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DSCN0764In this talk, we’ll introduce the first moment method in probabilistic combinatorics and prove a few cute olympiad problems using it. We’ll also include a proof of a beautiful result due to Erdős and, if time permits, discuss some ongoing research that originated from it.

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February Happenings

Thank you all for attending Dr. Benjamin’s Mathemagic show.  His joy of math, curiosity, and connection with the group made the presentation come alive for all who attended.  If you’d like to learn more about how you can engage in problem-solving activities in the area or other upcoming speakers, please email kathy.cordeiro@gmail.com.

February 21, 2015 – There will be no math circle, therefore, it is a great time to take a tour of AwesomeMath Academy!  Drop by anytime classes are in session:  http://www.awesomemathacademy.org/classes.html.

February 25, 2015 – MMC will be hosting the AMC 10B/12B.  Pr-registration is required.  Contact kathy.cordeiro@gmail.com for more information.

February 28, 2015 – MMC’s very own Jacob Cordeiro will be presenting at UTD’s Computer Science Education and Outreach program.  No math circle on this day.Screenshot 2015-02-19 18.24.48

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Don’t miss this amazing opportunity to see Dr. Arthur Benjamin, a Professor of Mathematics at Harvey Mudd College, perform his Mathemagics show this Saturday.  He has delighted a global audience with his mixture of math and magic and now Metroplex Math Circle will be able to enjoy this fast-paced and entertaining performance.  The event will be held in the TI Auditorium of the ECSS building on the campus of UTD.  This will be a popular session, so come early to ensure a seat.Screenshot 2015-01-16 09.32.58

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For some simple games, there is a clear winning strategy for one of the players, which makes the games a bit boring. Or does it? Well, only if you actually find the strategy!  Come join us for a fun look at games and the winning strategies behind them.

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Screenshot 2015-01-26 15.55.05There will not be a math circle this Saturday, however, if you are interested in attending a free problem-solving session led by Dr. Titu Andreescu, I encourage you to go to AwesomeMath Academy on January 31st between 4-5:30pm and receive excellent guidance for contests such as the AMCs, Purple Comet, and USAMTS.  Information and details are on the flyer.  Refreshments and door prizes will be offered.

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Come join us for Dr. Benjamin’s Mathemagics show at Metroplex Math Circle in the TI Auditorium from 2-4 pm.

Screenshot 2015-01-16 09.32.58

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fibonacciThe Fibonacci numbers are known for representing a simple pattern with incredible properties. Robert Bosch is here to talk about some of them, posing lots of interesting problems about the Fibonacci sequence and its connections. Whether you’re interested in the Fibonacci sequence or are completely new to the subject, you’ll be able to learn and derive a library of elegant formulas.

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If you compute the number 355/113, then you will see that it is a very good approximation to the number pi. How can we find such a fraction? And can we find approximations for other numbers as well? These are some of the questions we will answer in this talk, which will revolve around the rational numbers. We will start by looking at their counterparts, the irrational numbers. We will then discuss a way of writing rational numbers known as continued fractions, which turns out to have important applications. We will also introduce Farey sequences, which have several interesting properties, and will lead to a deeper understanding of the structure of rational numbers. This talk is aimed at a general audience, and one of the goals will be to touch on different branches of mathematics and show how they can connect with each other.

Please Note:  AMC 10/12 registration will take place starting at this lecture on January 17th.  There is a $10 fee to register.

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jonCounting Adult and Children Tickets

Suppose one afternoon a theater sells 10 adult tickets and 15 child tickets. In how many different orders can those tickets be sold? What if no more than two child tickets are sold between each sale of adult tickets? How about if 10 adult tickets and 10 child tickets are sold but as the tickets are sold, the number of child tickets sold is never allowed to exceed the number of adult tickets sold? We will discuss many variations of these types of problems and draw parallels to many other kinds of counting problems.

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gabrielJoin us this Saturday as we journey together to discover the answer to this question, “What do powers of 2 and primes have in common?”  We will start by discussing a problem de Polignac posed in 1849 that raised the question, “Which numbers can be written as the sum of a prime and of a power of 2?”  The conjecture was refuted by Paul Erdos in 1950 with the following theorem: there is an infinite arithmetic progression of odd numbers which cannot be written as the sum of a prime and of a power of 2.  After we reflect on Erdos’ theorem, we will compare the result with Romanov’s theorem which states that a positive proportion of positive integers are the sum of a prime and of a power of 2.

Gabriel Dospinescu, co-author of Problems from the Book and Straight from the Book, is an associate professor at l’Ecole Normale Supérieure de Lyon.

**Special Note:  While our MMC students enjoy this enlightening talk, parents can learn more information about Stanford University Online High School (OHS).  The Director of Admissions for the OHS, Claire Goldsmith, will be in the area offering presentations at local private/public schools and will stop by the math circle for the benefit of our community.

Stanford Online High School serves academically gifted and talented students in grades 7 – 12 from around the world. Students partake in interactive, real-time online seminars taught by expert instructors and are placed by ability, not grade level. Students also have access to a vibrant student life with over 50 clubs and organizations as well as local and regional meet ups. Students can attend full-time and graduate from Stanford OHS or enroll part-time, choosing courses from a catalog of over 60, many of which are AP or University level. For more information visit the school’s website https://ohs.stanford.edu/; or to speak with an Admission Officer, email ohsadmissions@stanford.edu.
Claire Goldsmith is Director of Admission and Financial Aid at Stanford OHS and also oversees external relations for Stanford Pre-Collegiate Studies. She has also run student life and taught History at Stanford OHS. Previously, Claire taught English and French and coached debate at the Harvard-Westlake School in Los Angeles. She graduated magna cum laude in History and Literature from Harvard College and holds a Masters in Policy, Organization, and Leadership Studies from Stanford University Graduate School of Education.

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