Archive for July, 2010

I’ve added a new link to the blog of a remarkable young man, Holden Lee.  Holden was an instructor at this year’s AwesomeMath and he is the author of widely read and insightful essay on the personal challenges of competitive problem solving.

Please take some time to read the problems and personal observations on Mental Wilderness.

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There was a great article today on Dr. Andreescu’s summer camp, AwesomeMath.  Here is an excerpt.

UTD program challenges the best and brightest young mathletes

08:04 AM CDT on Wednesday, July 21, 2010

By KATHERINE LEAL UNMUTH / The Dallas Morning News

For the select group of academically gifted middle and high school students training intensively this summer at the University of Texas at Dallas, math is a sport.

The problems they work in geometry, algebra, combinatorics and number theory far exceed the curriculum used at Texas high schools.

“These are the athletes of the mind,” said Titu Andreescu, 53, director of the three-week AwesomeMath program. “Most of them are a lot better than students in college, including math majors.”

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The Art of Problem Solving has just announced a new course starting this fall in Group Theory.   Like all of the AOPS courses this is sure to be an excellent offering.   Here is the AOPS course description:

Group theory is the study of symmetry. Objects in nature (math, physics, chemistry, etc.) have beautiful symmetries and group theory is the algebraic language we use to unlock that beauty. This example-driven course will focus specifically on building groups from other groups, ways that groups can act on various sets, and using the tools of group theory to construct fields.

Group theory is the gateway to abstract algebra, one of the two core branches of higher mathematics. (Just as calculus is the gateway to the other core branch, analysis.) Algebra and analysis together hold the tools for most areas of advanced mathematics, from geometry to topology to applied mathematics and beyond. Algebra is what tells us (among many other things) that you can’t trisect an angle, that there are finitely many regular polyhedra, and that there is no closed form for solving a quintic, for example. In this class we will get a glimpse of the mathematics underlying these famous questions.

Note: We will not assume prior knowledge of what a group is. Group theory is a topic that is generally reserved for a sophomore or junior level abstract algebra course, but this class attempts to present the most important concepts and examples on a level appropriate for very strong high school students. The goal of this class, as with all of our classes, is to provide a much richer curriculum that challenges students who are otherwise exhausting the subjects available to them.

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Congratulations to the US team at the 2010 IMO for taking third place.  Benjamin Gunby, a participant in last year’s AwesomeMath camp came away with a Gold medal in his first IMO!  Here are the members of the US team and their achievements:

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