Archive for September, 2008

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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While many students take the AMC 10 or 12 to qualify to take the AIME test (in the hopes of progressing to the USAMO or IMO), there is another opportunity by participating in the USAMTS contest. The USA Mathematical Talent Search differs from these other tests because it is taken over several weeks and stresses the importance of clearly explaining a solution.

As opposed to most mathematics competitions, the USAMTS allows students a full month to work out their solutions. Carefully written justifications are required for each problem. The problems range in difficulty from being within the reach of most high school students to challenging the best students in the nation. Students may use any materials – books, calculators, computers – but all the work must be their own.

Richard Rusczyk’s Art of Problem Solving Foundations is the primary sponsor of USAMTS and he will certainly be able to answer any questions at his talk on September 20th.

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This is the continuation of the interviews with the 2006 US IMO team. The first speaker, is ZEB Brady. ZEB spent part of his summer at UT Dallas working at Dr. Andreescu’s prestigious summer camp, AwesomeMath. ZEB was a gold medalist at the 2006 IMO.

These particular problems are much harder than the level normally discussed at math circles, but the strategies of problem solving can be very similar. It is interesting to hear how even these brilliant students struggled with problem number 6.

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Metroplex Math Circle RSS Feed

To stay current on all announcements and articles from the Metroplex Math Circle you might consider subscribing to the RSS feed. RSS feeds allow you to to read updates to all of your favorite blogs and sites through a single interface. MMC chose a blog format to keep its community of students and friends aware of upcoming MMC meetings as well as other events like contests that may be of interest.

Please click on the icon below if you would like to subscribe.

RSS Subscription

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As we prepare for our first lecture of the year by Richard Rusczyk, we will share links to some articles that show his excellent observations on problem solving, education and their role in a full life. One of these outstanding articles is The Calculus Trap which begins with the following:

You love math and want to learn more. But you’re in ninth grade and you’ve already taken nearly all the math classes your school offers. They were all pretty easy for you and you’re ready for a greater challenge. What now? You’ll probably go to the local community college or university and take the next class in the core college curriculum. Chances are, you’ve just stepped in the calculus trap.

For an avid student with great skill in mathematics, rushing through the standard curriculum is not the best answer. That student who breezed unchallenged through algebra, geometry, and trigonometry, will breeze through calculus, too. This is not to say that high school students should not learn calculus – they should. But more importantly, the gifted, interested student should be exposed to mathematics outside the core curriculum, because the standard curriculum is not designed for the top students. This is even, if not especially, true for the core calculus curriculum found at most high schools, community colleges, and universities…

Please visit the Art of Problem Solving site to continue reading this and other articles by Richard and his colleagues.

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The Road to the IMO

Several postings have concerned the International Math Olympiad which is a bold aspiration for many Math Circle participants. But there are several steps on the road to representing the US on the IMO team and each one of those steps has its own challenges and rewards.

The IMO team is selected from among the top performers on the USAMO (United States of America Math Olympiad).

The USAMO is a six question, two day, 9 hour essay/proof examination. All problems can be solved with pre-calculus methods. Approximately 500 of the top scoring AMC participants (based on a weighted average) are invited to take the USAMO.

Just sitting for the USAMO requires a distinguished performance on the AIME, AMC 12 or AMC 10 tests.

The AIME (American Invitational Mathematics Examination):

The AIME (American Invitational Mathematics Examination) is an intermediate examination between the AMC 10 or AMC 12 and the USAMO. All students who took the AMC 12 and achieved a score of 100 or more out of a possible 150 are invited to take the AIME. All students who took the AMC 10 and had a score of 120 or were in the top 1% also qualify for the AIME.

The AMC 10 and AMC 12 test are administered to hundreds of thousands of high school students. Many of the universities who routinely reject applicants with 800 SAT Math scores are requiring submission of AMC test scores.

A special purpose of the AMC 12 is to help identify those few students with truly exceptional mathematics talent. Students who are among the very best deserve some indication of how they stand relative to other students in the country and around the world .

To prepare for these challenging and potentially life altering tests, AMC offers the AMC 8 eligible to students through the 8th grade.

The AMC 8 is a 25 question, 40 minute multiple choice examination in junior high school (middle school) mathematics designed to promote the development and enhancement of problem solving skills. The examination provides an opportunity to apply the concepts taught at the junior high level to problems which not only range from easy to difficult but also cover a wide range of applications. Many problems are designed to challenge students and to offer problem solving experiences beyond those provided in most junior high school mathematics classes.

Math Circles have a great deal to offer beyond improving performance on this series of tests. However, Metroplex Math Circle is particularly fortunate to have as its Director, Dr. Titu Andreescu, the former Director of AMC and Coach of the US IMO team. He has generously shared his experience with MMC students to help them prepare for these critical steps on the road to the IMO.

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A fascinating book for anyone interested in Olympiad problem solving or educations is Count Down: The Race for Beautiful Solutions at the International Mathematical Olympiad.

“Count Down” is a narrative account of the 2002 International Mathematical Olympiad, which was held at George Mason University just outside Washington, D.C. It follows the six members of the U.S. team, their coach, and their guide (who was a team member several years ago), describing the qualities that led the Olympians to be among the best high-school-aged mathematical problem solvers in the world. More broadly, Count Down explores the following question: How does anyone learn how to do something extremely well?

The book prominently features the Director of MMC, Dr. Andreescu, as well as many other friends of the Metroplex Math Circle.

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