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eigenvaluesA dynamical system is a set of functions that depend on each other. For example, dynamical systems are often present in ecosystems: more plants mean more plant-eaters, and more plant-eaters mean fewer plants. These systems can be difficult to predict, as one thing affects another, which affects the first, which affects the other, and so on.

Fortunately, dynamical systems can be simplified. This lecture focuses on an important type of dynamical system that can be solved with some creative usage of matrices. We’ll also discuss the related concept of “eigenvalues,” a simple concept with some very interesting implications.

Please join us for the last math circle of the Spring Semester!


PascalsTriangleCoefficientThe first hour of this talk will be targeted primarily at the younger part of our audience (roughly in grades 4-7) – we will explain the fundamental rules of counting that can be used to solve even very hard problems: rule of sum (addition principle), rule of product (multiplication principle), pigeonhole principle, and the inclusion-exclusion principle. We will use them to solve a number of interesting problems from various competitions. For those students already familiar with these concepts, we will have a set of problems to keep them busy during the first hour.

The second hour will be targeted at the more experienced members of the Math Circle community (roughly grades 8-12). First, we will discuss several techniques used to prove combinatorial identities (combinatorial arguments, algebraic manipulations, and the method of generating functions). We will prove several important combinatorial identities using all of these techniques, illustrating the diversity of approaches found in combinatorics. After that we will look at applications of combinatorics in number theory, geometry, and graph theory, illustrating them with more interesting and challenging problems. While the younger part of our audience may not be able to follow everything during the second hour, it will be a great exposure to advanced mathematical topics, to show them they have a lot more to learn.

Throughout the talk we will highlight the mathematicians who developed this beautiful mathematical field, from its beginnings in gambling to modern applications in medicine, science, and technology.

PascalTriangleAnimated2


armlMetroplex Math Team students practice for ARML. We plan to practice Team, Individual, and Relay rounds and discuss solutions to some of these challenging problems. Join us!


Cayley-graph-of-the-cyclic-group-Z-by-8Z-with-the-generators-S23Abstract Algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these structures are groups, rings, and fields.

In the following introduction to this topic, we will discuss Binary Operations, Groups, Subgroups, Cyclic Groups, Cayley Digraphs, and how they relate to each other. With a thorough understanding of these topics, students will have the basis to further examine the subject that is Abstract Algebra.


 polynomialThere are many times when we come across polynomial equations. In school, we certainly learn how to solve linear equations, then we learn how to solve quadratic and cubic equations, and finally we find out that we can view them as one mathematical object! That object is called a polynomial, it is simple and has very nice properties.
In our lecture we present a unified view of polynomials. This will help you understand concepts covered in school much better and much faster. There will be plenty of tricky Olympiad problems related to them and it will be fun!!

armlJoin us for another exciting ARML training session.  This team based contest will allow for students to work together solving interesting problems.  For more information, check out:  http://arml.com/arml_development/page/index.php

**Reminder – there is no Math Circle on February 15 because of the UTD Programming Contest and there is no Math Circle on February 22 because of the MATHCOUNTS competition.


amcmedalThe AMC 10A/12A is on February 4th and the AMC 10B/12B is on February 19th.  If you’d like a chance to learn some interesting tips and techniques to help with these competitions, then please join us for this enlightening Math Circle.  Adrian Andreescu, Vinjai Vale, and Dr. Titu Andreescu will be presenting problems to challenge and delight.

If you have yet to sign up for these tests and your school does not offer them, there is still room for both dates (these testing sites are not sponsored by Metroplex Math Circle).  Registration will be held outside the math circle room, ECSS 2.201.

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