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The Mathcamp Academic ProgramThe Mathcamp academic program gives students the opportunity to study advanced and unusual topics in mathematics in a challenging and fun environment. Throughout the day, there are activities at all levels, from beginning to the most advanced:
There is so much going on at every hour of the day and night that no one could possibly do it all! With the help of a faculty advisor, students design their own schedule and select the activities most appropriate to their level and interests. However, if you're really fascinated by a topic, don't worry about not having all the necessary background: we'll work with you to help you learn it!
ClassesHere are some weekly academic schedules and class descriptions from previous Mathcamps:
The Mathcamp schedule is so packed that it may seem daunting at first. However, it is important to remember that none of the classes are mandatory. We assume that you are at Mathcamp because you want to do math, but exactly how much time you spend in class is up to you. In fact, we discourage students from going to too many classes. Some of your most important learning experiences will take place outside of class: thinking about what you've learned, doing homework, talking to the visiting lecturers, solving problems with friends, or working on your independent project. Our goal is to put an enormous amount of fascinating mathematics within your reach, so that you can do as much as you want, in the way that is most enjoyable and productive for you. Notice that there are usually at least 4 classes offered at any one time, so you can choose the ones that interest you most. Read the detailed weekly class descriptions to find out more. Each class has a "star rating" to indicate its difficulty: from * (accessible to everyone) to **** (very advanced). The "one-star" classes aren't any less interesting than the "four-star" classes -- they just move at a more relaxed pace and assume less mathematical experience. You can choose the level you are most comfortable with or experiment by taking classes on many different levels; your academic advisor will help you choose courses that best match your background and interests. Course offerings vary from year to year, depending on the interests of the students and faculty. Some of the topics taught in previous years have included:
ProjectsStudents at Mathcamp are encouraged to work on a project, supervised by one of the mentors or faculty. Projects range in scope from creative applications of simple techniques to advanced problems connected to faculty research. Usually the mentors and faculty propose project ideas, and students can choose one they want to work on. However, if a student wants to propose a project of his or her own, there is usually someone on the staff willing to serve as an advisor.
One of the projects from Mathcamp 2004 resulted in a research paper coauthored by a student and two staff members (to appear in the Journal of Discrete and Computational Geometry). Visiting Speakers for Mathcamp 2008John H. Conway (Princeton University) One of the most creative thinkers of our time, John Conway is known for his ground-breaking contributions to such diverse fields as knot theory, geometry of high dimensions, group theory, transfinite arithmetic, and the theory of mathematical games. Outside the mathematical community, he is perhaps best known as the inventor of the "Game of Life." Scott Aaronson (MIT -- computer science) Scott Aaronson studies the mathematics of computation . He is interested in the limitations of quantum computers ("what we can't do with computers we don't have"), and more generally, in fundamental limits on what can efficiently be computed in the physical world. He is the creator of Complexity Zoo, an online encyclopedia of over 460 classes of computational problems -- so you can ask him not only about the famous ones like P and NP, but also about MA_EXP, NISZK, coC=P, and QMA/qpoly. He was a camper at Mathcamp'96, where a talk by Richard Karp gave him his first exposure to theoretical computer science. He is thrilled to be back! Allan Adams (MIT - physics) Allan Adams studies quantum versions of algebraic and differential geometry that play a fundamental role in string theory, and uses these tools to explore the fate of tachyons, moose diagrams, and other puzzles involving black holes and spacetime singularities. Allan believes that everyone should understand quantum mechanics, which is as beautiful and strange as it is true, and looks forward to discussing it at Mathcamp. Emina Alibegovic (University of Utah) Emina Alibegovic works on geometric group theory, a field of mathematics that lies at the crossroads of geometry, algebra, and topology. However, Emina uses geometric group theory to solve problems in... logic! You might think this is backwards: certainly, logic can help us solve problems in algebra and geometry, but what can algebra or geometry tell us about logic itself? Well, it turns out that problems don't care which methods you use to solve them, as long as they get solved! Emina is very interested and invested in education and spends time doing mathematics with high-school teachers. She is looking forward to working with high-school students as well. Javier Arsuaga (San Francisco State University) Javier is a mathematician who uses knot theory to study DNA. Most of the time, DNA is a long and skinny linear molecule, but under certain experimental conditions it becomes circular and knotted. At Mathcamp, Javier will show students how DNA knots can be used to study chromosome organization in some viruses, as well as to understand the action of certain enzymes. Their course will be highly interdisciplinary, combining molecular biology, random knot theory and the physics of polymers. (Don't worry, Javier will teach you all the background you need to know!) Greg Budzban (Southern Illinois University) Greg Budzban is interested in modeling various processes in the world as stochastic discrete dynamical systems. His main research involves studying these models using algebraic structures, especially transformation semigroups. He is particularly interested in problems that can be modeled using automata, and will discuss one such problem called the Road Coloring Problem that was recently solved after about 40 years of work. He previously was principal investigator (PI) at Martin Marietta Orlando Aerospace for stochastic computer vision models, and is currently co-PI for an NSF curriculum development grant with the Algebra Project. This grant is helping to design a challenging high-school curriculum for under-served minority students centered around mathematics problems with current research interest. Moon Duchin (University of California Davis) Moon Duchin is interested in geometry, topology, and dynamics, in lots of different combinations. Lately she's got geometric group theory on her mind. She also thinks about philosophy, cultural studies, gender theory, what they have to say about math, and what math has to say back! George Hart (SUNY Stony Brook - computer science) George Hart is both a professor of computer science and a mathematical sculptor. At Mathcamp, he leads hands-on workshops in which participants explore the geometry of three- (and four-) dimensional space using the mathematical construction set Zometool. Dave Patrick (Art of Problem Solving) Dave Patrick is a textbook writer and instructor at Art of Problem Solving (AoPS). He is the author of two of AoPS's textbooks (and is currently working on a third), and has taught problem-solving courses for AoPS at all levels from MATHCOUNTS to the Putnam and most everything in between. In his past life doing mathematics research (at MIT and the University of Washington), Dave studied noncommutative algebraic geometry, in particular the classification and structure of noncommutative ruled surfaces. Josh Tenenbaum (MIT -- cognitive science) Josh Tenenbaum is a professor in MIT's Department of Brain and Cognitive Science. In his research, he builds mathematical models of human and machine learning, reasoning, and perception. His interests also include neural networks, information theory, and statistical inference. Mathcamp Faculty for 2008Mira Bernstein (Wellesley College)
Mira Bernstein has been one of the main organizers of Mathcamp since 1997. She received her PhD from Harvard University in 1999 and did her postdoctoral work at University of California Berkeley, before coming to Wellesley in 2002. Her training is in algebraic geometry, but she is increasingly interested in applied mathematics. Lately, she has been working on a project in mathematical population genetics in collaboration with a lab at the Harvard Medical School. David Savitt (University of Arizona)
Originally from Vancouver, Canada, David Savitt was the first-ever counselor at Mathcamp, and this year he will be working at his eleventh Mathcamp. David received his PhD at Harvard University in 2001 (where his work focused on an extension of the results which led to the proof of Fermat's Last Theorem) and did his postdoctoral research at McGill University (Montreal) and Institute des Hautues Etudes Scientifiques (Paris). Alfonso Gracia-Saz (University of Toronto, Canada)
Alfonso Gracia-Saz has been involved with Mathcamp since 2004. Originally from Spain, he received his PhD from the University of California at Berkeley and spent one year at Keio University in Japan . He counts both mathematicians and physicists among his collaborators. Outside of math, he loves folk dancing -- contra and square dancing in particular -- and is fascinated by the amount of mathematics (geometry, abstract algebra, topology, and even category theory) that can be found in the patterns. Mark Krusemeyer (Carleton College)
Mark Krusemeyer, who has been at Mathcamp every year since 1997, is Professor of Mathematics at Carleton College. He is one of the authors of the Wohascum County Problem Book, published by the MAA (Mathematical Association of America), and he has been a problem poser for the William Lowell Putnam Mathematical Competition, a annual contest for undergraduates across the U.S.A. and Canada. He has received an award for Distinguished College or University Teaching of Mathematics from the North Central Section of the MAA. His non-mathematical interests include early music (at Carleton, he also teaches recorder), hiking, bridge, and table tennis. Yvonne Lai (University of Michigan)
Yvonne Lai has been working for Mathcamp since 2000 after being a student in 1996. She received her PhD from the University of California at Davis, where she founded the Davis Math Circle and helped create the Explore Math Programs. This fall, she will begin post-doctoral training at the University of Michigan. Her work examines Coxeter group actions on hyperbolic spaces. Mathcamp 2008 Counselors
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