pythagoras-3-4-5Please join us this Saturday for a discussion about the Pythagorean Theorem.  We will look at this famous theorem from various angles and illustrate with interesting applications.

Cordeiro2014-10Jacob Cordeiro will discuss the NACLO (North American Computational Linguistics Olympiad), and the skill which you can pick up in order to take part in this clever and fun competition. We’ll solve some favorite problems in group discussions, and learn the logic behind computational linguistics. Linguistic experience is by no means required–there will be something for all ages and all levels of skill.

topologistIt is known how important it is to be able to “recognize” shapes in 3D. A way to achieve this is by using concepts of modern topology (a part of mathematics studying shapes). In the talk, in a down to earth form, we introduce important concepts from Algebraic Topology and show examples of how they work. We explain also how these can be used in identifying the shape of objects in 3D.

Titu PortraitCome join us November 1st and hone your skills for this year’s problem solving season.  AMC 8 is this month, making it a great time to delve into various interesting problems.  Combinatorics, Number Theory, Geometry, and Algebra problems will be presented with multiple difficulty levels to challenge and delight our math circle patrons.  Whether you are new to problem solving or looking for some additional challenges, this is a great circle for working with peers and under the instruction of Dr. Titu Andreescu, who has been coaching and educating mathletes for over 30 years.

bulgarianacademyIn this talk we discuss a new geometric characterization of the so called Napoleon n-gons characterized by the property that the centers of the regular n-gons erected outwardly on its sides are vertices of a regular n-gon. As a consequence, we obtain a new proof of the well-known theorem of Barlotti-Greber that an n-gon is Napoleon if and only if it is affine-regular. Moreover, we generalize this theorem by obtaining an analytic characterization of the n-gons leading to a regular n-gon after iterating the above construction k  times.
The talk is based on a joint work with Prof. T. Andreescu, University of Texas at Dallas and
Prof. V. Georgiev, University of Pisa, Italy accepted for publication in American Mathematical Monthly.

Later in the session, you will learn more about the High School Students Institut of Mathematics and Informatics established in 2000 by the Union of Bulgarian Mathematicians on the occasion of the World Year of Mathematics.

poshenIt’s easy to generate large numbers for their own sake.  A more interesting question is whether huge numbers ever arise naturally from simple-looking situations.  In this talk, we will explore two examples of this phenomenon.  The first will be a surprise from the International Mathematical Olympiad.  The second concerns Szemeredi’s Regularity Lemma, a result of central significance in graph theory.
This talk will be accessible to a general audience.  Only understanding of arithmetic is required: addition, subtraction, multiplication, division, and exponentiation.  Nevertheless, only about 50 (out of 500+) International Math Olympiad contestants correctly solved the corresponding problem during the IMO contest, and so the talk will be of interest to students spanning the full range of experience.
About the speaker:
As a math professor at Carnegie Mellon University, Po-Shen Lo conducts research on a variety of topics that lie at the intersection of combinatorics (the study of discrete systems), probability theory, and computer science.  Po-Shen also works to connect the worlds of research and school math, as the national lead coach of the USA International Math Olympiad team.  He was a member of the 1999 USA IMO team, which was led by Titu Andreescu.  To further develop the talent base in the USA (and the world), he recently teamed up with a number of math/science contest stars to create an open web platform (expii.com), which empowers the world to collaboratively create interactive expositions on math and science topics.

MMC LogoPlease 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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