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Please join us for a fun look at permutation patterns. We will count some special classes of permutations. For example, there are “132-avoiding” permutations, which are those (like 546231) that never have three entries in order smallest-largest-middle. Among the n! permutations of size n, how many are 132-avoiding? And how many are 123-avoiding? That question is just the beginning. Next, we can count the number of permutations with 3 “descents”—downsteps between consecutive entries—again, like 546231—or the number of permutations with 3 “excedences”—cases of pi(i)>i—again, like 546231. There is a connection, which is another beginning. All this can be unified, and we’ll try to do that using “triangular functions.”

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Come join us this Saturday for a fun session of AMC 8 level problems and beyond. November 18, 2014 (Tuesday) is the AMC 8 test, so come study with Dr. Titu Andreescu, former director of the American Mathematics Competition for 5 years, former coach of the US IMO team, and of course, the director of Metroplex Math Circle and AwesomeMath.

If you have a child who would like to participate in the AMC 8 tests, but his/her school does not offer the opportunity, you can register with Kathy Cordeiro after math circle ($10 registration fee).

Remember, we are now meeting in room 2.312 of the ECSS building.

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Please join us for another exciting math circle where we are pleased to welcome Dr. Imre Leader. Dr. Leader is a professor of Pure Mathematics at the University of Cambridge, an IMO medalist, and a 10 times national champion of Othello!

He will give a presentation this Saturday on Van Der Waerden’s Theorem which “is a theorem in the branch of mathematics called Ramsey theory. Van der Waerden’s theorem states that for any given positive integers *r* and *k*, there is some number *N* such that if the integers {1, 2, …, *N*} are colored, each with one of *r* different colors, then there are at least *k* integers in arithmetic progression all of the same color. The least such *N* is the Van der Waerden number *W*(*r*, *k*). It is named after the Dutch mathematician B. L. van der Waerden.^{[1]}“

Here is a question to get you thinking, “Suppose that we are given a long string of beads. The beads come in two colors, red or blue, but there may be no `pattern’ to the sequence of colors. Can we guarantee to find three equally-spaced beads of the same color? For example, if the 4th, 6th and 8th beads were blue then this would count.”

This topic will be accessible for even young students as long as they understand power notation, e.g. 3^10.

**REMINDER: We are meeting in room 2.312 of the ECSS building**

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(Image credit: Wikipedia)

Come join us in learning about number sequences! We will start with a story about Leonardo Pisano, better known as Fibonacci, his often forgotten fundamental contributions to mathematics (do you know what they are?), and his ubiquitous sequence of Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, …

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Please join us for this kick off event for Math Circle! Naoki Sato will give an enlightening talk about Game Theory as described below:

When playing a two-player game, what is the best move? What is the best overall strategy? And is there a way to determine who can win? In this talk, we will be exploring the basics of combinatorial game theory, starting with simple two-player games, such as Nim. Along the way, we will see how we can determine winning positions, and we will give techniques for analyzing other types of games.

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