September 14, 2013 – Adithya Ganesh – “Pólya-Burnside Enumeration in Combinatorics”
September 28, 2013 – Dr. Branislav Kisačanin – “A Tour of Mathematical Functions”
In this talk we will learn about the art of protecting information, some incredible (but true) stories from the history of cryptography, and how the all-important RSA code ( http://en.wikipedia.org/wiki/RSA_(algorithm) ) works. To get there, we will need a bit of Number Theory, in particular the Fermat’s Little Theorem ( http://en.wikipedia.org/wiki/Fermat%27s_little_theorem ) and the Euler’s Theorem ( http://en.wikipedia.org/wiki/Euler%27s_theorem ). In the process we will also learn how to solve a class of problems that might be seen at AMC competitions, such as:
- What is the remainder when 2^1000 is divided by 997?
- Determine the last digit of 1^1 + 2^2 + 3^3 + … + 2009^2009.
October 05, 2013 – Dr. Jonathan Kane – “Rose of Roses”
October 12, 2013 – Cosmin Pohoata – “Non-standard Induction”
Please join us this Saturday as Titu Andreescu leads the group through a selection of some of the most interesting AMC 8 problems.
January 11, 2014 –Mathew Crawford – “Mathematical Research as Problem Writing”
Please join Dr. Titu Andreescu and Mathew Crawford as they offer an American Regions Mathematics League (ARML) session for students interested in learning more about the contest and wishing to be exposed to the types of problems they would encounter. This will be a very interactive math circle where students will have the opportunity to work together to solve interesting problems. Here is the plan for this first practice as detailed by Mathew Crawford:
- We plan to talk about our goals for the team.
- Discuss the rules and format for ARML, the primary event for the Metroplex Math Team
- Practice three of the four rounds from a past ARML contest (Individual, Team, and Relay)
We will practice the fourth ARML round (the Power Round) as the Metroplex Math Team participates in the ARML Power Contest the following weekend.
For this first contest, we’re picking an ARML contest that isn’t from the past few years both in hopes that fewer students have seen the problems and also because the problems from older contests are a little more accessible to beginners. We plan to use more recent practice problems as the team progresses.
Veterans of ARML are encouraged to show up to this first practice to help make new students comfortable with the process and also because leadership matters—and we will practice like we play, as a team.
If you know of talented high school students or extremely motivated younger students in the Dallas Metroplex area who may want to attend this event, please pass this link along.
January 25, 2014 –Emily Herzig – “Matrix Operations and Applications”
The 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.
A 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.