## September 27, 2014 – Dr. Imre Leader – “Van Der Waerden’s Theorem”

September 23, 2014 by Metroplex Math Circle

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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