Archive for the ‘math circle’ Category

probability1.s600x600MIT 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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imagesThis 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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While Metroplex Math Circle is on Thanksgiving break please enjoy this replay of the excellent talk given by Mathew Crawford in our last session:

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This weekend we have a very special guest lecturer.  Mathew Crawford, who will be well known to many MMC attendees as the author of the popular AOPS titles:  Introduction to Number Theory and  Intermediate Algebra.   Mr. Crawford will be bringing with him 50 copies of problem materials which will be available only to the first 50 families to join us.  If you are unfamiliar with Mathew Crawford and his extensive work, the following information comes from the AOPSWiki:

Mathew Crawford is the founder and CEO of MIST Academy, a school for gifted and talented students, headquartered in Birmingham, Alabama. Crawford won numerous national math championships as a student before attending Washington University in St. Louis on a Compton Fellowship where he studied mathematics and worked on the Human Genome Project at the Institute for Biomedical Computing. After spending several years on Wall Street and eventually running a finance operation from the basement of his apartment, Crawford founded his first education company in 2001, Universal Set Educational Resources, with childhood friend Cameron Matthews. In 2003, Crawford became the first employee of Art of Problem Solving where he helped to write and teach most of the online classes during the first three years of the AoPS online school.

His competition achievements include:

  • National MathCounts written test champion in 7th grade (perfect score of 46) and second place in 8th grade (score of 44).
  • Two-time perfect scorer on the AHSME.
  • Perfect score on the AIME as a freshman.
  • Three-time invitee to the Mathematical Olympiad Summer Program.
  • Member of a top 4 Putnam team.
  • Youngest winner of the National Mu Alpha Theta convention.
  • Only 5-time winner of the Alabama State Written Examination (Algebra II/Trig once, Comprehensive four times).
  • Twice among ARML high scorers (tie-breakers) and Zachary Sobol Award winner.

Crawford also writes competition problems and performs duties for many math competitions:

  • USAMTS problem writer and grader (2004-2006)
  • iTest head test writer (2007 and 2008)
  • Birmingham and Alabama MATHCOUNTS coordinator
  • Mu Alpha Theta test writer and proof reader
  • Co-coach of the Missouri ARML team (1996,1997)
  • Coach of the San Diego ARML team (2005,2006)
  • Coach of the Alabama ARML team (2008, 2010-present)
  • Headed up the grading of the Power Round for the Georgia ARML site (2010)
  • San Diego Math League test writer and problem writer for the San Diego Math Olympiad (2004-6)

His first book, Introduction to Number Theory was published by AoPS in June, 2006. He is also coauthor of the Intermediate Algebra text, which came out in April, 2008.

Crawford’s user page can be found here.

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We are very fortunate this week to have Dr. Titu Andreescu return to present some more challenging problems and strategies for solving them.

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Cosmin Pohoata will return to the Metroplex Math Circle this week to give a talk on symmedians.  This will be an excellent lecture particularly for some of our more advanced students and those preparing for mathematical contests where symmedians can be a powerful part of their tool kits.

Abstract: We will introduce symmedians from scratch and prove the entire collection of interconnected results that characterize them.  Applications from contests around the world will also be presented if time permits.

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The AMC 8 is an important contest to introduce younger students (grades 8 and below) to problem solving and discrete mathematics topics.  Even very young students should begin working with these problems and participate in the AMC 8 in as many years as possible to be well prepared for the AMC 10 and 12 whose results are often requested by elite universities as part of the admissions process.

Metroplex Math Circle attendees are particularly fortunate to have Dr. Andreescu lead us through a discussion of some of his favorite AMC 8 problems.  Dr. Andreescu is the former director of the AMC and the former coach of the US International Mathematical Olympiad team whose members are ultimately chosen from the very best participants in the AMC sponsored contests.

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Last year one of our most popular sets of lectures were on Calculus.  Take this opportunity to hear, Dr. Branislav Kisačanin, introduce even our younger students to this beautiful topic.  Here is a description of the talk in his own words:

In this session we will look at calculus and try to dispel the mystery that often surrounds it. We will begin by looking at examples of limiting processes, and show for example that as x approaches 0, the value of \frac{\sin x}{x} approaches 1. Based on several other examples of limits, we will be able to determine line equations for tangents of various curves. This will bring us to the doorstep of the first derivative.

We will look at other interpretations of the first derivative and also look at how it is applied to maximization and minimization, Newton’s method of tangents for solving equations, etc. In the second hour we will look at another major part of calculus, integration, and will show how integration is used to compute areas and volumes. We will also look at the methods used by Archimedes to compute the volumes of solid spheres, which are remarkably similar to modern integration. Of course, there is much more to calculus than we can learn in one day, but this will be a good start!

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Machine learning is a fascinating scientific discipline concerned with the design of algorithms that enable a computer to automatically learn and improve with experience. Learning algorithms operate by recognizing complex patterns in data, which can then be applied to make intelligent decisions. As the amount of electronic data grows, so does the importance of machine learning. In fact, machine learning is one of the fastest-growing subareas of artificial intelligence, and is the core technology underlying many successful software applications, such as speech recognizers, spam filters, and product recommendation systems.

In this talk, Dr. Ng will give you an overview of the basics of machine learning, including its major paradigms, some of its successful stories, and the inner workings of one of the earliest machine learning algorithms that was popularly used in the 1990s.

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Do you grab an umbrella when the weatherman calls for an 80% chance of rain?  50%?  20%?  How do you make decisions about something as uncertain as the weather?

Life in general, and business specifically, can be just as uncertain as the weather.  Unfortunately, most companies and highly paid executives rely on a combination of deterministic tools, heuristic thinking and averages to make their decisions.  This “flaw of averages” leads many business leaders to oversimplify problems and to be far more confident in their decisions than they have any right to be.

For our last session of the 2011-2012 season, David Cordeiro will give an introduction to Monte Carlo simulation and its application to a wide variety of important business decisions.  Mr. Cordeiro will share his first hand experience witnessing how deterministic decision making led to falling stock prices, work force reductions and ruined careers.  It is never too late or too early to learn the art of stochastic forecasting and how to use these powerful techniques to make better decisions and avoid the Flaw of Averages.

Once requiring the power of a mainframe computer, Monte Carlo simulation software now runs on a standard laptop and can take advantage of the logic of standard Excel spreadsheets.  This software should be in the toolkit of anyone trying to make decisions about future outcomes (i.e. everyone).  

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