Archive for November, 2008


Our very good friends at the Art of Problem Solving have worked very hard to develop a new online learning system called “Alcumus.”  Alcumus is a game that students can play to compete against themselves, compare their progress on the leader’s board and identify gaps or weaknesses in their math preparation.

Alcumus features over 1100 different problem representing a wide variety of subjects.  In addition, the Art of Problem Solving instructors have developed over 60 video tutorials to help students better understand the subjects they are likely to see on contests like AMC 8, AMC 10 and AMC 12.

Alcumus is currently free to members of the Art of Problem Solving community so login or create an account today.


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Upcoming Contests

We would like to wish good luck to all of the MMC students who will be participating in the MEANT Math Olympiad this weekend or the AMC 8 test next week.  Following are some of the awards given to students who perform exceptionally well on the AMC 8:

  • A Certificate of Distinction is given to all students who receive a perfect score.
  • An AMC 8 Winner Pin is given to the student(s) in each school with the highest score.
  • The top three students for each school section will receive respectively a gold, silver, or bronze Certificate for Outstanding Achievement.
  • An AMC 8 Honor Roll Certificate is given to all high scoring students.
  • An AMC 8 Merit Certificate is given to high scoring students who are in 6th grade or below.

If you are interested in the distribution of scores in previous years and how individuals and schools performed in 2007 please click on the link below.  Best of luck again to our students!

AMC 8 2007 General Statistics

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One of the greatest enterprises on the Internet has been the posting of course materials by elite universities.  MIT’s Open Courseware (OCW) has been a leader in bringing the benefits of their unique curriculum to the world.

Getting a glimpse into introductory courses is critical because they often weed out those students who are unprepared to pursue studies and later careers in fields like Computer Science.  However, I am glad to say that many of our students who have been coming to Math Circle and participating in MATHCOUNTS or AMC tests will find many of the topics in this course very familiar.

Please click below to download some of the excellent lecture notes and tests.


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Our November 19, 2008 Special Presentation will be by Dr. Arthur Benjamin, who in addition to being a sought after speaker is also a successful author.  Many people are familiar with Dr. Benjamin from the course that he authored for the Teaching Company entitled Joy of Mathematics. Following is an excerpt from the course description:

Fun with Numbers

Here is an example:

Think of a number between 1 and 10. Triple it. Add 6. Then triple again. Now take your answer, probably a two-digit number, and add the digits of your answer. If you still have a two-digit number, add those digits again. You should now be thinking of the magical number 9. The reason this works is based on algebra and the fact that the digits of any multiple of 9 must sum to a multiple of 9.

This is one of the many wonders of modular arithmetic, sometimes called clock arithmetic, where numbers wrap around in a circle. A useful application of this field is casting out nines, a simple and ancient technique for checking the answers to arithmetical problems.

Modular arithmetic also provides a very handy method for mentally computing the day of the week for any date in history.

This connection between entertaining number tricks and the deeper properties of mathematics reflects Dr. Benjamin’s specialty, which is combinatorics, the branch of mathematics that deals with the subtleties of counting. Some examples: How many different six-symbol license plates are possible? And for the book collector, how many ways are there of arranging 10 books on a shelf? (Would you believe more than 3 million?) These simple questions introduce concepts such as the factorial function.

Drawing on his dual fascination with combinatorics and games, Dr. Benjamin used his analytical skill to win first place in the American Backgammon Tour in 1997.

In addition to his scholarly articles, Dr. Benjamin has also written books that are highly accessible to the public.  One such book is Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks co-written with Michael Shermer with a foreword by Bill Nye the Science Guy.  Praise for this book includes:

secretsofmentalmath-bookcover“A great introduction to the wonder of numbers, from two superb teachers.”
— Brian Greene, author of The Elegant Universe

“A magical mystery tour of mental mathematics! Fascinating and fun.”
— Joseph Gallian, president of the Mathematical Association of America

“The clearest, simplest, most entertaining, and best book yet on the art of calculating in your head.”
— Martin Gardner, author of Mathematical Magic Show and hundreds of Mathematical Games columns for Scientific American.

“This book can teach you mental math skills that will surprise you and your friends. Better, you will have fun and have valuable practical tools inside your head.”
— Dr. Edward O. Thorp, mathematician and author of Beat the Dealer and “Beat the Market”

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benjamin-colorheadshot_tnMetroplex Math Circle is very pleased to announce a special presentation by Dr. Arthur Benjamin, November 19th, 2008 at 7:00 PM in the TI Auditorium, room 2.102 in the Engineering and Computer Sciences building (ECSS) on the campus of the University of Texas at Dallas.

Dr. Benjamin is a very distinguished mathematician at the prestigious Harvey Mudd College who has authored multiple books and scholarly papers.

But he is also very well known as an entertainer and “mathemagician.”  Dr. Benjamin’s program should be inspiring and entertaining for adults and students of all ages.

Following are just some of the accolades that Dr. Benjamin has received from reviewers and audiences:

“He talks like a peformer, acts like a magician, and multiplies faster than a calculator.”
— The Los Angeles Times.

“Someone you can count on!”
— People Magazine

“Please allow me to express our sincere thanks for your amazing performance at the 2008 Archer User Group Summit in Orlando, Florida. Your gift for mental calculation is truly astounding. The technology, risk management and compliance professionals who attended the Summit were completely captivated by your presentation, and we appreciate the excitement that you brought to our event. You had the complete attention of everyone in the room throughout your entire presentation, and your feats of mind were a major point of discussion for the remainder of the Summit. We would wholeheartedly recommend your presentation to any organization planning an event for professionals who like a good mental challenge. You inspired us all to use our brains a little bit more, and we will never forget your incredible show.”
— Alex Bender, Vice President of Marketing, Archer Technologies, 2008

“Doctor Benjamin’s presentation ranks among the very best. He is able to entertain, motivate, stimulate, and educate simultaneously, a rare ability that helps to bring the joy of math and science into the lives of his audiences.”
— Dr. Steven Murov, Director, Modesto Area Partners in Science

“Parents, teachers, and children, with multiple layers of math phobia, related easily to your imaginative style of storytelling and theater that brings math to a ‘Wow!’ level.”
Sarah Orleans, Director of Programs, The Franklin Institute Science Program

“Dr. Arthur Benjamin made two presentations at Millersville University as part of the 21st annual Brossman Science Lectureship. The audience for the afternoon presentation consisted of 5th through 9th graders. The audience for the evening performance consisted of children through adults including university students and faculty. There was standing room only for both presentations (750 each). These were the largest crowds to ever attend the Science Lectureship. Dr. Benjamin appealed to all ages. His presentations were energetic and humorous as well as being informative. He had people excited about mathematics. One teacher stated: ‘Dr. Benjamin was a fantastic lecturer and truly inspiring to the students.'”
— Dr. Lyman Rickard, Millersville University

“Arthur Benjamin, the `mathemagician,’ wowed the crowd with his demonstration of lightning calculation. It’s hard to believe that watching someone do math would be entertaining, but Arthur is a knockout.”
— Magic Magazine, November 2007

“That was one of the most incredible finishing acts we’ve ever had!”
— Carmie Henry, Vice President, Electric Cooperatives of Arkansas, 2008

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Here is a nice, longer biography of our November 8th speaker, Simion Filip.  This prize appears to be just one of many past and future distinctions.  In addition to being a great lecturer, he is nearer to many of our students in age and should be a great inspiration.

princeton_universitygifGeorge B. Wood Legacy Junior Prize

The recipient of this year’s George B. Wood Legacy Junior Prize was Simion Filip. The award is given to a member of the senior class in recognition of exceptional academic achievement during the junior year.

Filip lives in Chisinau, Republic of Moldova, where he graduated from Liceul Orizont, the Moldo-Turkish Lyceum. Before matriculating at Princeton, he won a bronze medal at the International Mathematical Olympiad in Greece and a silver medal at the Balkan Mathematical Olympiad in Bulgaria, both in 2004, and, in 2005, a silver medal at the International Mathematical Olympiad in Mexico, a gold medal at the Balkan Mathematical Olympiad in Romania and a bronze medal at the International Olympiad in Informatics in Poland.

An A.B. candidate, Filip is concentrating in mathematics, a subject he studied in the spring of his sophomore year at the Independent University of Moscow. At Princeton, Filip won the Shapiro Prize for Academic Excellence for his sophomore year and the Andrew H. Brown Prize for outstanding junior work in mathematics. In the summers of 2007 and 2008, he won first prize at the International Mathematics Competitions in Bulgaria.

Filip’s research interests in mathematics lie in areas with applications to mathematical physics, in particular, ergodic theory and algebraic geometry. His senior thesis will likely focus on questions about the ergodic theory of moduli spaces of Riemann surfaces.

Last year, Filip took 13 courses, including seven graduate seminars. Outside the classroom, he is interested in yoga and rock climbing. He is a member of Forbes College.

After graduation, Filip hopes to pursue a Ph.D. in mathematics, with the long-run goal of becoming a research mathematician.

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This Saturday, November 8th, Simion Filip will present the way our understanding of the physical world shaped the geometric problems that we considered throughout history.  Examples will be drawn mostly from elementary Euclidian geometry and the talk should be accessible to anyone who is familiar with angles and triangles.

Mr. Filip is a senior at Princeton University, studying mathematics with an interest in mathematical physics. After graduation, he plans to pursue a Ph. D. in mathematics.  While in high-school, Simion Filip took part in both the International Mathematics and Informatics Olympiads, where he received silver and bronze medals respectively.

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