National
Science Foundation Workshop
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for High School Teachers of Mathematics & Science
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ABSTRACTS |
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COLIN ADAMS
MAKING CALCULUS FUN: HOW TO ENTERTAIN AT PARTIES This talk is about how to make calculus fun: for your
students, for your taxidriver, for the person sitting next to you on the
plane. That's right, you will learn how to talk about calculus AND be
popular at the same time. |
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DENNIS S. BERNSTEIN
HOW FEEDBACK CHANGED THE WORLD It's fun to debate the most important inventions of all time. Defensible choices include: the alphabet, Hindu-Arabic numerals, eyeglasses, moveable type, the transistor, the PC, the pill, and so on. In this talk I will discuss four inventions that are perhaps less known but which have had an enormous impact on society. These are: the escapement, the governor, the aileron, and the amplifier. Why are these important? Because they made possible, respectively, accurate timekeeping and the scientific revolution, the steam engine and the industrial revolution, controlled flight and the space age, and useful electronics and the radio/TV/ computer age. In this talk I will discuss how these relatively invisible inventions have one thing in common, namely, they are all based on feedback control principles. I will relate the interesting and very human history of each invention and explain how each one works |
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CHRISTOS G. CASSANDRAS
WHEN COMPUTERS CONTROL -- JOYS AND PERILS OF AUTOMATION One of the definitions of the word "control" is "to govern or direct according to rule" (Merriam-Webster dictionary). In science and engineering, these "rules" have traditionally been dictated by the laws of nature -- such as gravity or conservation of mass. Computer technology, however, has enabled us to build complex systems that have become essential to our daily life, from automated factories to computer networks -- with intelligent highways and pilotless planes not too far in the horizon. The "rules" that these systems must obey are as arbitrary as human imagination can make them (as in designing a video game where one may create a virtual world where anything goes). While this is exciting, it is also dangerous -- it takes but one minor "bug" or "virus" to bring a multimillion factory to a standstill, the Internet to crash, or the Mars exploration vehicle to erroneously "think" that its landing legs were deployed, effectively forcing it to commit electronic suicide. Many of the dangers of automation stem from the lack of designers and engineers with appropriate skills that are cultivated through an understanding of what a "system" is and how to evaluate the effectiveness of a controller before deployment. This new breed of sophisticated engineers will combine the knowledge of basic mathematics, system science, economics, and computers to produce the educated technological leaders of a society demanding multidisciplinary skills. This presentation will employ simple computer simulation examples to illustrate the difference between physical processes subject to the laws of nature and human-made processes that must satisfy human-made rules. We will then show how "automatic control" can be used and demonstrate both its benefits and risks. An interesting easy-to-build experimental environment for an automated human-made system is a LEGO computer-controlled car factory that students can both build and design simple control mechanisms for. The presentation will include a tour of the factory (see also http://vita.bu.edu/cgc/newlego/) and explain how simple principles of automation can be illustrated in this environment.
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RAFFAELLO D'ANDREA
THE ROBO FILES: BUILDING THE BEST ROBOT SOCCER TEAM IN THE WORLD. As engineering systems become more and more complex, there is an increasing need from industry for engineers who not only have expertise in a particular engineering discipline, but who also possess diverse interdisciplinary skills, can integrate system components, can ensure total system operability, and can understand the various economic forces in the marketplace. This skill set and process is often referred to as Systems Engineering (SE). In order to effectively teach SE principles to students, we have developed a project course which embodies many of the key elements of SE. The project entails the construction of fully autonomous, fast moving robots which work together as a team to compete against similar teams of robots in a robot soccer match. This yearly competition, known as the Robot World Cup Initiative (or simply RoboCup), is described in www.robocup.org. In this talk, we discuss how students from Mechanical and Aerospace Engineering, Electrical Engineering, Computer Science, and Operations Research at Cornell University crossed disciplinary boundaries and worked together as a team to build the winning squad at the 1999 RoboCup championships in Stockholm, Sweden. The talk includes video footage from the competition. |
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THEODORE E. DJAFERIS
AUTOMATIC CONTROL: A FASCINATING FIELD OF STUDY We are literally surrounded by natural and man-made systems that are automatically controlled. The human body includes a multitude of systems that operate without our conscious intervention, keeping us alive and well. On a daily basis we encounter man-made systems that operate automatically and may have electrical, mechanical, chemical, hydraulic, financial or ecological characteristics. In most instances, we are not even aware of their automatic operation until there is some malfunction. A quick reflection will certainly convince anyone of the importance of automatic control in nature. It is also true that automation played a major role in the development of our highly complex technological society in the past and will surely continue to do so in the future. Automatic control is a fascinating field of study! The theory and practices developed over the years can be applied to a wide range of automation problems, giving the field its universal character. Automatic control is truly multidisciplinary as problems frequently involve a number of disciplines. One cannot help but wonder about how automatic control is achieved and the objective of this talk is to answer this question. We will do so by considering a specific example. This will give us a better understanding of the pieces involved in the automatic control puzzle and the process leading up to successful solutions. Basic principles and practices will be introduced and the design process will be explored in some detail. The example chosen is the design of an automatic control system for vehicle collision avoidance. The design process begins with the development of a conceptual block diagram for the solution that is inspired by manual control. It will be evident that feedback plays a crucial role in the design and that a number of other components are also required (i.e., sensor, actuator and controller). The design process continues with the development of a model for the system to be controlled. Frequently, such models are expressed in terms of differential equations for which a rich controller design theory exists. Computer simulations allow us to test proposed designs and develop further insight into the problem. The process concludes with the validation of the design by experiments on the actual system. Implementation issues may necessitate further adjustments and redesign. The design process is thus a blend of theory, computer simulations and physical experiments. We will demonstrate the entire process by developing a collision avoidance automatic control system for a Computer Intelligent Model Car (CIMCAR).
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KATSUHISA FURUTA
UNDERSTANDING PHENOMENA THROUGH REAL
PHYSICAL OBJECTS Pendulum has been a good example of physical objects which has observed behaviors for a long time. Galileo Galilei found that the pendulum swung around the pendant position with same period. The pendulum since then used for the mechanism for the clock. The pendulum then is found to keep upright when vibration is given to the hinge. Also by controlling the position of the hinge the pendulum can be swung up from the pendant to upright position. The control law for such swing up will be presented at the workshop with video.
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Dr. Alan Kay
POWERFUL IDEAS IN THE WORLD OF THE CHILD Maria Montesorri realized that children were set up by Nature to learn the world around them through play. She pointed out that a better way to help children grow up in the 20th century -- as opposed to the 10th century -- would be to give them 20th century toys and playplaces rather than to try to give them watered down university classroom schooling as is currently prevalent. Seymour Papert realized that interactive computers could be a Montesorri playplace for mathematical toys that would have a strong projection into the playworld of children. This talk will show one of the current states of this art: how children can and do learn powerful ideas in math and science within a special kind of interactive computer and network environment, called Squeak. |
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IVAN OSORIO, M.D MARK G. FREI, Ph.D.
USING MATHEMATICS FOR EPILEPTIC SEIZURE WARNING We present a method for mathematical analysis of brain wave signals that quantifies signal characteristics as they occur and allows short-term prediction of epileptic seizures. The method has been implemented into hardware and software to produce a prototype device capable of rapid and accurate detection of signal changes that occur before the patient is aware that a seizure is coming. We will outline the method and point out the many different ways in which mathematics was applied to obtain the solution. We will also discuss the benefits of a multidisciplinary approach to research and describe the roles of mathematics, medicine, engineering, computer science, physics and other disciplines in contributing to the overall success of the system. |
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Brian Rosen
CONTROLLING THE FICTIONAL WORLD: The recent success of animated films such as "Toy Story 2" and "A Bug's Life" show that computers can be used to create compelling images that tell enduring stories. While these films are a product of dozens of artists and writers, the underlying technology of the computer animation process rests firmly on a foundation of mathematics. Computer graphics is therefore a treasure trove of real world applications of math readily accessible by high school students. This talk will give you a basic understanding of how computer images are created and suggest ways that this technology could be worked into a math curriculum. |
Last updated June 19, 2000
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