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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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In this fun and interactive talk, Dr. Frank Wang will introduce students to the concepts and “big ideas” of Group Theory.  Dr. Wang has given this talk at math teacher conferences, on live cable television, and to students as young as fourth grade in schools, large and small, throughout the country.  Dr. Wang is a mathematician by training (PhD in pure math from MIT), textbook author (with Saxon Publishers), and former textbook  publisher (formerly CEO of Saxon Publishers) whose passion and mission are to make the concepts of higher math accessible and interesting to students of all ages and abilities.  In recent years, he has worked with students in Los Angeles Unified, Chicago Public Schools, NYC Public Schools, Clark Co. Public Schools and here at DISD.  This summer, he will become the president of the Oklahoma School of Science and Mathematics, succeeding the founding president who has served since the school opened its doors in 1990.  Dr. Wang gives this talk in thanks to the wonderful support he has gotten from and the many friendships he and his family has made in the north Dallas community.

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We are looking forward to Ivan Borsenco’s return to UT Dallas.  Ivan, a former mathematical olympian, AwesomeMath instructor and current MIT student will present a number of problems and their solutions using the Pigeonhole and Extremal Principles.

The pigeonhole and the extremal principles are heuristical principles that are not tied to any subject but are applicable in all branches of mathematics.  Their beauty lies in the fact that they can justify existence of an object with a certain properties.  We will learn the use of these principles by going through a couple of classical theorems and solving lots of entertaining problems that have unexpected solutions.

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Congratulations to the winners of this year’s contest held at MIT:

  1. Victoria Xia, VA
  2. Danielle Wang, CA
  3. Julia Huang, CA
  4. JungYoon (Sara) Kim, VA
  5. Frances Ding, TN
  6. Sheela Devadas, MA
  7. Christina Chen, MA
  8. Megan Chen, IL
  9. Angela Gu, CA
  10. DiYun (Susan) Sun, Canada

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We look forward to seeing old and new friends today at the September 17  session of Metroplex Math Circle.  Next week we look forward to a lecture from Joshua Nichols-Barrer.   Dr. Nichols-Barrer earned his PhD at MIT and is the AwesomeMath Academic Director, a two time IMO silver medalist and a multiple winner of the USAMO.

Here is a description of the session in Dr. Nichols-Barrer’s own words:

Modular arithmetic is an essential tool for properly treating number theory problems in contest mathematics.  While there is far more to talk about than we have time for today, we will extensively cover the foundations of arithmetic mod an integer $m$, looking to differences between mod $m$ arithmetic and that which we are all familiar with, as well as those things which distinguish arithmetics mod $m$ for distinct values of $m$.  We will also begin to think about algebra mod $m$ should we have the time.

Modular arithmetic is one of the many fields ignored by standard math curricula but critical for success in math competitions or a career in mathematics or sciences.

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A Museum of Mathematics is scheduled to open next year in New York City.  They already have hosted speakers and their presentations are remarkably similar to what one finds in a typical math circle, a brilliant and passionate speaker talking about their favorite subject and their career in mathematics and problem solving.

Here is Erik Demaine talking about the mathematics of folding and his passion for origami.

Part 1 of 4

Part 2 of 4

Part 3 of 4

Part 4 of 4

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Number Theory is one of the cornerstones of math competitions and a vast field explored by professional mathematicians.  We are very fortunate to have Dr. Josh Nichols-Barrer present to us next week.  Dr. Nichols-Barrer was a very accomplished teenage competitive problem solver who has earned his doctorate at MIT.  In addition to Number Theory our students can learn a great deal from his personal experiences.  Here is a description of the session in Dr. Nichols-Barrer’s own words:

As you know, each positive integer may be factored uniquely into a product of powers of primes.  Do you know why?   In this class we will look at the structure of the integers in the simplest terms, and use that for a foundation from which we might actually prove that what we know to be true actually is.  In the first half we will recall some things about arithmetic that we know intuitively and can name (with maybe a surprise or two), and in the second half we will proceed to prove (along with some other things which are no less key) unique prime factorization in the integers.

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Here is an interesting article from MIT on patterns in high math achievement based on a study of AMC data.  This research follows on the heels of the paper written by Dr. Andreescu and his colleagues last year.  The study seems to conclude that girls (and presumably also boys) thrive when they are able to study math in a community that reinforces their interests and encourages their talents.

Here are some key excerpts from the article:

Ellison and Swanson arrived at their findings by using a novel source of data: the American Mathematics Competitions (AMC), a 60-year-old annual contest involving 125,000 exceptional high-school students. A select group of students who do especially well on the AMC compete in a series of annual competitions, the U.S. Mathematical Olympiad and the International Mathematical Olympiad. This focus on standout students differs from most studies about math and gender in schools…

The numbers Ellison and Swanson scrutinized indicate that the gender disparity among star math students widens as performance levels increase. In 2007, about 800,000 girls took the math SAT, compared to about 700,000 boys. Yet at the 99th percentile of the math SATs, boys outnumber girls two to one. In their research, Ellison and Swanson divide that upper tier into even smaller segments, using AMC results. Among students in the 94th percentile of the AMC tests, they found, the top boys outnumbered the top girls four to one; at the 99th AMC percentile, six to one; and at the 99.9th AMC percentile, 12 to one…

Ellison thinks this huge gender disparity is linked to another fact: Among those students scoring so highly on the AMC and participating in the math Olympiads, the range of high schools represented is much greater for boys than for girls. “The top boys in the Olympiads come from all over the United States,” says Ellison. “Some of them are from big powerhouse schools, and some are from schools where they’re the only student who’s really good at math. But it’s these 20 high schools where the majority of the girls are coming from.” Those institutions range from Phillips Exeter Academy, an elite New England prep school, to a fistful of public high schools in Northern California, from Palo Alto to San Jose. By contrast, Ellison and Swanson note, half of the boys in the Olympiads come from about 200 high schools…

O’Keeffe, who has a daughter who competed in the math Olympiad, is inclined to agree. “Anecdotally, I do think the difference a community makes is enormous,” she says. “If you’re lucky enough to be at a school with a math club, you might be the only girl in it. At Exeter or Stuyvesant [a prominent Manhattan public high school], you might be in a minority, but you won’t be alone.” To be more rigorous, though, Ellison wants to track many individual students over time…

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Next Saturday we are pleased to have Brian Basham join us to give a lecture that will touch on conditional probability and graph theory.  Brian is well known to many of the country’s top problem solvers as a teaching assistant at both AwesomeMath and IdeaMath.  Brian is currently a mathematics major at MIT and like many of our speakers may share his experiences of getting into and studying at a top tier university.  Brian’s other accomplishments include:

  • Two time USAMO qualifier
  • MOSP qualifier 2007
  • 1st Place HMMT Combinatorics Subject Test 2008
  • AMC 10 Perfect Score 2005

Brian describes the content of his lecture in this way:

A quest to defeat the cannibals that inhabit my favorite math problem. Our journey will start with conditional probability and what it has to with medical diagnoses. We will travel into graph theory and learn how turning people into points can make problems much easier to solve. Finally we discover a concept in computer science which will help us claim victory over the cannibals and keep us from becoming dinner.

Like many of our lectures, Brian’s talk should be accessible to novice problem solvers but challenging to even the most experienced.

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rsi_logo_headerOne of the more elite camps for high school juniors is the Research Science Institute held at MIT.  Following is a brief description of the program.

Each summer approximately 75 high school students gather for six of the most stimulating weeks of their young lives. Selected from the United States and other nations, these students participate in a rigorous academic program which emphasizes advanced theory and research in mathematics, the sciences, and engineering.This is the Research Science Institute (RSI).

Students attend college-level classes taught by distinguished professors. Nationally recognized teachers conduct classes designed to sharpen research skills. In addition, students complete hands-on research with top mentors at corporations, universities, and research organizations.

Many RSI students use their RSI research projects as a basis for entry to science competitions, garnering top awards in the annual Intel Science Talent Search, the Siemens-Westinghouse Science and Technology Competition, and the All-USA High School Academic Scholarship.

The uniqueness of CEE lies in its commitment to help RSI alumni throughout their academic careers – from college selection through search for graduate fellowships, fostering a community with both camaraderie and intellect. CEE’s follow-up program includes helping alumni find suitable summer employment, sponsoring trips to other nations for alumni as Junior Ambassadors, and many other activities.

RSI is open to students who have completed the third year of high school, or the equivalent, by the summer of 2009. The twenty-sixth annual summer session of RSI will be held at the Massachusetts Institute of Technology from June to August, 2009.

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