake, Educational Theory and Practice, Erich Nold, Mathematics Education, Florida State University
Abstract: The course addresses State and National standards, using spreadsheets, geometry software, hands-on modeling activities, and class discussions. We engage prospective teachers in both self-motivated mathematical reasoning and pedagogical explanation. In assigning free form portfolios and providing oral feedback time, assessment becomes integral in motivating students’ genuine questions.
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The Sunshine State Scholars Program
William Caldwell, University of North Florida
Abstract: The scholars program began in 1998 to recognize outstanding seniors in mathematics and science in Florida. The current status and future of the project will be discussed.
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Engineering Calculus at the University of Miami: CAS, Connections to Physics, etc
Chris Cosner, University of Miami
Abstract: A few years ago the University of Miami revised its freshman-engineering curriculum. The current curriculum is a type of learning community where there is some coordination (although it is relatively weak) between calculus and physics. The calculus course uses the CAS “MAPLE” in labs. This talk describes our curriculum.
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Student Construction of Decision Trees in Second-Semester Calculus
Pam Crawford, Jacksonville University
Abstract: Results will be presented of a study involving two structured tasks promoting student construction of decision trees for techniques of integration and tests for convergence of series. Students were asked to comment on tasks, particularly regarding benefit on student awareness of integration techniques and tests for convergence of series.
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Periodic Solutions of a Class of Ordinary Differential Equations
Harley Flanders, Jacksonville University and University of North Florida
Abstract: The system dx/dt = –yj, dy/dt = xk, where j and k are odd integers, has periodic solutions. The ratio of the periods for (j,k) and for (k,j) is always an algebraic number. These, and other relations, all determined experimentally, are rather unexpected. Another “fact”: the periods for (j,j) approach limit as j goes to infinity.
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Success of Students in Entry Level Mathematics with the Aid of Integrated Review Classes
Bahram Foroughi, Embry Riddle-Aeronautical University
Abstract: A procedure was developed for placing students into early semester review classes. The purpose of this is to aid them in an entry-level pre-calculus course. After four sessions of review, they were returned to their regular class or a lower level class; results of the study will be given in the presentation.
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New Bounds for Large Regular Planar Graphs
Erich Friedman, Stetson University
Abstract: Lately there has been considerable progress and interest in the “Degree-Diameter” problem: to find the largest graph with specified maximum degree and diameter. We consider the same problem restricted to regular planar graphs, and improve the best known lower and upper bounds. We give lots of pictures and a few proofs.
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Difficulties in Assessing Students’ Understanding of Mathematics in an Online Course.
Alicia Giovinazzo
Abstract: This paper illustrates difficulties that exist when assessing students’ understanding of mathematics in an online mathematics course. These illustrations focus on the use of whiteboards and high-quality audio and video in the delivery of tests of an online Intermediate Algebra I course for college students.
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The History of the Theorem of Pythagoras
Shamita Dutta Gupta, Florida International University
Abstract: An introduction to the various forms of the Pythagorean Theorem from ancient times.
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Mathematics at Indian Tribal Colleges
Don Hill, Florida A&M University
Abstract: In 1998 I visited ten of the thirty Indian Tribal Colleges located in the USA. From an historical view we will look at the similarities of these colleges and their strengths and weaknesses.
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A (as much as possible) Non-technical Look at Wiles’ Proof of Fermat’s Last Theorem
Scott H. Hochwald, University of North
Abstract: I will tell how Wiles used elliptic curves to prove Fermat’s Last Theorem. Some of this information will be communicated through pictures of various elliptic curves. At the conclusion of the talk you’ll be able to add points on elliptic curves.
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Laboratories in Elementary Statistics
Bob Hollister, Jacksonville University
Abstract: Comments (mostly favorable) on the use of laboratories in an elementary statistics course.
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Jordan Forms of Induced Linear Transformations between Wedge Products of Vector Spaces
John Hunter, University of Central Florida
Abstract: Given a linear transformation from a vector space into itself and knowing the Jordan form of that linear transformation; we ask the question: What is the Jordan form of the induced linear transformation which takes the k-fold wedge product into itself?
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Some Problems Related to maxima and minima
M.S.Jagadish, Barry University
Abstract: In the usual calculus courses many interesting problems related to maxima-minima cannot be dealt with because they use the calculus of variations. However there are problems that can be solved without the formal use of variational calculus. This talk presents some problems of this kind related to finding shortest paths.
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Quandles and State-Sums
Daniel D. Jelsovsky, University of South Florida
Abstract: Quandles are algebraic structures that were designed specifically for use in knot theory. From these quandles, we can create a coloring of knots, and a new knot invariant, the state-sum. This talk is based on the work of J.S. Carter, D. Jelsovsky, S. Kamada, L. Langford, and M. Saito.
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The Mathematics Major in the U.S., 1945-1995
Chuck Lindsey, Florida Gulf Coast University
Abstract: In this talk we provide an overview of the evolution of the requirements for a Bachelor’s degree in mathematics during the second half of the 20th century. Using catalogs of a sample of American universities, “typical” mathematics programs at ten-year intervals from 1945-1995 will be presented. The results will be used to initiate a discussion of the current state of the undergraduate major and desirable directions for progress.
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Is Calculus Rigorous?
Lubomir Markov, Barry University
Abstract: This presentation will deal with some of the subtle inconsistencies typically found in an elementary (and often times advanced) calculus course, as well as various ways of avoiding them. Special attention will be paid to different definitions of the exponential and trigonometric functions and their inverses.
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The Zen of Mathematics Homework
Gregory McColm, University of South Florida
Abstract: One important thing we want to teach our students is how to solve hard problems. We take a tour through old-fashioned pedagogy, and modern cognitive science, and see where they agree. We look at techniques used by writing, art, and even (ancient) philosophy teachers, and consider applications to mathematics teaching.
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Magic Squares — An Artful Application
Cynthia McGinnis, Okaloosa — Walton Community College
Abstract: Magic Squares are arrays of numbers in which the sum of each row, column, and diagonal is identical. There are varying methods for constructing Magic Squares, and in the technological world, computer programs can produce Magic Squares. This paper discusses various methods of constructing Magic Squares and the captivating visual effects of Magic Square art.
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Modeling Data Sets in College Algebra
Michael Nancarrow & Sanjay Rai, Jacksonville University
Abstract: Methods of providing college algebra students with experience searching for, recognizing, modeling, and reporting about linear and exponential data will be discussed. Use of the Internet to gather data will be emphasized. Specific data resources, sample assignments, and examples of student work provided.
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Sowing Games
Deborah Nelson, University of South Florida
Abstract: We will look at a combinatorial game called “Beans and Pots”. We will explore John Conway’s game values applied to this game. We will also look at game trees for this game, and discuss early results of ongoing investigation of the positions of this game.
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A Quintic Approach to Teaching Limits.
Deepankar Pal and Jie Gao
Abstract: The idea of limits is so important in Calculus. When limits are taught graphically, numerically, analytically, by epsilon-delta definition and computer algebra system for verification, the students seem to have a more comprehensive understanding of limits.
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On a Student Research Project in Epidemiology
Sanjay Rai, Jacksonville University
Abstract: This talk will present a student research project in Epidemiology. First a brief description of population biology of infectious diseases will be given. SIR, SIRS and a disease transmission model with a population of varying size will be introduced. Local stability analysis of the disease transmission model with a population of varying size will be introduced.
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Folding and Fanning Complete Even Unimodular Lattices
Katherine Roegner, Eckerd College
Abstract: An algebraic method for studying even unimodular lattices with complete root systems will be presented. A brief explanation of how this tool can be used to aid in classification problems is also given.
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The Analytic Continuation of the Fibonacci Numbers
Sam Sakmar, University of South Florida
Abstract: Similar to the even and odd continuations of the partial waves in high energy scattering theory we give even and odd continuations of the Fibonacci Numbers. The relations between Fibonacci Numbers have their counter-parts in continuum form, like integrals. We also derive sum formulas.
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Properties of Tournaments among Well Matched Players
James Weaver, University of West Florida (with C. Eschenbach, Georgia State University; F. Hall, Georgia State University; R. Hemasinha, University of West Florida, S. Kirkland, University of Regina; Z. Li, Georgia State University; B. Shader, University of Wyoming; J. Stuart, University of Southern Mississippi)
Abstract : In an n player round robin tournament, each player plays n-1 matches, one match against each of the other n-1 players.. We are interested in understanding tournament matrices and the corresponding tournaments among players who are well matched in the sense that each player has won essentially half of the matches he or she has played.
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Why will 2003 Divide the Numerator of
Li Zhou, Polk Community College University
Abstract: I'll give an elementary proof to the result: If p>3 is a prime, then there exists a positive integer m such that the numerator of the fraction 1 - 1/2 + 1/3 - 1/4 + ... + ((-1)^(m+1))/m is divisible by p. The result is a solution and generalization to Problem 657 in College Mathematics Journal (9/99 issue).
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A Calculus Course for Business Students
Raymond Young, Embry-Riddle Aeronautical University
Abstract: Research done in the past teaching business majors showed some methods that improved results. That research is reconsidered with current students.
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