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## Schedule 2011-2012

January 21, 2012 – Roberto Bosch Cabrera – “Equations and Systems of Equations via Inequalities”

This lecture will focus on three well known inequalities:

1. x^2>=0
2. AM – GM
3. Cauchy – Schwarz

January 28, 2012 – Dr. Jonathan Kane – “My Favorite Circle Problems”

Dr. Kane will guide students through the usual theorems from the results about angles in circles to the theory of inversion.  He will then derive parametric equations for hypocycloids and similar curves.   Finally, the students will tackle many circle related problems which can be solved using these theorems.

February 4, 2012 – Dr. Titu Andreescu – “AMC Preparation”

The AMC 10 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 2010-2011 school year there will be two dates on which the contest may be taken: AMC 10A on Tuesday, February 7, 2012 , and AMC 10B on Wednesday, February 22, 2012 .

February 11, 2012 – Krassimir Penev – “Nonstandard Geometric Problems”

Bulgarian Olympiad winner, Krassimir Penev will consider a variety of problem-solving techniques and important facts used for solving nonstandard geometric problems. The examples include but are not limited to the Nine Point Circle, Euler’s line, Ceva’s Theorem and cyclic quadrilaterals.  These mathematical tools could be used for math competitions such as the AMC10,12, AIME, USAMO and Intel talent search.

February 18, 2012 – Dr. Branislav Kisačanin – “Introduction to Graph Theory”

Graph theory was born when Leonhard Euler solved the Seven Bridges of Koenigsberg problem and has since grown into a mathematical discipline with beautiful theoretical results and with applications in disciplines like theory of dynamic systems, electrical engineering, computer vision, neuroscience, and social networking.

February 25, 2012 – No Math Circle

March 3, 2012 – Dr. Titu Andreescu – “More Contest Problems”

March 10, 2012 – No Math Circle – UTD Spring Break

March 17, 2012 – No Math Circle – UTD Spring Break

March 24, 2012 – Ivan Borsenco – “Solving Problems with Pigeonhole and Extremal Principle”

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 the 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.

March 31, 2012 – Dr. Frank Wang – “Group Theory with Fruits – A Fun and Intuitive Introduction to Abstract Algebra & Beyond”

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 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.

April 7, 2012 – Dr. Dimitar Grantcharov – “Inequalities”

April 14, 2012 – No Math Circle – Circle on the Road

April 21, 2012 – David Cordeiro – “The Flaw of Averages: Monte Carlo Simulation and Problem Solving Applied to Business Decisions”

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.  Unfortunately, most companies rely on a combination of deterministic tools, heuristic thinking and averages to make their decisions.  This “flaw of averages” leads many business leaders to over simplify problems and to have a greater confidence in their decisions than is warranted.  Mr. Cordeiro will share his first hand experience witnessing how such cartoonish 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.

## Fall Semester 2011

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

In this session we will discuss some elementary mathematics that is 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.

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

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.

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

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!

October 8, 2011 – Dr. Titu Andreescu – “Digits of Positive Integers”

The presentation will feature several interesting problems related to digits of positive integers, most problems having a contest flavor.

October 15, 2011 – Dr. Titu Andreescu – “Prime and Composite Numbers””

Next Saturday Dr. Andreescu will return to share some of his favorite problems related to primes and composite numbers. Not only are these subjects major components of mathematical contests, they are also used widely in applied math topics like cryptography. The presentation will contain interesting problems involving primes and numbers that can be written as product of primes.

October 22, 2011 – Dr. Branislav Kisačanin – “Second Encounter with Calculus”

Following his very successful lecture on October 1, Dr. Kisačanin will continue his introduction to calculus.  Students who have already studied some calculus will gain a deeper insight into this beautiful and useful tool.  Those who have not yet studied calculus should not be put off, however, as Dr. Kisačanin is very skilled at explaining mathematical concepts so that they can be appreciated by a broad audience.

October 29, 2011 – Cosmin Pohoata – “Apollonius’ Delight: Ruler and Compass Constructions”

Constructions using only the compass and the unmarked ruler (straightedge) have always been something to be enjoyed by triangle geometers throughout time and to inspire many Olympiad problems nowadays. Here, we will see why this subject can be so appealing and will cover a few basic constructions for afterwards to challenge ourselves and see how these serve as natural “macros” for constructions which at first sight seem out of reach.

November 5, 2011 – Dr. Titu Andreescu – “AMC 8 Preparation”

If you are a student who has not yet passed 8th grade, please make every effort to attend next week’s math circle.  The AMC 8 contest is the first in a series of competitions eventually used to select the team for the International Mathematical Olympiad.  While few students will ever represent the US on this elite team, the scores from the AMC tests become an important component of any transcript when applying to a STEM program in an elite college.

With today’s international and competitive application environment, elite universities routinely see many 800 SAT math scores.  The more rigorous AMC test provides these schools a more meaningful measure of students who will succeed in their math or science programs.

Our students have a great advantage learning directly from Dr. Titu Andreescu.  Dr. Andreescu was the director of the AMC (you will see his name on the certificate above) and the coach of the US IMO team.  Do not miss this opportunity to improve your understanding and performance on the AMC 8 which will prepare you for the more advanced competitions to come.

November 12, 2011 – MEANT 6th Annual Math Olympiad

November 19, 2011 –  No Math Circle to Accommodate Thanksgiving Travel

November 26, 2011 – No Math Circle to Accommodate Thanksgiving Travel

December 3, 2011 – Dr. Branislav Kisačanin – “Solving Recursions”

Sequences of numbers are often defined using a recursive relation and initial conditions, for example, the sequence of Fibonacci numbers is defined with F_{n+2} = F_{n+1} + F_{n} and initial conditions F_{1} = 1, F_{2} = 1. In this lecture we will see (a) how to solve various types of recursions (b)How to determine various sequence properties of number sequences directly from the recursions, and (c) how this knowledge can come in handy in many competition problems as well as in the study of computer science.

December 10, 2011 – Dr. Ivor Page – “Thinking as Exercise”

In this talk we will solve problems from multiple areas of mathematics and computer science. We will discuss Euler circuits and paths and their use in designing postman routes, finding Steiner points with soap bubbles, counting cannon balls in stacks, continued fractions, the ubiquity of Fibonacci numbers in Computer Science and nature, problems that are intractable for computers, and more.Bring your brain!

December 17, 2011 – No Math Circle Until we Reconvene in January!