On November 6, 2012, voters will go to the polls to choose our next president. We vote, but how are our votes tallied to give the winner? In 1787, the Constitutional Convention established our rather unusual electoral college which necessitates an assignment of representatives to the states; how is this allocation done?

Karen Saxe is Professor of Mathematics at Macalester College, and current Chair of the Department of Mathematics, Statistics, and Computer Science. After receiving her Ph.D. at the University of Oregon, she held a FIPSE post-doctoral fellowship at St. Olaf College before joining the faculty at Macalester. Her teaching skill has been recognized with the Mathematical Association of America North Central Section's Distinguished Teaching Award, and with the Macalester College Excellence in Teaching Award. She is current Editor of the MAA's Anneli Lax New Mathematical Library, and is on the editorial board of the MAA's Math Horizons. Karen has been a resource in Minnesota on redistricting, consulting with city governments, and recently served on Minnesota Citizens Redistricting Commission, created to draw congressional districts following the 2010 census. This election season semester she is team-teaching a course on Math and Democracy with a political scientist.

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Convex polyhedra are familiar objects. Cubes and pyramids are common in kindergartens. Polyhedra, in their high-dimensional versions, are widely used in applied mathematics. Their beauty and simplicity appeal to all, but very few people know of the many easy-to-state but difficult-to-solve mathematical problems that hide behind their beauty.This lecture introduces the audience to some fascinating open questions on the frontiers of mathematical research and its applications.

Jesus De Loera received his B.S. degree in Mathematics from the National University of Mexico in 1989, a M.A. in Mathematics from Western Michigan in 1990, and his Ph.D in Applied Mathematics from Cornell University in 1995. An expert in the field of discrete mathematics, his work approaches difficult computational problems in applied combinatorics and optimization using tools from algebra and convex geometry.

He has held visiting positions at the University of Minnesota, the Swiss Federal Technology Institute (ETH Zurich), the Mathematical Science Institute at Berkeley (MSRI), Universität Magdeburg (Germany), and the Institute for Pure and Applied Mathematics at UCLA (IPAM). He arrived at UC Davis in 1999, where he is now a professor of Mathematics as well as a member of the Graduate groups in Computer Science and Applied Mathematics.

His research has been recognized by an Alexander von Humboldt Fellowship, the 2010 INFORMS computer society prize, and a John von Neumann professorship at the Technical University of Munich. He has received over three million dollars in national and international grants. He is associate editor of the journals SIAM Journal of Discrete Mathematics and Discrete Optimization. For his dedication to outstanding mentoring and teaching he received the 2003 UC Davis Chancellor's fellow award, the 2006 UC Davis award for diversity, and the 2007 Award for excellence in Service to Graduate students by the UC Davis graduate student association. He has supervised seven Ph.D students, five postdocs, and over 20 undergraduate theses.

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We will describe some of the beautiful images that arise from the "Chaos Game."  We will show how the simple steps of this game produce, when iterated millions of times, the intricate images known as fractals. We will describe some of the applications of this technique used in data compression as well as in Hollywood.  We will also challenge members of the audience to "Beat the Professor" at the chaos game and perhaps win his computer.

Robert L. Devaney is currently Professor of Mathematics at Boston University and President-Elect of the Mathematical Association of America. He received his undergraduate degree from the College of the Holy Cross in 1969 and his Ph.D. from the University of California at Berkeley in 1973 under the direction of Stephen Smale. He taught at Northwestern University and Tufts University before coming to Boston University in 1980.

His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua, Sierpinski curves, and Cantor bouquets.

He is the author of over one hundred research papers in the field of dynamical systems as well as a dozen pedagogical papers in this field. He is also the (co)-author or editor of fourteen books in this area of mathematics.

In 1994 he received the Award for Distinguished University Teaching from the Northeastern section of the MAA and in 1995 he was the recipient of the MAA Deborah and Franklin Tepper Haimo Award for Distinguished University Teaching. In 2005 he received the Trevor Evans Award from the MAA for an article entitled Chaos Rules published in Math Horizons.

In 1996 he was awarded the Boston University Scholar/Teacher of the Year Award. In 2002 he received the National Science Foundation Director's Award for Distinguished Teaching Scholars. In 2002 he also received the ICTCM Award for Excellence and Innovation with the Use of Technology in Collegiate Mathematics. In 2003 he was the recipient of Boston University's Metcalf Award for Teaching Excellence. In 2004 he was named the Carnegie/CASE Massachusetts Professor of the Year. In 2009 he was inducted into the Massachusetts Mathematics Educators Hall of Fame. And in 2010 he was named the Feld Family Professor of Teaching Excellence at Boston University.

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The role of experimentation and computation in mathematics is historical, rich, and growing and changing at a remarkable pace. Computers are more than number crunchers: They check hypotheses, make conjectures, enable discoveries, and assist in proofs. While the computer is the primary tool facilitating experimentation, it is not the only source of experimental information bringing new ideas into mathematics. I illustrate these points by describing a collection of fun examples. In the first part of the talk, I'll explain some aspects of this interaction related to my own research interests in public key cryptography. Then I'll give a quick tour of some fundamental and surprising instances of the interaction of mathematics and the computer.

Jill Pipher is Professor of Mathematics at Brown University, and Director of the Institute for Computational and Experimental Research in Mathematics (ICERM). She received her Ph.D. from UCLA in 1985, spent five years at the University of Chicago as Dickson Instructor and then Assistant Professor, and came to Brown as an Associate Professor.

Pipher’s research interests include harmonic analysis, partial differential equations, and cryptography. She has published papers in each of these areas of mathematics, co-authored an undergraduate cryptography textbook, and jointly holds four patents for the NTRU encryption and digital signature algorithms. She was a co-founder of NTRU Cryptosystems, Inc, now part of Security Innovation, Inc. Her awards include an NSF Postdoctoral Fellowship, NSF Presidential Young Investigator Award, Mathematical Sciences Research Institute Fellowship, and an Alfred P. Sloan Foundation Fellowship. In February 2011, she became President of the Association for Women in Mathematics.

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This lecture is jointly sponsored with the American Statistical Association in celebration of Mathematics Awareness Month.

Can government agencies really track what you are doing? Do credit card companies know what you are going to purchase before you do? And what about social networks? How much of your information do you want available - and what are they doing with it? In this talk, I will share some of my experiences as a data mining and statistical consultant for groups as varied as American Express, the National Security Agency, the office of the Attorney General of Vermont, and the Comptroller's Office of New York State. I'll talk about the methods analysts use to mine these large data repositories, what the limits are, and what the future might hold.

Richard (Dick) D. De Veaux is Professor of Statistics at Williams College. He holds degrees in Civil Engineering (B.S.E. Princeton), Mathematics (A.B. Princeton), Dance Education (M.A. Stanford), and Statistics (Ph.D., Stanford), where he studied with Persi Diaconis.

Before Williams, Dick taught at the Wharton School and the Engineering School at Princeton. He has also been a visiting research professor at INRA (the Institut National de la Recherche Agronomique) in Montpellier, France; the Université Paul Sabitier in Toulouse, France; and the Université René Descartes in Paris. De Veaux has won numerous teaching awards including a "Lifetime Award for Dedication and Excellence in Teaching" from the Engineering Council at Princeton. He has won both the Wilcoxon and Shewell (twice) awards from the American Society for Quality and was elected a fellow of the American Statistical Association (ASA) in 1998. In 2006-2007 he was the William R. Kenan Jr. Visiting Professor for Distinguished Teaching at Princeton University. In 2008 he was named the Mosteller Statistician of the Year by the Boston Chapter of the ASA.

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Every year, people across the United States predict how the field of teams will play in the Division I NCAA Men’s Basketball Tournament by filling out a tournament bracket for the postseason play. This talk discusses two popular rating methods that are also used by the Bowl Championship Series, the organization that determines which college football teams are invited to which bowl games. The two methods are the Colley Method and the Massey Method, each of which computes a ranking by solving a system of linear equations. We also touch on how to adapt the methods to take late season momentum into account.

Tim Chartier is an Associate Professor of mathematics at Davidson College. His ability to communicate math both in and beyond the classroom were recognized with the Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member from the Mathematical Association of America.  His research and scholarship were recognized with an  Alfred P. Sloan Research Fellowship. Tim serves on the Editorial Board for Math Horizons, a mathematics magazine of the Mathematical Association of America. He also serves as chair of the Advisory Council for the Museum of Mathematics. Tim has been a resource for a variety of media inquiries which includes fielding mathematical questions for the Sports Science program on ESPN.

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Chaos is a real-world phenomenon that arises in many different contexts, making it difficult to tell exactly what chaos is. Yorke will give examples of the aspects of chaos.

James A. Yorke earned his bachelor's degree from Columbia University in 1963. He came to the University of Maryland for graduate studies, in part because of interdisciplinary opportunities offered by the faculty of the Institute for Physical Sciences and Technology (IPST). After receiving his doctoral degree in 1966 in Mathematics, Yorke stayed at the University as a member of IPST. Today he holds the title of Distinguished University Professor and also is a member of the Mathematics and Physics Departments.

Professor Yorke's current research projects range from chaos theory and weather prediction and genome research to the population dynamics of the HIV/AIDS epidemic. He is perhaps best known to the general public for coining the mathematical term "chaos" with T.Y. Li in a 1975 paper entitled "Period Three Implies Chaos," published in the American Mathematical Monthly. "Chaos" is a mathematical concept in nonlinear dynamics for systems that vary according to precise deterministic laws but appear to behave in a random fashion.

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In the world of discrete mathematics, we encounter a bewildering variety of topics with no apparent connection between them. There are block designs in combinatorics, finite projective planes in geometry, round-robin tournaments and map colorings in graph theory, (0, 1)- matrices in linear algebra, quadratic residues in number theory, error-correcting codes on the internet, and the torus at the doughnut shop.

But appearances are deceptive, and this talk is about the (7,3,1) design, a single object with many names that connects all of these topics. Along the way, we'll learn how Leonhard Euler was once spectacularly wrong, how P. J. Heawood was almost completely right, and what happened when Richard Hamming got mad at a computer.

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In a paper by de Smit and Hendrik Lenstra (Notices of the AMS, April 2003), it is shown that well known mathematical results about elliptic curves imply that what Escher was trying to achieve in this work has a unique mathematical solution. This discovery opened up the way to filling the void in the print. With help from artists and computer scientists, a completion of the picture was constructed at the Universiteit Leiden. The white hole turns out to contain the entire image on a smaller scale, which in the Dutch language is known as the Droste effect, after the Dutch chocolate maker Droste. In the talk, the mathematics behind Escher's print and the process of filling the hole was explained and visualized with computer animations.

Bart de Smit is a number theorist at Leiden University. He studied mathematics in Amsterdam and received his PhD from UC Berkeley in 1993. After various PostDoc positions, he continued his research in algebraic number theory in the Netherlands on a five year grant of the Royal Netherlands Academy of Arts and Sciences. He is currently running a four year research project of 12 research institutes on the interface of arithmetic geometry, number theory and applications to coding theory and cryptography.

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When you send your credit card number over the Internet, cryptography helps to ensure that no one can steal the number in transit. Julius Caesar and Mary Queen of Scots used cryptography to send secret messages, in the latter case with ill-fated results. More recently, cryptography is used in electronic voting, and it is also used to "sign" documents electronically. While cryptography has been used for thousands of years, public-key cryptography dates only from the 1970's. Some recent exciting breakthroughs in public-key cryptography include elliptic curve cryptography, pairing-based cryptography, and identity-based cryptography, all of which are based on the number theory of elliptic curves. This talk will give an elementary introduction to cryptography, including elliptic curve and pairing-based cryptography.

Alice Silverberg is a Professor of Mathematics and Computer Science at the University of California, Irvine. Her research interests include number theory and cryptography. She graduated summa cum laude in mathematics from Harvard University, and earned a Certificate of Advanced Study from Cambridge and a PhD and a Master's degree in mathematics from Princeton University. Gender equity issues are a long-standing concern of hers, as an outgrowth of her time spent studying at traditionally male institutions. She was awarded Humboldt, Bunting, Sloan, IBM, and NSF Fellowships, and has held a number of visiting or consulting positions in the US and abroad, including at IBM, Bell Labs, Xerox PARC, DoCoMo USA Labs, the Mathematical Sciences Research Institute in Berkeley, the University of Erlangen and the Max Planck Institute in Germany, the Institut des Hautes Études Scientifiques in France, and Macquarie University in Australia. Silverberg consulted for the TV show NUMB3RS, and occasionally writes mathematically-inspired Scottish country dances.

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The notion of `holonomy' in mechanical systems has been around for over one hundred years and gives insight into daily operations as mundane as steering and parallel parking and in understanding the behavior of balls (or more general objects) rolling on a surface with friction. A sample question is this: What is the best way to roll a ball over a flat surface, without twisting or slipping, so that it arrives at at given point with a given orientation?

In geometry, holonomy has turned up in many surprising ways in the last 100 years and continues to be explored as a fundamental invariant of geometric structures.

In this talk, I will illustrate the fundamental ideas in the theory of holonomy using familiar physical objects and explain how it is also related to group theory and symmetries of basic geometric objects.

Robert Bryant is the Director of the Mathematical Sciences Research Institute of Berkeley, CA. A North Carolina native, he received his PhD in mathematics in 1979 at the University of North Carolina at Chapel Hill, working under Robert B. Gardner. After serving on the faculty at Rice University for seven years, he moved to Duke University in 1987, where he held the Juanita M. Kreps Chair in Mathematics until moving to the University of California at Berkeley in July 2007. He has held numerous visiting positions at universities and research institutes around the world. He visited MSRI during the 2001-02 academic year as a Clay Mathematics Visiting Professor and he was in residence at MSRI during the Fall 2003 term as a co-organizer of the program in Differential Geometry.

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How do we fit a three-dimensional world onto a two-dimensional canvas? Answering this question will change the way you look at the world. We'll learn where to stand as we view a painting so it pops off that two-dimensional canvas seemingly out into our three-dimensional space. We'll explore the mathematics behind perspective paintings, which starts with simple rules and will lead us into really lovely, really tricky puzzles. For example, why do artists use vanishing points? What's the difference between 1-point and 3-point perspective? Why don't your vacation pictures look as good as the mountains you photographed? Dust off those old similar triangles, and get ready to put them to new use in looking at art!

Annalisa Crannell is a Professor of Mathematics at Franklin & Marshall College and recipient, in 2008, of the MAA's Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics. Her primary research is in topological dynamical systems (also known as "Chaos Theory"), but she also is active in developing materials on Mathematics and Art. Prof. Crannell has worked extensively with students and other teachers on writing in mathematics, and with recent doctorates on employment in mathematics. She especially enjoys talking to non-mathematicians who haven't (yet) learned where the most beautiful aspects of the subject lie.

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150 years ago B. Riemann discovered a pathway to understanding the prime numbers. But today we still have not completed his vision. I will give an introduction to Riemann's Hypothesis, one of the most compelling mathematics problems of all time, and describe some of its colorful history.

Brian Conrey is the founding Executive Director of the American Institute of Mathematics (AIM). He received his BS from Santa Clara University in 1976 and his PhD from the University of Michigan in 1980. He held a Visiting Assistant Professorship at the University of Illinois from 1980 - 1982. He received an NSF Postdoctoral Fellowship in 1982 and was a Member of the Institute for Advanced Study (IAS) during 1982 - 1983. In 1983 he joined the faculty at Oklahoma State University, where he remained until 1997, serving as Head of Mathematics from 1991 - 1997. He received a Sloan Fellowship in 1987 and spent the year 1987-1988 at IAS. Conrey is active in outreach programs for junior high and high school students and is one of the founders of the Math Teachers' Circles program. His area of specialty is Analytic Number Theory, especially the theory of L-functions. In recent years he has become very interested in using Random Matrix Theory to model the statistical behavior of L-functions. He received the Levi Conant Prize in 2007 for his paper "The Riemann Hypothesis."

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This talk explored some of the connections and analogies between mathematics and music in an attempt to explain why mathematicians tend to be musical.

James Stewart is Emeritus Professor of Mathematics at McMaster University and Professor of Mathematics at the University of Toronto. He received the M.S. degree from Stanford University and the Ph.D. from the University of Toronto. His research has been in harmonic analysis and his many books include a widely used series of calculus textbooks, which have been translated into a dozen languages. He was concertmaster of the McMaster Symphony Orchestra for many years and also played professionally in the Hamilton Philharmonic Orchestra. One of his greatest pleasures is playing string quartets. Stewart was named a Fellow of the Fields Institute in 2002 and its library is named after him. The James Stewart Centre for Mathematics was opened in 2003 at McMaster University, which awarded him an honorary D.Sc.

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Tiger Woods has an amazing record of winning golf tournaments. He has gained the persona of a player who is a winner, a player that when near the lead or in the lead can do whatever it takes to win. In this lecture I investigate whether in fact, he is a winner. A mathematical model is created for the ability of Tiger Woods, and all PGA Tour golfers to play 18 holes of tournament golf. The career of Tiger Woods is replayed using the mathematical model for all golfers and the results are very consistent with Tiger Woods’ actual career. The idealized Woods plays every hole the same, but with Woods’ natural variability from one hole to the next. This “Woods” plays no better or worse when he’s close to winning. Woods has not needed any additional winning dimension–only his pure golfing ability. So Woods is not a “winner” – but instead he is just a much better golfer than everyone else.

Scott M. Berry is President and Statistical Scientist at Berry Consultants. Since 2000 he has been involved in the design of more than 50 Bayesian adaptive clinical trials for pharmaceutical and medical device companies. His research interests are in Bayesian methods in clinical trials, adaptive clinical trials, Bayesian computation, and hierarchical models. He is also a world renowned sports statistician, with over 40 articles, including JASA and ESPN the Magazine. He received his PhD from Carnegie Mellon (1994) and his BS from the University of Minnesota (1990). He spent 5 years at Texas A&M University in the Statistics Department (1995-2000).

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Robots have been with us for only half a century, but the idea of man made mechanisms that can work and think goes back to ancient civilizations. The lecture presents the most important historical developments in robotics, emphasizing its interplay with mathematics. The first part of the lecture summarizes the pioneering work of Heron of Alexandria, Philo of Byzantium, Al-Jazari, Leonardo da Vinci, and other scientists up to the twentieth century. The second part is dedicated to artificial intelligence and the mathematical tools involved. The lecture concludes with the latest developments in robotics, and presents some open research problems in engineering, computer science, and mathematics, that need to be solved in order to fulfill the long standing promises of robotics.

Florian Potra earned a Ph.D. in Mathematics from the University of Bucharest, Romania. After an Andrew Mellon Postdoctoral Fellowship at the University of Pittsburgh, he joined the faculty of the University of Iowa, first as an Associate Professor of Mathematics, and then as a Professor of Mathematics and Computer Science. Between 1997-1998, he served as a Program Director in Applied and Computational Mathematics at the National Science Foundation. Since 1998 he has been a Professor of Mathematics and Statistics at the University of Maryland Baltimore County. He is also a Faculty Appointee at the Mathematical and Computational Sciences Division of The National Institute of Standards and Technology. Dr. Potra has published over 120 research papers in prestigious professional journals. He is the Regional Editor for the Americas of the journal "Optimization Methods and Software", and serves on the editorial board of three other well known mathematical journals.

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The process of applying mathematics to the real world is undergoing a radical change through our ability to gather data at a massive scale. This is particularly true at Google, where we routinely process petabytes of human language, and interact with many millions of users. In this talk I'll describe some surprising realizations that arose from this data while trying to improve part of our search quality. It turns out that everything I thought I knew about similarity was wrong, and I should have been talking to psychologists.

Kevin McCurley is a Research Scientist at Google, where he has worked since 2005. He previously held positions at IBM Almaden Research Center, Sandia National Laboratories, and University of Southern California. He has published in the areas of information retrieval, algorithms, parallel computing, cryptography, and number theory.

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Film making is undergoing a digital revolution brought on by advances in areas such as computer technology, computational physics, geometry, and approximation theory. Using numerous examples drawn from Pixar's feature films, this talk will provide a behind the scenes look at the role that math plays in the revolution.

Tony DeRose is currently a Senior Scientist and lead of the Research Group at Pixar Animation Studios. He received a BS in Physics in from the University of California, Davis, and a Ph.D. in Computer Science from the University of California, Berkeley. From 1986 to 1995 Dr. DeRose was a Professor of Computer Science and Engineering at the University of Washington. In 1998, he was a major contributor to the Oscar winning short film "Geri's game", in 1999 he received the ACM SIGGRAPH Computer Graphics Achievement Award, and in 2006 he received a Scientific and Technical Academy Award for his work on surface representations

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What if the universe had an edge? Since “universe” is construed to indicate “all that is,” such an edge would have to be inaccessible, “infinitely far away.”

In this talk, we travel to a hypothetical universe, whose inhabitants, along with all the matter they use to measure their space, shrink as they approach the edge. In this shrinking-ruler universe, that boundary is indeed inaccessible.

The picture of what we call “hyperbolic wallpaper” helps us imagine this cosmos: In the world of the shrinking ruler, all of the peacock fans are exactly the same distance across. All of them. And there are infinitely many copies hidden down there near the edge, unseen by our outsider eyes.

Frank Farris completed a five-year term as editor of Mathematics Magazine in 2005 and now serves again through 2009, aspiring to continue its tradition of challenging and inspiring 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.

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The last decade of this past century has been witness to a revolution in the development and application of mathematical techniques to origami, the centuries-old Japanese art of paper-folding. The techniques used in mathematical origami design range from the abstruse to the highly approachable. In this talk, I will describe how geometric concepts led to the solution of a broad class of origami folding problems – specifically, the problem of efficiently folding a shape with an arbitrary number and arrangement of flaps, and along the way, enabled origami designs of mind-blowing complexity and realism, some of which you’ll see, too. As often happens in mathematics, theory originally developed for its own sake has led to some surprising practical applications. The algorithms and theorems of origami design have shed light on long-standing mathematical questions and have solved practical engineering problems. I will discuss examples of how origami has enabled safer airbags, Brobdingnagian space telescopes, and more.

Robert J. Lang is recognized as one of the foremost origami artists in the world as well as a pioneer in computational origami and the development of formal design algorithms for folding. With a Ph.D. in Applied Physics from Caltech, he has, during the course of work at NASA/Jet Propulsion Laboratory, Spectra Diode Laboratories, and JDS Uniphase, authored or co-authored over 80 papers and 45 patents in lasers and optoelectronics as well as 8 books and a CD-ROM on origami. He is a full-time artist and consultant on origami and its applications to engineering problems but moonlights as the Editor-in-Chief of the IEEE Journal of Quantum Electronics. In 2009 he was awarded Caltech’s highest honor, the Distinguished Alumni Award for his work in origami.

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The fourth dimension sounds eerie, mysterious, and exciting; and it is. Untying knots, stealing gold bricks from closed iron safes, unfolding hypercubes and linking spheres are all part of the journey.

We are transported to this abstract domain by a powerful method of creating ideas, namely, thinking insightfully about the world that we know well. A deep understanding of the simple and familiar is the key to exploring the complex and mysterious, and the fourth dimension illustrates that principal magnificently.

Michael Starbird is a University Distinguished Teaching Professor at The University of Texas at Austin and a member of UT’s Academy of Distinguished Teachers. He received his B.A. degree from Pomona College and his Ph.D. in mathematics from the University of Wisconsin, Madison. He has been in the Department of Mathematics of UT except for leaves including one to the Institute for Advanced Study in Princeton, New Jersey and one to the Jet Propulsion Laboratory in Pasadena, California.

He has received more than a dozen teaching awards including several that are awarded to only one professor at UT annually and including the Mathematical Association of America’s 2007 national teaching award. He is a popular lecturer, having presented more than a hundred invited lectures since 2000. Starbird’s books include, with co-author Edward B. Burger, the award-winning mathematics textbook for liberal arts students The Heart of Mathematics: An invitation to effective thinking and the trade book Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas. With David Marshall and Edward Odell he co-authored Number Theory Through Inquiry. His Teaching Company video courses in the Great Courses Series include Change and Motion: Calculus Made Clear, Meaning From Data: Statistics Made Clear, What are the Chances? Probability Made Clear, and Mathematics from the Visual World. These courses reach tens of thousands of people in the general public annually. In 1989, Starbird was UT’s Recreational Sports Super Racquets Champion.

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Primes are the building blocks from which the integers are made, and so it is of interest to understand how they are distributed. Questions abound:

How many primes are there?
How many primes are there up to a given point?
Is there a good formula that tells us what is a prime and what is not?
Is there a way to find out quickly whether a given integer is prime?
How many primes are there in certain patterns?
Do polynomials take on many prime values?
How about consecutive prime values?
How are primes spaced?

Versions of some of these questions are considered to be among the most difficult open problems in mathematics. On the other hand there has been spectacular recent progress on several of these questions. We will discuss all this and more in this lecture.
Andrew Granville is the Canadian Research Chair in number theory at the University of Montreal. He specializes in analytic number theory and especially properties of prime numbers. His recent research has centered around the (mathematical) notion of "pretentiousness". His awards include the Presidential Faculty Fellowship from President Clinton in 1994, and the Chauvenet Prize (from the MAA) in 2008, he gave the Erdos Memorial lecture of the American Mathematical Society, and was elected a Fellow of the Royal Society of Canada in 2007.

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News increasingly depends on a careful dissection of numbers. Statistics are everywhere, from how many people lack health insurance to how to improve math education. Yet for being so prevalent, statistics are badly understood by the general public.

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.

In this talk, I'll illustrate how the press can misuse and even abuse statistics using examples of news coverage. 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 point out what science says, what it doesn't, and what it can't.

Rebecca Goldin is a professor of mathematics at George Mason University. She received her undergraduate degree from Harvard, and her PhD from MIT. She taught at University of Maryland as a National Science Foundation postdoctoral fellow before joining George Mason in 2001. She currently serves as the Director of Research for Statistical Assessment Service (STATS), a nonprofit media education and watchdog group affiliated with George Mason. When she's not thinking about statistics in the media, she's pursuing her research interests in group actions on manifolds and symplectic geometry. Last year, Goldin won the Ruth I. Michler Memorial Prize for mathematics.

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Children build models with 3-dimensional cubes. Mathematicians build them with higher dimensional cubes. Many physical systems can be represented by geometric models based on cubes. Using an example from robotics, we will investigate how such models are constructed and what can we learn from their strange, but beautiful geometry.

Ruth Charney is Professor of Mathematics at Brandeis University. She received her undergraduate degree from Brandeis and her PhD from Princeton. She taught at Berkeley, Yale, and Ohio State University before returning to her alma mater in 2003. She currently serves as Chair of her department and as a Vice President of the American Mathematical Society. She was never sure whether she was a topologist or an algebraist, and is now happily immersed in geometric group theory, a combination of the two.

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Regular patterns appear all around us: from vast geological formations to the ripples in a vibrating coffee cup, from the gaits of trotting horses to tongues of flames, and even in visual hallucinations. The mathematical notion of symmetry is a key to understanding how and why these patterns form. In this lecture Professor Golubitsky will show some of these fascinating patterns and explain how mathematical symmetry enters the picture.

Martin Golubitsky is Distinguished Professor of Mathematics and Physical Sciences at the Ohio State University, where, beginning in September, he will serve as Director of the Mathematical Biosciences Institute. He received his PhD in Mathematics from M.I.T. in 1970 and has been Professor of Mathematics at Arizona State University and Cullen Distinguished Professor of Mathematics at the University of Houston.

Dr. Golubitsky works in the fields of nonlinear dynamics and bifurcation theory studying the role of symmetry in the formation of patterns in physical systems and the role of network architecture in the dynamics of coupled systems. His recent research focuses on some mathematical aspects of biological applications: animal gaits, the visual cortex, the auditory system, and coupled systems. He has co-authored four graduate texts, one undergraduate text, two nontechnical trade books, (Fearful Symmetry: Is God a Geometer with Ian Stewart and Symmetry in Chaos with Michael Field) and over 100 research papers.

Dr. Golubitsky is a Fellow of the American Academy of Arts and Sciences, a Fellow of the American Association for the Advancement of Science, and a past President of the Society for Industrial and Applied Mathematics.

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An Interview with Martin Golubitsky 

At four distinct stages in the development of modern society, mathematics (in particular, acquisition of the ability to carry out new kinds of computation) changed in a fundamental, dramatic, and revolutionary way how we humans understand the world and live our lives.

The fourth such change is taking place during our lifetime, brought about by the invention of machines that can be instructed to compute for us. The others occurred in 8,000 B.C., the 13th century, and the 17th century. I'll look at how human life and cognition changed at each of those three stages.

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Which natural numbers occur as the area of a right triangle with three rational sides?  This is a very old question and is still unsolved, although partial answers are known (for example, five is the smallest such natural number).  In this talk we will discuss this problem and recent progress that has come about through its connections with other important open questions in number theory.

Karl Rubin is the Thorp Professor of Mathematics at the University of California, Irvine.  His research deals with elliptic curves and other aspects of number theory.  Rubin attended Washington DC public schools, was a Putnam Fellow as an undergraduate at Princeton, and received his Ph.D. from Harvard.  He was a professor at Ohio State, Columbia, and Stanford before moving to UC Irvine in 2004.  Rubin received the Cole Prize in Number Theory from the American Mathematical Society, a National Science Foundation Presidential Young Investigator award, a Humboldt Research Award, and Guggenheim and Sloan fellowships.

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Mathematicians believe, correctly, that they are uniquely qualified to answer complicated questions in science and engineering. But it very often happens that such problems are unsolvable or intractable in their original form. Is it acceptable to say politely "I'm sorry; this problem is impossible" and then return to answering questions that can be answered? Or should we do more? How can we do more? This talk, intended for a general audience, will describe, with examples from the speaker's experiences in optimization, how mathematicians can become local heroes after they say they're sorry.

Margaret H. Wright is Silver Professor of Computer Science and Mathematics and chair of the Computer Science Department in the Courant Institute of Mathematical Sciences, New York University. She received her B.S., M.S., and Ph.D. from Stanford University. Her research interests include optimization, scientific computing, and real-world applications. Prior to joining NYU, she worked at Bell Laboratories (AT&T/Lucent Technologies) and Stanford University. She was elected to the National Academy of Engineering (1997), the American Academy of Arts and Sciences (2001), and the National Academy of Sciences (2005). During 1995-1996 she served as president of the Society for Industrial and Applied Mathematics (SIAM).

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Doodling has many mathematical aspects: patterns, shapes, numbers, and more.  Not surprisingly, there is often some sophisticated and fun mathematics buried inside common doodles.  Vakil will begin by doodling, and there is no telling where it could take him.

Ravi Vakil is Professor of Mathematics at Stanford University.  He was born in Toronto, Canada, and studied at the University of Toronto, where he was a four-time winner of the Putnam competition (``Putnam Fellow'').  He received his Ph.D. from Harvard in 1997, and taught at Princeton and MIT before moving to Stanford in 2001.  He is an algebraic geometer, and his work involves many other parts of mathematics, including topology, string theory, applied mathematics, combinatorics, number theory, and more.  His awards include the Alfred P. Sloan Research Fellowship, the National Science Foundation CAREER Award, the American Mathematical Society Centennial Fellowship, the Dean's Award for Distinguished Teaching, and the Presidential Early Career Award for Scientists and Engineers.  He works extensively with talented younger mathematicians at all levels, from high school (through math circles, camps, and olympiads), through recent Ph.D.'s.  Vakil runs a problem-solving seminar each  fall for Stanford undergraduates, involving up to 150 students, as well as a masterclass for experts.  He is also the faculty advisor to the Stanford Math  Circle. You can read more at Prof. Vakil's Home Page.

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What is the role of proof in mathematics? Most of the time, the search for proof is less about establishing truth than it is about exploring  unknown territory. In finding a route from what is known to the result one believes is out there, the mathematician often encounters unexpected insights into seemingly unrelated problems. I will illustrate this point with an example of recent research into a generalization of the permutation matrix known as the "alternating sign matrix." This is a story that began with Charles Dodgson (aka Lewis Carroll), matured at the Institute for Defense Analysis, drew in researchers from combinatorics, analysis, and algebra, and ultimately was solved with insights from statistical mechanics. This talk is intended for a general audience and should be accessible to anyone interested in a window into the true nature of research in mathematics.

David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College. He served in the Peace Corps, teaching math and science at the Clare Hall School in Antigua, West Indies before studying with Emil Grosswald at Temple University and then teaching at Penn State for 17 years, eight of them as full professor. He chaired the Department of Mathematics and Computer Science at Macalester from 1995 until 2001. He has held visiting positions at the Institute for Advanced Study, the University of Wisconsin-Madison, the University of Minnesota, Université Louis Pasteur (Strasbourg, France), and the State College Area High School.

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Gröbner bases are a fun method for solving algebraic equations. See how it works, why it is useful, and what you should do with the change in your pocket.

Bernd Sturmfels received doctoral degrees in Mathematics in 1987 from the University of Washington, Seattle, and the Technical University Darmstadt, Germany. After two postdoctoral years at the Institute for Mathematics and its Applications, Minneapolis, and the Research Institute for Symbolic Computation, Linz, Austria, he taught at Cornell University, before joining UC Berkeley in 1995, where he is Professor of Mathematics and Computer Science. His honors include a National Young Investigator Fellowship, a Sloan Fellowship, and a David and Lucile Packard Fellowship. Sturmfels served as von Neumann Professor at TU Munich in Summer 2002, as the Hewlett-Packard Research Professor at MSRI Berkeley in 2003/04, and he was a Clay Senior Scholar in 2004. A leading experimentalist among mathematicians, Sturmfels has authored or edited 13 books and about 150 research articles, in the areas of combinatorics, algebraic geometry, symbolic computation and their applications. He currently works on algebraic methods in statistics and computational biology.

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An Interview with Bernd Sturmfels

It is now appreciated that cancers can be composed of multiple clonal subpopulations of cancer cells which differ among themselves in many properties, including, growth rate, ability to metastasize, immunological characteristics, production and expression of markers, and sensitivity to therapeutic modalities. Such tumor heterogeneity has been demonstrated in a wide variety of tumors, including those that originate in the prostate. In an effort to assist in the understanding of recurrent prostate cancer and the cellular processes which mediate this disease, I will present a mathematical model that describes both the pre-treatment growth and the post-therapy relapse of human prostate cancer xenografts. The goal is to evaluate the interplay between the multiple mechanisms which have been postulated as causes of androgen-independent relapse. At the end of the the talk, I will also comment on possible causes of tumor heterogeneity including the Cancer Stem Cell Hypothesis.

Trachette Jackson is an associate professor at the University of Michigan. She received a Ph.D. in Applied Mathematics in 1998 from the University of Washington. Her research interests focus on applying mathematics to modeling the growth and control of cancer. Professor Jackson has held post doctoral positions at Duke University, the Institute of Mathematics and its Applications at the University of Minnesota, and the National Health and Environmental Effects Research Laboratory of the Environmental Protection Agency. She is the recipient of an Alfred P. Sloan Research Fellowship and the Career Enhancement Fellowship from the Woodrow Wilson National Foundation. At the University of Michigan she received the Amoco Faculty Undergraduate Teaching Award. She is currently a Co-PI on an NSF grant for a program that will allow undergraduate students to develop knowledge and acquire skills in research areas that are at the interface of Biology and Mathematics. Professor Jackson is a frequent invited lecturer at conferences and universities.

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An Interview with Trachette Jackson (pdf)

Doron Zeilberger is a Board of Governors Professor of Mathematics at Rutgers University. He is widely known for the development of "WZ" (Wilf-Zeilberger) Theory and Zeilberger's algorithm that are used extensively in modern computer algebra software. Zeilberger was the first to prove the elusive result in combinatorial theory known as the alternating sign matrix conjecture. Among his honors are: the MAA Lester R. Ford award for a paper in the American Mathematical Monthly; the American Mathematical Society Steele Prize for seminal contributions to research (co-recipient with Herb Wilf); the Institute of Combinatorics and Its Applications Euler Medal for "Outstanding Contributions to Combinatorics;" the Laura H. Carnell Professorship at Temple University; in the spirit of Paul Erdos, challenge cash prizes from Richard Askey, George Andrews and Ron Graham; and Persi Diaconis's favorite living mathematician!

The citaton for the Euler Medal describes him as "a champion of using computers and algorithms to do mathematics quickly and efficiently." In his opinion "programming is even more fun than proving, and, more importantly it gives as much, if not more, insight and understanding."

An Interview with Doron Zeilberger

I will describe the explosive development of splines and their application over the past 40 years. Splines are piecewise polynomials which are extremely useful in approximation theory and numerical analysis for fitting and approximating functions. They have also found applications in many areas of business, engineering, medicine, science, and elsewhere. I will discuss some of these applications. The talk will be quite general with little mathematical background needed.

Dr. Schumaker is a Stevenson Professor at Vanderbilt University. His research areas include approximation theory and computer aided graphical design. He is an author or co-author of 37 books or proceedings. He has been the advisor of 21 Ph.D. students. Dr. Schumaker has won the Alexander von Humboldt Prize and he has been elected a foreign member of the Norwegian Academy of Science and Letters.