Invited Addresses
 Erik Demaine, Massachusetts Institute of Technology
I love algorithms in general, and geometric folding in particular. I enjoy doing research that many people---not just mathematicians---can appreciate as fun, interesting, and beautiful. These lectures describe some of my research that I think best achieves this goal, as well as some open problems that I hope will inspire students to continue in this vein.
Erik Demaine is Associate Professor and Esther and Harold E. Edgerton Professor in computer science at the Massachusetts Institute of Technology.
Demaine’s research interests range throughout algorithms, from data structures for improving web searches to the geometry of understanding how proteins fold to the computational difficulty of playing games. He received a MacArthur Fellowship (2003) as a “computational geometer tackling and solving difficult problems related to folding and bending–moving readily between the theoretical and the playful, with a keen eye to revealing the former in the latter.”
Recently, Demaine published a book about folding, together with Joseph O’Rourke, called Geometric Folding Algorithms: Linkages, Origami, Polyhedra, (Cambridge University Press, 2007). He has also co-edited Tribute to a Mathemagician (A K Peters, 2003), in honor of the influential mathemagician Martin Gardner.
LECTURE 1: MATHEMATICS MEETS ART, PUZZLES, AND MAGIC
Thursday, July 31, 10:30 a.m. – 11:20 a.m.
Solving and designing puzzles, creating sculpture and architecture, and inventing magic tricks all lead to fun and interesting algorithmic problems. I will describe some of our explorations into these areas (much together with my father, Martin Demaine).
PUZZLES. Solving a puzzle is like solving a research problem. Both require the right cleverness to see the problem from the right angle, and then explore that idea until you find a solution. The main difference is that the puzzle poser usually guarantees that the puzzle is solvable. Puzzles also lead to the meta-puzzle of how to design algorithms that themselves can design families of puzzles.
ART. Elegant algorithms are beautiful. A special treat is when that beauty translates visually. Sometimes this is by design, when you develop an algorithm to compose artwork within a particular family. Other times the visual beauty of an algorithm just appears, without anticipation.
MAGIC. Mathematics is the basis for many magic tricks, particularly “self-working'' tricks. One of the key people at the intersection of mathematics and magic is Martin Gardner, whose work has inspired several of the results described in this talk. Algorithmically, our goal is to automatically design classes of magic tricks.
LECTURE 2: ORIGAMI, LINKAGES, AND POLYHEDRA: GEOMETRIC FOULDING ALGORITHMS
Friday, August 1, 9:30 a.m. – 10:20 a.m.
What forms of origami can be designed automatically by algorithms? What shapes can result by folding a piece of paper flat and making one complete straight cut? What polyhedra can be cut along their surface and unfolded into a flat piece of paper without overlap? When can a linkage of rigid bars be untangled or folded into a desired configuration? Geometric folding algorithms is a branch of discrete and computational geometry that addresses these and many other intriguing questions. I will give a taste of the many results that have been proved in the past few years, as well as the several exciting open problems that remain open. Many folding problems have applications in areas including manufacturing, robotics, graphics, and protein folding.
LECTURE 3: TRANSFORMERS: RECONFIGURABLE ROBOTS AND HINGED DISSECTIONS
Saturday, August 2, 9:30 a.m. – 10:20 a.m.
How might we build reconfigurable robots like Transformers or Terminator 3? There are several geometric folding algorithms related to this question. I will focus on one such problem: designing a hinged chain of polygons or polyhedra that can be folded into several desired shapes. In particular, I will describe a brand new solution to an open question that goes back implicitly to 1902 and has been studied extensively in the past ten years: do every two polygons of the same area have such a hinged dissection? It turns out that they do, as do any finite collection of polygons. Furthermore, the hingings can be folded continuously without self-intersection, and the number of pieces is somewhat reasonable. Our result (joint with Timothy Abbott, Zachary Abel, David Charlton, Martin Demaine, and Scott Kominers) generalizes and indeed builds upon the result from 1814 that polygons have common dissections (without hinges). We also extend our result to edge-hinged dissections of solid 3D polyhedra that have an (unhinged) dissection, as determined by Dehn's 1900 solution to Hilbert's Third Problem. All of our proofs are constructive with algorithms to compute the hinged dissections and motions between configurations. In addition to reconfigurable robots, hinged dissections have possible applications to programmable matter and nanomanufacturing.
MAA INVITED ADDRESS
INTELLECTUAL NEED AND ITS ROLE IN MATHEMATICS INSTRUCTION
Guershon Harel, University of California at San Diego
Guershon Harel is Professor in the Mathematics Department at the University of California, San Diego. Previously he served as Associate Editor of the American Mathematical Monthly, co-editor of the Research in Collegiate Mathematics Education Series, and Chair of the Editorial Board of the Journal for Research in Mathematics Education, and currently, he serves on the Editorial Board of ZDM-The International Journal on Mathematics Education. Harel has research interests in cognition and epistemology of mathematics and their application in mathematics curricula and the education of mathematics teachers. Until the mid-nineties, Harel’s research interest revolved around the Multiplicative Conceptual Field and Advanced Mathematical Thinking, with particular attention to the concept of function, proof, and the learning and teaching of linear algebra. He is co-editor of two books in these areas: The Development of Multiplicative Reasoning in the Learning of Mathematics and The Concept of Function; Aspects of Epistemology and Pedagogy. Since the mid-nineties, he centered his attention on the learning and teaching of proof and on the development of a conceptual framework for the teaching of mathematics, called DNR-based instruction in mathematics.
Thursday, July 31, 8:30 a.m. – 9:20 a.m.
Most students, even those who desire to succeed in school, are intellectually aimless in mathematics classes because often they do not realize an intellectual need for what we intend to teach them. The notion of intellectual need is inextricably linked to the notion of epistemological justification. Generally speaking, epistemological justification refers to the learner's discernment of how and why a particular piece of knowledge came to be. We will discuss historical and philosophical aspects of these two notions, as well as ways teachers can be aware of students' intellectual need and address it directly in the undergraduate mathematics classroom.
MAA INVITED ADDRESS
ECOLOGICAL AND EVOLUTIONARY CONSEQUENCES OF SPECIES INTERACTIONS
Claudia Neuhauser, University of Minnesota
Claudia Neuhauser is HHMI Professor and head of the Department of Ecology, Evolution and Behavior (EEB) at the University of Minnesota, Twin Cities and Director of the Center for Learning Innovation at the University of Minnesota, Rochester. She received her Diploma in mathematics from the Universität Heidelberg (Germany), and a PhD in mathematics from Cornell University. Before joining EEB, she was a faculty member in mathematics departments at the University of Southern California, UW-Madison, University of Minnesota, and UC Davis.
Her work is at the interface of ecology and evolution. She investigates effects of spatial structure on community dynamics; in particular, the effect of competition on the spatial structure of competitors and the effect of symbionts on the spatial distribution of their hosts. In addition, her research in population genetics has resulted in the development of statistical tools for random samples of genes.
Neuhauser is currently director of an NSF funded Integrative Graduate Education Research Training (IGERT) grant on “Non-equilibrium dynamics across space and time: a common approach for engineers, earth scientists, and ecologists,” which provides interdisciplinary education and training to graduate students from ecology, geology, civil engineering, and computer science. Her interest in furthering the quantitative training of biology undergraduate students has resulted in a textbook on Calculus for Biology and Medicine.
Thursday, July 31, 9:30 a.m. – 10:20 a.m.
Community genetics is a synthesis of community ecology and population genetics. It takes into account the interplay between genetic variation and community dynamics, which is of importance when selective forces are strong. Selective forces may be particularly strong when systems undergo large perturbations, such as habitat fragmentation or introduction of new organisms. Mathematical modeling can play an important role in predicting the outcome of such interactions and in assessing when both ecological and evolutionary forces need to be taken into account. We will discuss models on host-symbiont systems, evolution of resistance to transgenic plants, and persistence of populations in fragmented habitats to highlight the importance of including both ecological and evolutionary forces into account.
MAA LECTURE FOR STUDENTS
SUDOKU: QUESTIONS, VARIATIONS AND RESEARCH
Laura Taalman, James Madison University
Laura Taalman is an Associate Professor of Mathematics at James Madison University. She received her PhD inmathematics from Duke University, and her undergraduate degree from theUniversity of Chicago. Her research includes singular algebraic geometry,knot theory, and the mathematics of puzzles. She is the author of atextbook that combines calculus, pre-calculus, and algebra into onecourse, and is one of the organizers of the Shenandoah UndergraduateMathematics and Statistics (SUMS) Conference at JMU.
Taalman is a recipientof the Trevor Evans Award and the Alder Award from the MathematicalAssociation of America. As part of Brainfreeze Puzzles, she is an authorof the puzzle book Color Sudoku.
Thursday, July 31, 1:00 p.m. – 1:50 p.m.
Sudoku puzzles and their variants are linked to many mathematical problems involving combinatorics, Latin squares, magic squares, polyominos, symmetries, computer algorithms, the rook problem, graph colorings, and permutation group theory. In this talk we will explore variations of Sudoku and the many open problems and new results in this new field of recreational mathematics. Many of the problems we will discuss are suitable for undergraduate research projects. Puzzle handouts will be available for all to enjoy!
MAA INVITED ADDRESS
THE CHAOTIC EVOLUTION OF NEWTON’S UNIVERSE
Donald Saari, University of California at Irvine
As an undergraduate at Michigan Technological University then graduate student at Purdue, Dr. Saari found he fell in love with whatever mathematics topic he happened to be studying at the moment. Finally settling on dynamics his thesis analyzed the collision orbits of the Newtonian N-body problem.
After graduate school he took a postdoctoral position in the Yale University Astronomy Department, and a year later joined the Mathematics Department at Northwestern University where he served as chair of the department and became the first Pancoe Professor of Mathematics. Much of his early research centered on dynamical issues such as the evolution of the universe. Through conversation with students he found himself fascinated by the challenges of the social sciences—an interest that resulted in his becoming a member of the Department of Economics, the Department of Applied Mathematics and Engineering Science, and the Center for Mathematical Studies in Economics. His research shifted to emphasize dynamics of the social sciences, such as the “Invisible Hand” story, and to modify dynamical concepts to address concerns coming from the social and behavioral sciences. Becoming intrigued by the innovative, high-powered research being done at the UCI IMBS, after three decades at NU, in July 2000, he moved to UCI where he was appointed a Distinguished Professor of Economics and Mathematics as well as the Director of the Institute for Mathematical Behavioral Sciences.
As for other activities, Dr. Saari is the Chief Editor of the Bulletin of the American Mathematical Society and on editorial boards of several journals on analysis, dynamics, economics, and decision analysis; a member of the National Academy of Sciences, the AAAS, a Guggenheim Fellow, the past chair of the US National Committee of Mathematics, chair of the US delegation to the 2002 general assembly of the International Mathematical Union, and a member of several NRC committees including Math Science Education Board. His honorary doctorates come from Purdue, Université de Caen, and Michigan Technological University. He says he is particularly proud of receiving over 10 awards for teaching, being honored (twice at Northwestern) by students with a “Most Influential Professor” award, and, for over 20 years, serving as the “Santa Claus” for departmental Christmas parties.
Friday, August 1, 8:30 a.m. – 9:20 a.m.
After solving the two-body problem, Newton claimed that the three-body problem gave him a headache. It should; this is where chaos was discovered. In this talk, I will describe some of this story while showing why "chaos" must be expected in n-body systems. Then I will describe the asymptotic evolution of all n-body systems; i.e., how our universe evolves.
BUILDING MATHEMATICAL COMMUNITIES
T. Christine Stevens, Saint Louis University
T. Christine Stevens is Professor of Mathematics and Computer Science at Saint Louis University, where she served for five years as department chair. A graduate of Smith College, she earned her PhD in mathematics at Harvard University. Her research interests are in topological groups, especially Lie groups, and in the history of mathematics. In 1994, together with the late Jim Leitzel, she founded Project NExT (New Experiences in Teaching), an MAA program that has thus far helped over 1000 new mathematics faculty to launch their careers. In 1984-85, she was the AMS/MAA/SIAM Congressional Science Fellow. In this capacity, she worked as a legislative assistant on issues involving defense, arms control, higher education, and science and technology. Her service to professional organizations includes membership on numerous committees dealing with education, science policy, and minority participation in mathematics. She also served on a committee of the National Research Council that published a report entitled “Evaluating and Improving Undergraduate Teaching in Science, Technology, Engineering, and Mathematics.” In 1997 she received the MAA’s Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics, and in 2004 she received the MAA’s Yueh-Gin Gung and Dr. Charles Y. Hu Distinguished Service to Mathematics Award. This award is made for service to mathematics that has been widely recognized as extraordinarily successful, and which influences the field of mathematics or mathematical education in a significant and positive way on a national scale. Largely because of her work with Project NExT, in 2005 she was named a Fellow of the American Association for the Advancement of Science.
Friday, August 1, 10:30 a.m. – 11:20 a.m.
Now in its fifteenth year, Project NExT (New Experiences in Teaching) is an MAA program that has welcomed more than a thousand new Ph.D.s into our profession. We will describe some of the achievements of this remarkable community of mathematical scientists and explore their impact on the mathematical community at large. We will also reflect on the nature of professional communities and the role that they might play in pursuing the MAA's mission of advancing the mathematical sciences.
NAM DAVID BLACKWELL LECTURER
RANDOM DYNAMICS AND MEMORY: STRUCTURE WITHIN CHAOS
Salah-Eldin A. Mohammed, Southern Illinois University-Carbondale
Salah-Eldin A. Mohammed is Professor and Distinguished Scholar in the Department of Mathematics, Southern Illinois University in Carbondale, Illinois. Born on May 20, 1946, he grew up in an obscure village in Sudan and earned his PhD in mathematics from the University of Warwick, England in 1976. His research areas include stochastic analysis; deterministic and stochastic hereditary dynamical systems; probabilistic analysis of PDEs, and stochastic PDEs. He has given over 75 invited presentations nationally and internationally, received numerous research awards, and has maintained professional collaborations around the world.
Friday, August 1, 1:00 p.m. – 1:50 p.m.
We give an overview of the dynamics and long-term evolution of probabilistic models with finite memory. Such models are widely used to analyze dynamical systems whose evolution is influenced by random fluctuations and past history. These models are important in diverse areas such as signal processing, option-pricing, economic and labor models, aircraft dynamics, materials science and population dynamics. The dynamics of random systems with memory is treated at two different levels: distributional and pathwise. On the distributional level, the dynamics is described in terms of semigroup theory; on the pathwise level, the ergodic theory of stochastic flows is used to characterize the long-term behavior of the random evolution in the models near their statistical equilibria. This characterization is expressed via the existence of random flow-invariant stable and unstable manifolds near statistical equilibria. Thus, in spite of its inherent randomness, the system dynamics generically exhibits a definite structure near its statistical equilibria! A key idea behind the analysis is to encode the system memory by “slicing'' each random evolution path at any time. Each slice is viewed as representing an infinite-dimensional “state" of the random dynamical system at a particular moment. The existence of stable and unstable manifolds is established using a combination of diverse techniques from probability, stochastic calculus, stochastic differential equations, functional analysis, ergodic theory and dynamical systems. Further details, please visit the weblink: http://sfde.math.siu.edu/Blackwellabstract1.pdf
AWM-MAA ETTA Z. FALCONER LECTURE
THE USE AND ABUSE OF STATISTICS IN THE MEDIA
Rebecca Goldin, George Mason University
Rebecca Goldin received her PhD from MIT in 1999 under the guidance of Victor Guillemin. She then went to the University of Maryland with a National Science Foundation Postdoctoral Fellowship before joining the faculty at George Mason University, where she is currently an associate professor of mathematics. She is also the director of research at STATS, a nonprofit affiliate of George Mason which aims to educate the public and journalists about the responsible use of statistics in reporting. Recently, Goldin was elected to the council of the American Mathematical Society, where she serves on the Science Policy Committee. Goldin’s mathematical research centers on questions in symplectic geometry and group actions on manifolds.
She has had numerous grants from the National Science Foundation to support her work, and has attended conferences and given talks in many international venues. Last year, Goldin became the first recipient of the Ruth I. Michler Award.
Saturday, August 2, 8:30 a.m. – 9:20 a.m.
The use and abuse of statistics in the media
News increasingly depends on a careful dissection of numbers. Statistics are everywhere, from how many people are not covered by health insurance to whether Vitamin E is good for you or not. Yet for being so prevalent, statistics are awfully badly understood by the general public.
In this talk, I'll illustrate how the press can misuse and even abuse statistics. Since news sources are the main avenue by which the public understands many public health issues, these misguided representations of science can actually shape public policy, legislation, and individual choices. We will see why it is so important that media writers understand basic concepts from statistics, epidemiology and even toxicology. I will also show how powerful the work can be when the press goes beyond politics and morality to get the science right.
These examples come from my experience as the research director for Statistical Assessment Service (STATS), a nonprofit media education and watchdog group affiliated with George Mason University, where I am a professor of mathematics as well. STATS takes critical aim at the poor use of statistics to justify false claims or to back-up ideological agendas, while serving as a resource for journalists and producers who want to engage in high-level responsible reporting that takes into account what the science says, what it doesn't, and what it can't.
Mark Twain popularized the quote that "There are three kinds of lies: lies, damn lies, and statistics." While this quote suggests the scary idea that statistics can be manipulated to say anything, I will argue that statistics can tell us lots of useful things when used appropriately, and that the more the media does this for us, the more educated we can be as news consumers, and the better we will be at truly evaluating risk for ourselves and others.
MAA INVITED ADDRESS
GENERALIZING "2": THE COMBINATORICS OF l-SEQUENCES
Carla Savage, North Carolina State University
Carla D. Savage received the PhD in mathematics from the University of Illinois in 1977, under the direction of David E. Muller. She worked in the area of parallel algorithms and architectures until 1988 when, inspired by talks of Donald Knuth and Herbert Wilf at the SIAM Discrete Math Conference, she became interested in combinatorics.
Since then she has worked (with many wonderful collaborators) on Gray codes, Hamilton cycles, the middle levels problem, Venn diagrams, integer partitions, lecture hall partitions, etc. Her special interest is in recursive techniques that unveil the stucture of a class and exploit it to count, generate, represent, and relate combinatorial families. Recent efforts focus on the family of integer partitions and tools for linear Diophantine enumeration.
She has been on the editorial board of the SIAM Journal on Discrete Mathematics since 1997 and is currently Chair of the SIAM Activity Group on Discrete Mathematics.
Saturday, August 2, 10:30 a.m. – 11:20 a.m.
The l-sequences, cousins of the Fibonacci sequence, are defined by the recurrence a(n) = l a(n-1) - a(n-2), with initial conditions
a(0)=0, a(1)=1. They arise in diverse areas of combinatorics and we will highlight some of their fascinating properties. Many fundamental identities in combinatorics involve binomial coefficients and their interpretations. We use l-sequences to define the ``l-nomial coefficent'', a generalization of the binomial coefficient, and consider extending classical binomial combinatorics to the ``l-world''. |
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