Dr. Branislav Kisačanin – Geometry of Triangles

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

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April 6, 2013 – Purple Comet! Problems and Student Presentations

Join us in the first hour to hear MMC students present some of their favorite problems and mathematical concepts.  In the second hour we will work on problems from the Purple Comet! contest and talk about this exciting opportunity to compete with other students around the world.

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March 2, 2013 – Dr. Titu Andreescu – More Interesting Problems

With the AMC tests behind us and the AIME to come, don’t miss this opportunity to hear Dr. Andreescu talk about some of his favorite problems!

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February 23, 2013 – Dr. Dimiter Nickolov Vassilev – “Inversion and conformal transformations in the plane and 3-D space.”

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.

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February 16, 2013 – Dr. Branislav Kisačanin – “A Tour of Mathematical Functions II”

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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February 9, 2013 – Dr. Tatiana Shubin

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.

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February 2, 2013 – Dr. Branislav Kisačanin – “A Tour of Mathematical Functions”

Parabola or catenary?

In this lecture we will retrace the steps of Archimedes, Newton, Euler, and other great mathematicians and learn about important mathematical functions, their properties, history, and applications. We will look at several interesting competition topics that often show up on AMC 10/12, related to exponential, logarithmic, trigonometric, hyperbolic, and other functions. We will also see how these functions turn up in solutions of some fundamental problems in math, physics, and engineering. We will have fun using them to draw important curves: cicloids, cardioids, catenaries, circles, ellipses, hyperbolas, parabolas, and will discover which one of them is brachistochrone and which one is tautochrone.

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January 26, 2013 – Dr. Jonathan Kane – “Constructions with Straight Edge and Compass and Other Implements”

Learn all about the classic theory of geometric objects with only straight edge and compass. What can you construct, and what is impossible? Which regular polygons can you construct? What if you have help by being given a fixed parabola? Come with your pencils and be ready to draw (compasses provided, or bring your own)!

To perform well on geometry problems on math competitions it is necessary to have a deep understanding.  This understanding can be achieved by retracing the footprints of the very first mathematicians whose only tools were a straight edge and compass.

Dr. Kane is one of our most popular lecturers and is recently retired from his position as a professor at the University of Wisconsin – Whitewater.  Along with Dr. Andreescu he is the co-founder and coordinator of the Purple Comet! Math Meet.  Dr. Kane is also the co-chair of the AIME committee and a faculty member at the AwesomeMath summer camp.

Along with his wife, Jane E. Mertz, Jonathan Kane is the author of several important research papers on the role of culture and gender in mathematical achievement including “Debunking Myths about Gender and Mathematics Performance.”

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January 19, 2013 – Ivan Borsenco – “Exploring the world of Probability”

MIT student and four time International Mathematical Olympiad participant, Ivan Borsenco, will return to the Metroplex Math Circle this week!

Ivan will introduce the classical probability theory. There will be many interesting examples and several unexpected results. Students will solve a few mathematical paradoxes, find out how to build simple probabilistic models, and have lots of fun.

A deep understanding of probability is not only useful for contest preparation, but is critical for anyone planning a career in science or business.

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December 15, 2012 – Dr. Titu Andreescu – “Some of my Favorite Problems”

This next meeting will be our last before the holiday break at UTD and the end of the Fall semester.  Students preparing for the 2013 AMC 10 and 12 will not want to miss this session when Dr. Andreescu share some of his favorite problems and approaches for solving them.

All students should make a serious effort to register and prepare for the AMC 10 or 12 exam.  There is no limitation on how young a student can participate and no restriction on how many years you take the exam until you reach 10th and 12th grades respectively.  The AMC results are requested by many elite colleges to differentiate among the many applications they see with 800 SAT scores.

Here is some additional information about this year’s AMC 12:

The AMC 12 is a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. Calculators are not allowed starting in 2008. For the 2012-2013 school year there will be two dates on which the contest may be taken: AMC 12A on Tuesday, February 5, 2013 , and AMC 12B on Wednesday, February 20, 2013 .

 

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