The math skills learned in our math circles have been helpful to students hoping to improve their scores on the AMC tests or the AIME. But to be successful in olympiads or to answer the questions from USAMTS or AOPS requires that students can also articulate their problem solving in the form of proofs.

A preferred tool for writing proofs and indeed for writing many scientific papers is the typesetting system called LaTeX. Whether you are a student who has never tried LaTeX and proof writing or you just want to improve your skills, this Saturday’s workshop is for you. Even younger students will enjoy how easy it is to create very advanced mathematical expressions by mastering LaTeX.

The LaTeX typesetting system (pronounced “Lay-Tek” or “Lah-Tek”) is widely used to produce well-formatted mathematical and scientific writing. With LaTeX, it is very easy to produce expressions like

Nearly every serious student of math and science will use LaTeX frequently.

In the second hour of the Metroplex Math Circle we will have a special private screening and discussion of the documentary Hard Problems. If you have not seen it, Hard Problems recounts the selection and success of the US team at the 2006 International Mathematics Olympiad. In this excellent film you will see many friends of MMC including Dr. Zuming Feng.

Please remember that the Metroplex Math Circle is on break March 21st due to the UT Dallas spring break. Math Circle will return on March 28th when Dr. Razvan Gelca will discuss “Invariants”

The invariance principle is an important mathematical tool in both mathematical Olympiads and fundamental mathematical research. In this talk we will cover examples from combinatorics, number theory, geometry, and algebra. Then we will explain how invariants are being used in recent mathematical research on knot theory and mathematical physics.

Dr. Andreescu once again offered UT Dallas as a higher education site for this year’s AMC 10/12B. We were very proud of all of the Metroplex Math Circle participates who took the test. Following are the students who scored above 100 points (out of 120) on the AMC 10 and above 90 points on the AMC 12.

AMC 10

RUSSELL HOUSTON *
DANIEL HUANG *
AMY CHYAO * (SA)
MICHAEL HWANG * (SA)
ERIK NGUYEN *
JACOB CORDEIRO
NIHAL KODURI (SA)
SANGJUN YOO
DOMINIC YURK
JOSHUA CAI

AMC 12

ARNOLD LIAO *
KEVIN CHANG *
SIDDHANT MITTAL *
YEJIN KIM
ARI GAO
ROBERT TUNG

* = AIME qualifier

(SA) = Metroplex Math Circle Student Advisor

Please join me in congratulating these students on their strong performance. If you are a math circle participant who scored in this range on the 10/12A or at your own school please feel free to post in the comments below or e-mail your score to be recognized. Students who would like to receive their scores from the 10/12B can e-mail djcordeiro@sbcglobal.net

Dr. Titu Andreescu, former director of AMC and coach of the US IMO team will be giving a special lecture for those preparing for the American Invitational Mathematics Examination (AIME). This will be a very challenging session befitting the caliber of the AIME examination. However, students who did not qualify this year but are working on AMC 10 and 12 preparation should benefit from the unique insights and strategies that Dr. Andreescu will provide.

Here is some information about the AIME:

The AIME (American Invitational Mathematics Examination) is an intermediate examination between the AMC 10 or AMC 12 and the USAMO. All students who took the AMC 12 and achieved a score of 100 or more out of a possible 150 or were in the top 5% are invited to take the AIME. All students who took the AMC 10 and had a score of 120 or more out of a possible 150, or were in the top 1% also qualify for the AIME. For the 2008-2009 school year the date for the AIME I is Tuesday, March 17, 2009 and the AIME II is Wednesday, April 1, 2009.

The AIME is a 15 question, 3 hour examination in which each answer is an integer number from 0 to 999. The questions on the AIME are much more difficult and students are very unlikely to obtain the correct answer by guessing. As with the AMC 10 and AMC 12 (and the USAMO), all problems on the AIME can be solved by pre-calculus methods. The use of calculators is not allowed.

In his lectures about combinatorics, Mr. Davis touched upon various topics. He gave students problems about counting the ways to rearrange and pick items, using candy as a visual to help the students understand. He also talked about the various strategies used to solve these problems. These strategies included using “bars and stars” to represent the problem, and using the Inclusion-Exclusion Principle. Lastly, he demonstrated the numerous applications of the famous Pascal’s Triangle.

Sample Problems:

Say there are 5 Jolly Ranchers and 3 Starbursts. How many ways are there to pick a Jolly Rancher or a Starburst? How many are there to pick a Jolly Rancher and a Starburst?

How many different ways are to rearrange the letters in the word ALABAMA?

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How many paths are there from point A to point B only going up and right?

If there are 3 people and 5 different candies, how many ways are there to distribute the candies if each person has to get at least one candy?

Alan Davis will continue his previous talk on Combinatorics with more challenging problems and concepts. Those who missed his first talk are encouraged to attend promptly for a quick review at 2:00.

For the curious students who are eager to sharpen their problem-solving skills in Combinatorics, Mr. Davis recommends these two collections that Titu Andreescu and Zuming Feng collaborated on: