Below are the session abstracts for the NYC PDO Group's “Mathematical Modeling in the Real World” 2011-2012 course. Visit the NYC Professional Development and Outreach Group info page for course details and registration information, or check out session abstracts and handouts from previous years:
Mathematics to support business decision making: Watson and beyond with Brenda Dietrich 8/30/11
Decades of advances in computing and data access were demonstrated in early 2011 when the Watson computer defeated human champions at the game of Jeopardy! This talk will give a view of the science behind the Watson project. It will also discuss how elements of that technology have been used, together with mathematical modeling, to support business decision making.
Presenter: Brenda Dietrich is an IBM Fellow and Vice President in the IBM Research Divisions. She leads IBM’s research activities in Business Analytics and Mathematical Sciences, and supports software products and consulting in these areas. She is responsible for both basic research in computational mathematics and related fields, and the development of novel business applications based on the application of mathematical models within industry. She has been the president of INFORMS, the world’s largest professional society for Operations Research and Management Sciences, and is an INFORMS Fellow. She serves on the Board of Trustees of SIAM. She has served on university advisory boards for Northwestern, CMU, MIT, and UC Berkeley, and on advisory boards for NSF sponsored Math Research Institutes. She holds more than a dozen patents, has co-authored numerous publications, and co-edited the book Mathematics of the Internet: E-Auction and Markets. She holds a BS in Mathematics from UNC and an MS and Ph.D. in OR/IE from Cornell. Her personal research includes manufacturing scheduling, services resource management, transportation logistics, integer programming, and combinatorial duality.
Modeling Human Behavior (Especially Cooperation) in Teams, Systems, Organizations, and Networks with Chris Arney 8/31/11
This is a math workshop and we will be doing plenty of mathematics, especially modeling, but we will also be doing plenty of behavioral and social science, especially modeling. The underlying philosophy is to examine the following anonymous quote: “If you want to be incrementally better: Be competitive. If you want to be exponentially better: Be cooperative.” We want to look at cooperative systems to see if they are or can be better than competitive systems. For this workshop, we will start with sports teams and work toward other elements of society that effect younger people in junior high and high school. We will model with networks and dynamical systems. Cooperation is not necessarily consensus or compromise or teamwork nor does it negate the value of diversity and independence of thought --- it relies on them. A cooperative system consists of people that share information or tasks to accomplish common objectives. Cooperation is used to accomplish a common purpose that is greater than the purpose of each individual. As John Donne suggested "No man is an island" -- people are part of a "community" with blood, friendship, or economic ties or connections. The connectivity of people in different ways is captured by a variety of well-known phrases: Facebook friends, instant messenger buddy lists, Twitter followers, network of friends, social connections, teammates, etc. It is not only people who have ties. Humans create ties between phones and web pages. Human societies create electrical and telephone networks and networks that deliver water and natural gas. In the end we seek through cooperation to find a harmony that will make human life better. And as in any workshop, we hope to have fun as we learn.
Presenter: Chris Arney graduated from the United States Military Academy and served 30 years in the Army, retiring in 2001. His graduate studies led to an MS in computer science and a PhD in mathematics from Rensselaer Polytechnic Institute. Chris spent most of his military career as a mathematics professor at West Point (NY) with other assignments in military intelligence at Schofield Barracks (HI), Fort Bragg (NC), Fort Huachuca (AZ), Norfolk Naval Base (VA), Fort Dix (NJ), and Fort Monmouth (NJ). He also served as the Dean of Mathematics and Sciences and as Interim Vice President for Academic Affairs at the College of Saint Rose in Albany and the division chief of the Mathematical Sciences Division of the Army Research Office (NC). There he managed and performed research in the area of cooperative systems, with particular interest in information networks, pursuit-evasion modeling, intelligence processing, artificial intelligence, and language for robots. Chris has authored 22 books, written over 120 technical articles, made over 240 presentations, and reviewed over 200 books. He is currently a professor of mathematics at the United States Military Academy, West Point (NY). His technical areas of interest include mathematical modeling, cooperative systems, and the history of mathematics and science. His primary teaching interests are in modeling and inquiry.
Adventures at the Interface of Physics and Biology with William Bialek 9/17/11
I am a theoretical physicist, fascinated by the phenomena of life. The goal, as with the rest of physics, is to provide a compact mathematical description of nature, but of course living systems are VERY complicated, so there are many challenges. In this presentation I will try to give you a sense for some of the phenomena that have captured my interest, and that of my colleagues. I hope to say something about the design of insect eyes, about the reliability of our perceptions, about how bacteria move and find food, and about how cells make decisions during the development of an embryo. In each case there is a "back of the envelope" calculation that brings (I hope!) some insight into what's going on.
After a break I'll take up a related problem: how do we educate people to think about the world in a way that crosses the traditional boundaries between scientific disciplines? I've been especially interested in the physics/biology interface, but this may be typical of the larger divide between the traditionally mathematical disciplines and the sciences that traditionally have taken a more qualitative, descriptive approach. I'll tell you a bit about what my colleagues and I have been trying to do for first year university students, and I'd like to learn from you about the current landscape in K-12 education.
Presenter: William Bialek is the John Archibald Wheeler/Battelle Professor in Physics, and a member of the multidisciplinary Lewis-Sigler Institute for Integrative Genomics, at Princeton University. In addition, he serves as Visiting Presidential Professor of Physics at the Graduate Center, City University of New York, where he is helping to launch an Initiative for the Theoretical Sciences.
He attended the University of California at Berkeley, receiving his PhD in Biophysics. In late 1990 worked with the NEC Research Institute (now the NEC Laboratories) in Princeton, where he became an Institute Fellow.
Professor Bialek’s research interests have ranged over a wide variety of theoretical problems at the interface of physics and biology, from the dynamics of individual biological molecules to learning and cognition. Best known for contributions to our understanding of coding and computation in the brain, Bialek and collaborators have shown that aspects of brain function can be described as essentially optimal strategies for adapting to the complex dynamics of the world, making the most of the available signals in the face of fundamental physical constraints and limitations. More recently he has followed these ideas of optimization into the early events of embryonic development and the processes by which all cells make decisions about when to read out the information stored in their genes. His hope is that these diverse biological phenomena may be understandable through some unifying theoretical principles, in the physics tradition.
"Stable Matching with Applications to School Choice" with Al Roth 10/22/11
"Matching" is the name economists give to the ways we get the many things we choose in life that also have to choose us, from spouses to jobs to places in NYC high schools. Some simple models of matching will be discussed, along with some powerful organizing ideas, like whether a particular matching is stable or unstable. The session will include a detailed description of the current system of matching students with NYC high schools.
Al Roth is the George Gund Professor of Economics and Business Administration in the Department of Economics at Harvard University, and in the Harvard Business School. His research, teaching, and consulting interests are in game theory, experimental economics, and market design. The best known of the markets he has designed (or, in this case, redesigned) is the National Resident Matching Program, through which approximately twenty thousand doctors a year find their first employment as residents at American hospitals. He has recently been involved in the reorganization of the market for Gastroenterology fellows, which started using a clearinghouse in 2006 for positions beginning in 2007. He helped design the high school matching system used in New York City to match approximately ninety thousand students to high schools each year, starting with students entering high school in the Fall of 2004. He helped redesign the matching system used in Boston Public Schools, adopted for students starting school in September 2006. He is one of the founders and designers of the New England Program for Kidney Exchange, for incompatible patient-donor pairs. He is the chair of the American Economic Association's Ad Hoc Committee on the Job Market, which has designed a number of recent changes in the market for new Ph.D. economists. He is a Fellow of the American Academy of Arts and Sciences and the Econometric Society, and has been a Guggenheim and Sloan fellow. He received his Ph.D at Stanford University, and came to Harvard from the University of Pittsburgh, where he was the Andrew Mellon Professor of Economics.
Statistics - Inside and Outside the Classroom with Andrew Gelman 11/19/11
This session will consist of three main topics: (1) Of Beauty, Sex, and Power: Statistical Challenges in the Estimation of Small Effects. A silly example of the frequencies of boy and girl babies leads us to some important research involving the meaning of statistical significance. (2) Mathematics, Statistics, and Political Science. We explore the differences between mathematical and statistical thinking, developing the ideas using examples from my own research in political science. (3) Statistics Teaching Activities. For twenty years I have been collecting class-participation demonstrations in statistics and probability.
Andrew Gelman is a professor of statistics and political science and director of the Applied Statistics Center at Columbia University. He has received the Outstanding Statistical Application award from the American Statistical Association, the award for best article published in the American Political Science Review, and the Council of Presidents of Statistical Societies award for outstanding contributions by a person under the age of 40. His books include Bayesian Data Analysis (with John Carlin, Hal Stern, and Don Rubin), Teaching Statistics: A Bag of Tricks (with Deb Nolan), Data Analysis Using Regression and Multilevel/Hierarchical Models (with Jennifer Hill), and, most recently, Red State, Blue State, Rich State, Poor State: Why Americans Vote the Way They Do (with David Park, Boris Shor, Joe Bafumi, and Jeronimo Cortina).
Andrew has done research on a wide range of topics, including: why it is rational to vote; why campaign polls are so variable when elections are so predictable; why redistricting is good for democracy; reversals of death sentences; police stops in New York City, the statistical challenges of estimating small effects; the probability that your vote will be decisive; seats and votes in Congress; social network structure; arsenic in Bangladesh; radon in your basement; toxicology; medical imaging; and methods in surveys, experimental design, statistical inference, computation, and graphics.
Mathematical Modeling in the Real World with Tim Chartier 12/10/11
Morning Session: "Dicey Math from Google to computer graphics" Life can be random or at least effectively modeled with random numbers. In this session, we will use random numbers produced by casting a die to explore math modeling. For example, a model of a random internet surfer lies at the heart of Google's search engine. We can explore Google's algorithm with a die and simple probability. Later, we will again use dice to create the continents of distant planets as they might be seen from space.
Afternoon Session: "Who's Number 1, at least mathematically?" In this session, we will learn to rank sports teams using linear equations. Forming such systems involve counting and fractions. Solving the systems requires a computer and is easily done on Excel. We will then learn how to integrate the use of functions to better model sports with the potential of making better predictions for the outcome of sporting events.
Associate Professor Tim Chartier received both a B.S. degree in applied mathematics and a M.S. degree in computational mathematics from Western Michigan University. After doctoral work in applied mathematics at the University of Colorado at Boulder and a VIGRE postdoctoral position at the University of Washington, he arrived at Davidson in 2003. Professor Chartier's work in numerical analysis and partial differential equations, sometimes in collaboration with Lawrence Livermore National Laboratory and with Los Alamos National Laboratory, has been supported by the Department of Energy and the Alfred P. Sloan Foundation. In 2007, he was recognized by the Mathematical Association of America with the Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member. Professor Chartier is also a mime and enjoys combining mathematics and art in public performances.
Mathematical Modeling in the Real World with George Hart 1/21/12
George W. Hart is Chief of Content at the Museum of Mathematics (MoMath) in New York City. His previous background as a sculptor, scholar, mathematician, engineer, writer, computer scientist, and educator lead him to MoMath. His geometric sculptures are recognized around the world for its mathematical depth and creative use of materials. He is a pioneer in using computer technology and solid freeform fabrication in the design and fabrication of sculpture. Examples of his artwork can be seen at major universities, such as M.I.T., U.C. Berkeley, and Princeton University. He has received praise and awards in numerous exhibitions, including a New York State Council for the Arts Individual Artist's Award.
Hart has numerous publications, including: his extensive online Encyclopedia of Polyhedra, Multidimensional Analysis text (Springer Verlag, 1995) and his Zome Geometry book (Key Curriculum Press, 2001). He is currently in the process of writing a book on the history of geometry in art. Hart's mathematical research centers on novel polyhedral structures and algorithms for producing them. He has produced algorithms for generating various new classes of polyhedra, which he then presents to the world in sculptural forms. (In past work, he developed methods for efficiently monitoring electrical loads, on which he holds several patents.) He is the associate editor for sculpture of the Journal of Mathematics and the Arts. He is on the board of directors of the Bridges Organization, which runs the Bridges conferences on mathematical connections in art, music, and science. He was co-organizer of a recent workshop on Innovations in Mathematics Education via the Arts.
Modeling for Optimization: blending physical objects, graphic representations, and geometric reasoning on ‘change’ and optimization with Walter Whiteley 2/11/12(rescheduled from 8/29/11)
Typically, mathematical modeling involves blending together two mental spaces: one with a basis in the physical world or in another discipline, along with its internal relationships and operations; and a second one with mathematical representations and associated mathematical reasoning. Together, we will explore a series of geometric optimization problems in which we can develop multiple representations: physical, graphic, geometric, and symbolic. By ensuring the two representations are solid, and the correspondences for the blends are strong, we can explore how the various forms of reasoning support one another and provide scaffolds for strong, ‘sensible’ problem solving.
Our goal is to generate accessible reasoning (without calculus) for classic problems such as: (i) the maximum volume box with a given surface area is a cube; (ii) the box with a fixed volume of minimum surface area is a cube; (ii) the maximum area rectangle of fixed perimeter is a square; (iv) the minimum perimeter rectangle of fixed area is a square. We will do this with some approaches to reasoning supported by physical models which are accessible from middle school on up. Of course, exploring variation, change, and optimization has interesting additional connections to pre-calculus and calculus reasoning, and even algebraic reasoning about the algebraic mean and the geometric mean of a set of numbers. These will be brought in after the initial geometric reasoning.
The day will include active investigations of what other problems can be accessed with these methods, how to generalize and specialize the reasoning and principles, encountered, and multiple ways to connect these results with natural settings.
Presenter: Walter Whiteley is a Professor of Mathematics and Statistics and a member of the Graduate Programs in Mathematics, in Education, in Computer Science, and in Interdisciplinary Studies at York University in Toronto, Canada. Professor Whiteley's mathematical research focuses on applications of discrete geometry in a range of disciplines: structural engineering, mechanical engineering, biochemistry, material sciences and computational geometry.
Professor Whiteley is Director of the Mathematics for Education mathematics major program at York University. His teaching is geometry courses for in-service teachers of mathematics and for pre- service teachers, as well as the capstone course for the Mathematics for Education program. He has been active in supporting mathematics education through the Ontario Association for Mathematics Education, the Canadian Mathematics Education Study Group, and the International Congress of Mathematics Education. Professor Whiteley led the university feedback to the most recent revision of the Ontario Mathematics Curriculum and contributed to the writing of the high school curriculum. Recently, he has been designing and researching mathematical tasks which support professional development of teachers, and provide opportunities for students to reason about, and make sense of, a number of big ideas in geometry and modeling. In 2009, the Canadian Mathematical Society awarded Professor Whiteley the Adrien Pouliet Award from for his contributions to Mathematics Education in Canada.
