Metroplex Math Circle's posts

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MMC and AwesomeMath alumnus talks about how studying problem solving informed his ideas about good game design.

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We are pleased to announce that the first topic of our 2013-2014 Metroplex Math Circle will be Pólya-Burnside Enumeration in Combinatorics, presented by our own Adithya Ganesh on September 14, 2013.

Burnside’s lemma from group theory has a broad scope of application in combinatorial enumeration problems. Pólya’s enumeration theorem, which generalizes Burnside’s lemma using generating functions, provides a remarkable framework to easily solve counting problems in which we want to regard two entities as equivalent under some symmetry.

Burnside’s lemma from group theory has a broad scope of application in combinatorial enumeration problems. Pólya’s enumeration theorem, which generalizes Burnside’s lemma using generating functions, provides a remarkable framework to easily solve counting problems in which we want to regard two entities as equivalent under some symmetry.

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I'm very happy to announce that +Mathew Crawford, the author of such popular AOPS titles as Introduction to Number Theory and Intermediate Algebra is founding a school in the Dallas Metroplex.

If you don't want to miss the opportunity to sign up for his inaugural classes (I expect them to fill quickly) I recommend going to his site to sign up for his newsletter.

If you don't want to miss the opportunity to sign up for his inaugural classes (I expect them to fill quickly) I recommend going to his site to sign up for his newsletter.

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This Saturday, April 20th Dr. Kisačanin will return for another of his fantastic lectures. Triangles factor into almost every math contest in addition to being endlessly fascinating objects in themselves. Here is Dr. Kisačanin’s description of the session with links to resources:

In this talk about geometry of triangles we will see two different proofs of Stewart’s theorem, derive formulas for important cevians, and solve several interesting geometric problems.

We will also look at other important points in triangles (Fermat point, centers of excircles, …) and look at the Euler line, the nine-point circle, and related problems.

http://en.wikipedia.org/wiki/Stewart%27s_theorem

http://en.wikipedia.org/wiki/Fermat_point

http://en.wikipedia.org/wiki/Excircle

http://en.wikipedia.org/wiki/Euler_line

http://en.wikipedia.org/wiki/Nine_point_circle

In this talk about geometry of triangles we will see two different proofs of Stewart’s theorem, derive formulas for important cevians, and solve several interesting geometric problems.

We will also look at other important points in triangles (Fermat point, centers of excircles, …) and look at the Euler line, the nine-point circle, and related problems.

http://en.wikipedia.org/wiki/Stewart%27s_theorem

http://en.wikipedia.org/wiki/Fermat_point

http://en.wikipedia.org/wiki/Excircle

http://en.wikipedia.org/wiki/Euler_line

http://en.wikipedia.org/wiki/Nine_point_circle

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For 2ⁿ – 1 to be prime we also need n itself to be prime, but that is not sufficient. For example, 2¹¹ – 1 is composite even though 11 is prime. However, if you look at tables of Mersenne primes it is interesting to note that if you start with 2 and use that to make a new number 2ⁿ – 1 with n = 2 you get 3, then recycling the 3 you get 7, use n = 7 and you get 127, another prime! How long could this go on?

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The Summer Program in Mathematical Problem Solving is now seeking instructors for this summer! It's a chance to be a part of creating a really amazing place where students who might otherwise have no exposure to this kind of community or mathematics get the preparation to keep up advanced study. If you know someone who might be interested, please point them here:

http://www.artofproblemsolving.org/spmps/jobs.html

Thanks!

http://www.artofproblemsolving.org/spmps/jobs.html

Thanks!

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We will consider angle preserving transformations in Euclidean space and learn about the differences between the 2-D and 3-D cases. Then we will focus on the most interesting case of such a transformation in the plane and how it can be used.

Bring your colored pencils to help drawing some pictures.

Bring your colored pencils to help drawing some pictures.

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In a follow up lecture on mathematical functions, we will explore more stories and problems related to polynomials, trigonometric functions, and functional equations. Furthermore, we will dive deeper into the original historical context of functions – curves such as cycloids, cardioids, catenaries, circles, ellipses, hyperbolas, parabolas. Finally, we will try to understand why exponential and trigonometric functions turn up in solutions of so many fundamental problems in math, physics, and engineering. Come and learn with us!

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This 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.

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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