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The Math Circle is a program of courses founded in 1994, designed for students who enjoy math and want the added challenge of exciting topics that are normally outside the school curriculum. Its teachers are experienced, committed, and enthusiastic. Our classes encourage a free discussion of ideas; while the courses are mathematically rigorous, the atmosphere is friendly and relaxed.
Bob and Ellen Kaplan write: "Our approach in The Math Circle is to pose questions and let congenial conversation take over. Conjectures emerge from a free-for-all, examples and counterexamples from the conjectures. Two steps forward are followed by a step back. What really is at issue here? How will we know when we've understood something? Is proving different from seeing? Where and with what should proofs begin, and how validate these beginnings? And if we get it, need we formalize it? Yes - following my old fencing-master's adage about holding the foil like a bird: tightly enough not to let it get away, not so tightly as to crush it. We don't want a '6Os feel-good sense of math as expressive hand-waving. We explain that rigor without mortis consists in fluency at making a connected path back to foundations that will stand up to scrutiny. In our exchanges the students are developing the knack of pushing insight adventurously ahead while protecting the supply-lines that fuel it."
The second Math Circle Summer Teacher Training Institute was help on the Campus of Notre Dame, in South Bend Indiana, from July 5th to 11th, 2010. The Institute included demonstrations of Math Circles, practice sessions in running Math Circles, discussions of theory and practice, and conversations about selected math topics.
**Robert Kaplan** has worked on mathematics with people from four up, most recently at Harvard University. In 1994, with his wife Ellen, he founded at Harvard The Math Circle, a program, open to all comers, for the enjoyment of pure mathematics. He has also taught Philosophy, Greek, German, Sanskrit and Inspired Guessing. He is the author of
*The Nothing That Is: A Natural History of Zero* (Oxford 2000), and with his wife,
*The Art of the Infinite: The Pleasures of Mathematics* (Oxford 2003), and
*Out of the Labyrinth: Setting Mathematics Free* (Oxford 2007).
*Hidden Harmonies: The Lives and Times of the Pythagorean Theorem,* will be published by Bloomsbury Press in January 2011. He lives with his wife in Massachusetts, but plays cricket for the Grange Club in Scotland, where he first became acquainted with naught.
Although
**Ellen Kaplan** was a classical archaeologist through graduate school at Harvard and in Germany, she has taught Biology, Greek & Latin, and the history of many places and times. She began teaching Mathematics to integrate an all-male department, but was so delighted by the breadth and depth of the field that she ended up co-founding the Math Circle with her husband, illustrating his book,
*The Nothing That Is* (Oxford 2000), and writing
*The Art of the Infinite* and
*Out of the Labyrinth: Setting Mathematics Free* (Oxford 2003 and 2007 respectively) with him. Their
*Hidden Harmonies: The Lives and Times of the Pythagorean Theorem,* will be published by Bloomsbury Press in January 2011. With their son Michael she has written
*Chances Are . . . Adventures in Probability* (Viking 2006), and
*Bozo Sapiens: Why to Err Is Human* (Bloomsbury). They are at work on their third book. For more details, see
*Who's Who in America.*

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