Archive for September, 2008

The day has finally arrived, the first lecture of the MMC 2008-2009 season!  We are very pleased to have Richard Rusczyk join us from San Diego.  Richard is the author of many books used by accomplished problem solvers for individual study or as the backbone of a classroom course.  One example is his new book Introduction to Algebra.

Introduction to Algebra

Learn the basics of algebra from former USA Mathematical Olympiad winner and Art of Problem Solving founder Richard Rusczyk. Topics covered in the book include linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and much more!

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Coming Prepared to Math Circle

Math Circle is a very inexpensive activity since all of the costs are generously underwritten by UT Dallas.  The only materials needed are pencil and paper.  Calculators are not necessary and not encouraged.

Some students find it useful to have a math notebook or a binder to collect notes and handouts from various sessions.  At the end of a semester these notes can be very useful for contest preparation or further study.

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Who are the Olympians?

Our friends at SDMC provide a link to a fascinating study at the Center for Mathematics Education. The PowerPoint presentation linked below provides some interesting demographic research on accomplished problem solvers.

Mathematical Olympians: Who are they, where are they from, and how did they get where they are?”,

The research sets out to answer the following question:

What aspects of the in-school and out of school experiences of IMO caliber students can be identified as promising for the encouragement of a broader population of students into sustained and advanced study of mathematics in secondary school and beyond?

Of particular interest is the strong role played by the family, the school, the challenge of contests and mentors (slide 15). Metroplex Math Circle attempts to bring all 4 factors together to help our students to achieve their full potential.

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In addition to being the subject of books like Count Down, the Director of Metroplex Math Circle, Dr. Titu Andreescu is also the author of multiple books on problem solving. These books draw on his many years of experience as the director of AMC, coach of the US International Math Olympiad team and author of many contest problems.

To help the Metroplex Math Circle community we have created an Amazon List with some of Dr. Andreescu’s currently available books. In addition to Dr. Andreescu’s books for experienced problem solvers we have also included some books and resources on the list for students just starting into problem solving.

Not only does Metroplex Math Circle benefit from Dr. Andreescu himself, but many of his co-authors are also friends of MMC and frequent lecturers.

Following are the author descriptions from the book 104 Number Theory Problems: From the Training of the USA IMO Team:

About the Authors

Titu Andreescu received his Ph.D. from the West University of Timisoara, Romania. The topic of his dissertation was “Research on Diophantine Analysis and Applications.” Professor Andreescu currently teaches at The University of Texas at Dallas. He is past chairman of the USA Mathematical Olympiad, served as director of the MAA American Mathematics Competitions (1998–2003), coach of the USA International Mathematical Olympiad Team (IMO) for 10 years (1993–2002), director of the Mathematical Olympiad Summer Program (1995–2002), and leader of the USA IMO Team (1995–2002). In 2002 Titu was elected member of the IMO Advisory Board, the governing body of the world’s most prestigious mathematics competition. Titu co-founded in 2006 and continues as director of the AwesomeMath Summer Program (AMSP). He received the Edyth May Sliffe Award for Distinguished High School Mathematics Teaching from the MAA in 1994 and a “Certificate of Appreciation” from the president of the MAA in 1995 for his outstanding service as coach of the Mathematical Olympiad Summer Program in preparing the US team for its perfect performance in Hong Kong at the 1994 IMO. Titu’s contributions to numerous textbooks and problem books are recognized worldwide.

Dorin Andrica received his Ph.D. in 1992 from “Babes-Bolyai” University in Cluj-Napoca, Romania; his thesis treated critical points and applications to the geometry of differentiable submanifolds. Professor Andrica has been chairman of the Department of Geometry at “Babes-Bolyai” since 1995. He has written and contributed to numerous mathematics textbooks, problem books, articles and scientific papers at various levels. He is an invited lecturer at university conferences around the world: Austria, Bulgaria, Czech Republic, Egypt, France, Germany, Greece, Italy, the Netherlands, Portugal, Serbia, Turkey, and the USA. Dorin is a member of the Romanian Committee for the Mathematics Olympiad and is a member on the editorial boards of several international journals. Also, he is well known for his conjecture about consecutive primes called “Andrica’s Conjecture.” He has been a regular faculty member at the Canada–USA Mathcamps between 2001–2005 and at the AwesomeMath Summer Program (AMSP) since 2006.

Zuming Feng received his Ph.D. from Johns Hopkins University with emphasis on Algebraic Number Theory and Elliptic Curves. He teaches at Phillips Exeter Academy. Zuming also served as a coach of the USA IMO team (1997-2006), was the deputy leader of the USA IMO Team (2000-2002), and an assistant director of the USA Mathematical Olympiad Summer Program (1999-2002). He has been a member of the USA Mathematical Olympiad Committee since 1999, and has been the leader of the USA IMO team and the academic director of the USA Mathematical Olympiad Summer Program since 2003. Zuming is also co-founder and academic director of the AwesomeMath Summer Program (AMSP) since 2006. He received the Edyth May Sliffe Award for Distinguished High School Mathematics Teaching from the MAA in 1996 and 2002.

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One of the many things taught and practiced at a Math Circle is the invaluable skill of communicating a solution to another person.  This is a skill that many students find translates to fields beyond math as well.

Richard Rusczyk, our September 20th 2008 speaker, has written an excellent guide to solution writing based on his extensive experience.  Here is the introduction:

You’ve figured out the solution to the problem – fantastic! But you’re not finished. Whether you are writing solutions for a competition, a journal, a message board, or just to show off for your friends, you must master the art of communicating your solution clearly. Brilliant ideas and innovative solutions to problems are pretty worthless if you can’t communicate them. In this article, we explore many aspects of how to write a clear solution. Below is an index; each page of the article includes a sample ‘How Not To’ solution and ‘How To’ solution. One common theme you’ll find throughout each point is that every time you make an experienced reader have to think to follow your solution, you lose.

To access the guide please click on How to Write a Solution.

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The San Diego Math Circle (SDMC), like our own Metroplex Math Circle, has been a leader in identifying talented young problem solvers.  On their beautifully redesigned web site, they have an interesting discussion of the impact their math circle has had on the number of USAMO qualifiers from their community.

The following chart shows the strong correlation between the rise in USAMO success and the founding of SDMC in 2002.  Click on the chart to read the rest of the page on Olympiads and Olympians.

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Our September 20th, 2008 speaker, Richard Rusczyk, is the author of several books designed to help teenage problem solvers. Introduction to Geometry is an excellent text that many of our Math Circle participants have used, often along with the Introduction to Geometry course at Art of Problem Solving.

Learn the fundamentals of geometry from former USA Mathematical Olympiad winner Richard Rusczyk. Topics covered in the book include similar triangles, congruent triangles, quadrilaterals, polygons, circles, funky areas, power of a point, three-dimensional geometry, transformations, and much more.

…the text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which geometric techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains over 900 problems. The solutions manual contains full solutions to all of the problems, not just answers.

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