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Archive for the ‘math circles’ Category


cosmin3Abstract: We prove a few combinatorial gems by using induction on unexpected quantities.

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network-securityIn this talk we will learn about the art of protecting information, some incredible (but true) stories from the history of cryptography, and how the all-important RSA code works. To get there, we will need a bit of Number Theory, in particular Fermat’s Little Theorem and Euler’s Theorem. In the process we will also learn how to solve a class of problems that might be seen at AMC competitions, such as:
  • What is the remainder when 2^1000 is divided by 997?
  • Determine the last digit of 1^1 + 2^2 + 3^3 + … + 2009^2009.

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tshubin02This coming Saturday, the Metroplex Math Circle is very fortunate to have Dr. Tatiana Shubin, one of the leaders in the global math circle movement speak to our circle!  We will post more details on the topic of her talk, but no opportunity to hear Dr. Shubin speak should be missed.

In addition to being the Director of the San Jose Math Circle, Tatiana Shubin (shubin[at]math.sjsu.edu) won the All-Siberian Math Olympiad when she was in the seventh grade. Her B.S. is from Moscow State University (Russia), and her PhD is from UC Santa Barbara. She served for 6 years as the California State Director of AMC-8, then became a co-founder of the Bay Area Math Adventures (BAMA), and has been on the BAMA steering committee ever since.

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Parabola or catenary?

Parabola or catenary?

In this lecture we will retrace the steps of Archimedes, Newton, Euler, and other great mathematicians and learn about important mathematical functions, their properties, history, and applications. We will look at several interesting competition topics that often show up on AMC 10/12, related to exponential, logarithmic, trigonometric, hyperbolic, and other functions. We will also see how these functions turn up in solutions of some fundamental problems in math, physics, and engineering. We will have fun using them to draw important curves: cicloids, cardioids, catenaries, circles, ellipses, hyperbolas, parabolas, and will discover which one of them is brachistochrone and which one is tautochrone.

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We are looking forward to Ivan Borsenco’s return to UT Dallas.  Ivan, a former mathematical olympian, AwesomeMath instructor and current MIT student will present a number of problems and their solutions using the Pigeonhole and Extremal Principles.

The pigeonhole and the extremal principles are heuristical principles that are not tied to any subject but are applicable in all branches of mathematics.  Their beauty lies in the fact that they can justify existence of an object with a certain properties.  We will learn the use of these principles by going through a couple of classical theorems and solving lots of entertaining problems that have unexpected solutions.

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If you are a student who has not yet passed 8th grade, please make every effort to attend next week’s math circle.  The AMC 8 contest is the first in a series of competitions eventually used to select the team for the International Mathematical Olympiad.  While few students will ever represent the US on this elite team, the scores from the AMC tests become an important component of any transcript when applying to a STEM program in an elite college.

With today’s international and competitive application environment, elite universities routinely see many 800 SAT math scores.  The more rigorous AMC test provides these schools a more meaningful measure of students who will succeed in their math or science programs.

Our students have a great advantage learning directly from Dr. Titu Andreescu.  Dr. Andreescu was the director of the AMC (you will see his name on the certificate above) and the coach of the US IMO team.  Do not miss this opportunity to improve your understanding and performance on the AMC 8 which will prepare you for the more advanced competitions to come.

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Please go visit the newly designed web site of our good friends at Mid-Cities Math Circle, (MC)^2.  You may also want to “like” their new Facebook Page to be notified about upcoming sessions and contests.

Speaking of which, this Saturday, May 14, Dr. Grantcharov will be sponsoring the annual 2011 UT Arlington Math Competition.

Both middle-school and high-school students are welcome to participate in the competition. There is no registration fee and no pre-registration is required. There will be on-site registration. If you wish to attend the competition, please plan to arrive around 8:30 am in PKH, UT Arlington.

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Evan O’Dorney, an active participant in the Berkeley Math Circle was the $100,000 winner of this year’s Intel Science Talent Search.  He joins last years’ winner, Amy Chyao, in continuing the connection between math circles and this prestigious contest.

WASHINGTON, D.C., March 15, 2011 – Honoring high school seniors with exceptional promise in math and science, Intel Corporation and Society for Science & the Public (SSP) today announced the winners of America’s most elite and demanding high school research competition, the Intel Science Talent Search.

Evan O’Dorney, 17, of Danville, Calif., won the top award of $100,000 from the Intel Foundation for his mathematical project in which he compared two ways to estimate the square root of an integer. Evan discovered precisely when the faster way would work. As a byproduct of Evan’s research he solved other equations useful for encrypting data. This furthered an interest he developed as early as age 2, when he was checking math textbooks out of the library.

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Metroplex Math Circle will kick off its spring 2011 semester with a presentation by Dr. Dimitar Grantcharov.    Dr. Grantcharov is an assistant professor at UT Arlington and the director of our neighbor, the Mid Cities Math Circle.  Dr. Grantcharov will use problems from last year’s UT Arlington Math Competition to help prepare our students for the upcoming AMC 10, 12 and AIME.  Here are some examples:

  • Which of the following numbers is a perfect square?
    (A) 98!99! (B) 98! 100! (C) 99! 100! (D) 99!101! (E) 101!101!
  • A square has sides of length 10, and a circle centered at one of its vertices has radius 10. What is the area of the union of the regions enclosed by the square and the circle?
  • A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token in the discard pile. The game ends when some player runs out of tokens. Players A, B, and C start with 15, 14, and 13 tokens, respectively. How many rounds will there be in the game?
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    Many students aren’t fortunate enough to live near a thriving math circle (much less the two that we have in Dallas, Metroplex Math Circle and the Mid Cities Math Circle).  To address this need an entrepreneurial young man in Wichita Falls, Shri Ganeshram, has launched the Online Math Circle.

    Shri was assisted in this effort by Holden Lee and Marius Craciunoiu.  He also received some of his inspiration from our own Dr. Titu Andreescu while attending AwesomeMath.

    Please help Shri by visiting and helping to promote his site.

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