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

With the AMC 10 and 12 contests behind us, some students will be preparing for the AIME while many will be working hard to improve their scores next year.  Both groups will not want to miss Dr. Titu Andreescu this weekend as he presents more of his favorite problems and solutions.

Titu Andreescu received his Ph.D. from the West University of Timisoara, Romania. The topic of his dissertation was “Research on Diophantine Analysis and Applications.” Professor Andreescu currently teaches at The University of Texas at Dallas. He is past chairman of the USA Mathematical Olympiad, served as director of the MAA American Mathematics Competitions (1998–2003), coach of the USA International Mathematical Olympiad Team (IMO) for 10 years (1993–2002), director of the Mathematical Olympiad Summer Program (1995–2002), and leader of the USA IMO Team (1995–2002). In 2002 Titu was elected member of the IMO Advisory Board, the governing body of the world’s most prestigious mathematics competition. Titu co-founded in 2006 and continues as director of the AwesomeMath Summer Program (AMSP). He received the Edyth May Sliffe Award for Distinguished High School Mathematics Teaching from the MAA in 1994 and a “Certificate of Appreciation” from the president of the MAA in 1995 for his outstanding service as coach of the Mathematical Olympiad Summer Program in preparing the US team for its perfect performance in Hong Kong at the 1994 IMO. Titu’s contributions to numerous textbooks and problem books are recognized worldwide.

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

The American Mathematics Contest (AMC) is an extremely important contest for any students interested in pursuing a STEM education and career.  Many of the elite universities use AMC scores to sort out the many applicants who easily achieve 800 SAT math scores.

Our Metroplex Math Circle students are particularly fortunate to have access to Dr. Titu Andreescu as they prepare themselves to take the test.  Dr. Andreescu was the director of the AMC and coach of the US International Mathematical Olympiad team, whose members are selected from among the very best performers in the AMC, AIME and USAMO sequence of contests.

Students should make sure that their schools are offering the A version of the AMC 10 and 12 tests on February 7th.  For those students who do not have access to the test at their school or who are homeschooled, Dr. Andreescu will be offering the test at UT Dallas on February 22, 2012.  Please leave a comment below if you would like to register to take the test at UT Dallas so we can order sufficient tests.

The “10″ and “12″ refer to the maximum grade in which the test may be taken, however, there is no lower limit on the age of the participant.  Many of our younger students take it with the goal of improving their performance each year and identifying areas to focus their studies.  One extraordinary elementary student, under Dr. Andreescu’s tutelage, even achieved a perfect score on the AMC 10!

 

 

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Dr. Andreescu at Julia Robinson Mathematics Festival

There is no Metroplex Math Circle this coming weekend, but if you are fortunate enough to be in the Houston area on Saturday, March 19, 2011 you can meet Dr. Titu Andreescu at the Julia Robinson Mathematics Festival.  Math Circle directors from around the country will be meeting in Houston and participating in this unique even which is open to the public with advance registration.

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March 12 – Dr. Andreescu – AIME is Practically Here!

OK, by popular demand following his March 5th AIME training session, Dr. Andreescu will return as next week’s speaker to continue training our students for AIME.  Whether you qualified this year or hope to in the future, do not miss this opportunity to train with the former Director of AMC and coach of the US IMO team.

Dr. Titu Andreescu, University of Texas at Dallas

Titu Andreescu received his Ph.D. from the West University of Timisoara, Romania. The topic of his dissertation was “Research on Diophantine Analysis and Applications.” Professor Andreescu currently teaches at The University of Texas at Dallas. He is past chairman of the USA Mathematical Olympiad, served as director of the MAA American Mathematics Competitions (1998–2003), coach of the USA International Mathematical Olympiad Team (IMO) for 10 years (1993–2002), director of the Mathematical Olympiad Summer Program (1995–2002), and leader of the USA IMO Team (1995–2002). In 2002 Titu was elected member of the IMO Advisory Board, the governing body of the world’s most prestigious mathematics competition. Titu co-founded in 2006 and continues as director of the AwesomeMath Summer Program (AMSP). He received the Edyth May Sliffe Award for Distinguished High School Mathematics Teaching from the MAA in 1994 and a “Certificate of Appreciation” from the president of the MAA in 1995 for his outstanding service as coach of the Mathematical Olympiad Summer Program in preparing the US team for its perfect performance in Hong Kong at the 1994 IMO. Titu’s contributions to numerous textbooks and problem books are recognized worldwide. Related articles on this site.

I also found out last week that many people were unfamiliar with the book Count Down by Steve Olson and the prominent role played in it by Dr. Andreescu as it describes the US team’s triumph at the IMO.

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March 5 – Dr. Andreescu – AIME is Coming up Soon!

Whether you are one of the Math Circle attendees who just qualified for the AIME or hope to some day, you do not want to miss a lecture by our own Dr. Titu Andreescu which will increase your odds of success on this prestigious test and potentially the chance to sit for the USAMO.

Elite universities look at AIME scores to differentiate between their accomplished applicants.  The test is a bit different from the AMC 8, 10 or 12 and requires new skills and strategies for success.

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.

The AIME provides the exceptional students who are invited to take it with yet another opportunity to challenge their mathematical abilities. Like all examinations, it is but a means towards furthering mathematical development and interest. The real value of the examination is in the learning that can come from the preparation beforehand and from further thought and discussion of the solutions.

 

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October 23 – Dr. Andreescu, AMC 8 Preparation

Dr. Titu Andreescu will give the lecture himself next week and focus on helping the students prepare for the upcoming AMC 8 test.  I’ll describe the importance of the AMC 8 below, but even students too old to take this particular test (over 8th grade) will find a great deal of value in this lecture from the former director of the AMC which they can apply to their preparation for the AMC 10 or 12.

AMC 8 is the first in a sequence of contests offered by the Mathematical Association of America.  The results of these tests are ultimately used to select the team that will represent the US at the International Mathematical Olympiad, but the scores are also critical to distinguish a college application from the many perfect SAT math scores received by the elite universities.

Here is information on the AMC 8 for those unfamiliar:

The AMC 8 is a 25 question, 40 minute multiple choice examination in middle school mathematics designed to promote the development and enhancement of problem solving skills. This school year it will be held Tuesday, November 16, 2010. Click here for a current brochure.

The examination provides an opportunity to apply the concepts taught at the junior high level to problems which not only range from easy to difficult but also cover a wide range of applications. Many problems are designed to challenge students and to offer problem solving experiences beyond those provided in most junior high school mathematics classes. Calculators are not allowed starting in 2008. High scoring students are invited to participate in the AMC 10.

A special purpose of the AMC 8 is to demonstrate the broad range of topics available for the junior high school mathematics curriculum. This is done by competencies. The AMC 8 has the potential to increase the perceptions of the importance of problem solving activities in the mathematics curriculum by stimulating these activities both preceding and following the examination —specifically by studying the solutions manual.

Additional purposes of the AMC 8 are to promote excitement, enthusiasm and positive attitudes towards mathematics and to stimulate interest in continuing the study of mathematics beyond the minimum required for high school graduation. Developmentally, junior high school students are at a point where attitudes toward school and learning, and perceptions of themselves as learners of mathematics are solidified. It is important that they be provided opportunities that foster the development of positive attitudes towards mathematics and positive perceptions of themselves as learners of mathematics. The AMC 8 provides one such opportunity.

We encourage all students in grades 6, 7 and 8 to participate in the AMC 8. All USA, USA embassy, Canadian and foreign school students in grade 8 or below are eligible to participate.

 

 

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AwesomeMath 2010 Early Application

AwesomeMath, Dr. Andreescu’s highly regarded summer camp for mathematically gifted students has just released its test and forms for early admission.  Early registration is due by February 5th.

For those of you who are unfamiliar with the camp here are some details for 2010:

What? A three-week intensive summer camp for mathematically gifted students from around the globe. An initiative in response to parents and teachers of bright students who have not yet shone at the Olympiad level, as well as of those who would like to expand what they have learned in programs such as MATHCOUNTS. These talented students wish to hone their problem solving skills in particular and further their mathematics education in general. Many of our participants seek to improve their performance on contests such as AMC10/12, AIME, or USAMO.

Why? To offer gifted math students the opportunity to attend a high-quality summer program.

When? July 6 – 27, 2010 and July 30 – August 20, 2010.

Who? Around 80 students in grades 6-11, distinguished faculty, a large group of mentors and assistants.

Where? At the University of Texas at Dallas (7/6-7/27) and the University of California, Santa Cruz (7/30-8/20).

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Telescoping Sums and Products (Example 1)

While we wait for the Metroplex Math Circle to continue again in mid January, I will be posting a series of problems and solutions from our last session. Those who were fortunate enough to attend learned useful techniques for solving problems common in math contests.

Telescoping Sums and Products

The telescoping sums and products idea is used to solve many problems involving sums or products in algebra. For problems involving sums, the idea is to use identities, to write the sum in the form

and then cancel out terms to get F(n+1)-F(1). Sometimes the desired identity is hard to find, but basically you are searching for it in the recursive form of the sequence, or you can look foor the “conjugates” for the terms you have. The first example is classical. You Certainly know these formulas.

What about ?

Example 1.  Prove that

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Summer Camps: AwesomeMath

One of the newest but most distinguished summer camps for young problem solvers is AwesomeMath.  AwesomeMath draws faculty and students from around the country and around the world.  This year AwesomeMath will occur in two separate sessions on two campuses, our own UTD campus and the University of California, Santa Cruz.

We will be providing more information on AwesomeMath in the coming weeks, but here is the basic information from the AwesomeMath website:

What? A three-week intensive summer camp for mathematically gifted students from around the globe. This is an initiative in response to numerous requests from parents and teachers of bright students who have not yet shone at the Olympiad level, as well as of those wishing to expand what they have learned in programs such as MATHCOUNTS. These talented students wish to hone their problem solving skills in particular and further their mathematics education in general. Many of our participants seek to improve their performance on contests such as AMC10/12, AIME, or USAMO.

When? July 6 – 27, 2009 and July 31 – August 21, 2009.

Who? over 100 students in grades 7-11, distinguished faculty, a large group of mentors and assistants .

Where? At the University of Texas at Dallas (7/6-7/27) and the University of California, Santa Cruz (7/31-8/21).

Why? To offer gifted math students the opportunity to attend a high-quality summer program. You may access the AMSP 2009 Academic Curriculum here.

Here is a link to our 2009 brochure. You may also visit the Frequently Asked Questions for more information about AMSP 2009.

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