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## October 1, 2011 – Dr. Branislav Kisačanin – “First Encounter with Calculus”

Many of our students have started taking Calculus or are curious about what it’s all about.  Take this opportunity to hear one of our favorite lecturers, 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 dispell the mistery 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 tangets 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 caclulus than we can learn in one day, but this will be a good start!

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
7. Christina Chen, MA
8. Megan Chen, IL
9. Angela Gu, CA

## Problem of the Month

This year we have a new opportunity to promote problem solving within the circle and to help our talented young problem solvers become better know to peers and Math Circle directors across the country (and around the world).

The Problem of the Month is a new initiative inspired by Dr. Dana Paquin, the former director of the Stanford Math Circle.  Each month our circle and others across the country will get a set of challenging problems.  Individual problem solving is fine but you are encouraged to collaborate with others to create the most elegant solutions.

Solutions will be sent to a group of Math Circle directors for evaluation and groups with correct and (especially) elegant responses will be publicly recognized by the world’s best Math Circles and other sponsoring organizations.  Keep in mind that many of these are the same individuals who are involved with the camps, contests and universities to which our students will be applying.

In addition to solving problems posed by professional problem writers, we are also being asked to provide problems written by our own students.  Writing problems is one of the best ways to improve your own problem solving, and the authors of those problems that are accepted for distribution will receive special recognition.

Please find in the attached PDF (Problem of the Month v1) some additional information about The Problem of the Month program.  If you have problems to submit please send them to circleofcircles@sbcglobal.net before the due date of September 30.  Problems can be submitted by students, parents or friends of Metroplex Math Circle.

## September 24, 2011 – Joshua Nichols-Barrer – “Modular Arithmetic in Contest Mathematics”

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.

## September 17, 2011 – Radu Sorici – “Mathematics of Computer Science”

Metroplex Math Circle will start its 2011-12 sessions with our own Radu Sorici!  This session should be very interesting for students beginning to work on computer programming or accomplished coders who want a better understanding of the mathematical principles behind their work.

In this session Radu will discuss some elementary mathematics that are useful for computer science. Some of the topics covered: logic notation, methods of proof, sets, graph theory, counting principles, etc.   In addition, we will look at some real world applications of the topics discussed.

## MO Math – The Geometry of Origami

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.

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