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2010 MathComp/MathFun

2010 MathComp/MathFun. Focusing on problem solving helps motivate our talented youth Dr. Titu Andreescu University of Texas at Dallas tandreescu@gmail.com. About the presenter. Since an early age I had a high interest in mathematics competitions

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2010 MathComp/MathFun

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  1. 2010 MathComp/MathFun Focusing on problem solving helps motivate our talented youth Dr. Titu Andreescu University of Texas at Dallas tandreescu@gmail.com

  2. About the presenter Since an early age I had a high interest in mathematics competitions 1973, 1974, 1975: I won the Romanian national problem solving contests organized by Gazeta Matematică. During the 1980s, I served as a coach for the Romanian IMO team 1990 emigrated to the USA

  3. About the presenter US IMO Team Leader (1995 – 2002) Director, MAA American Mathematics Competitions (1998 – 2003) Director, Mathematical Olympiad Summer Program (1995 – 2002) Coach of the US IMO Team (1993 – 2006) Member of the IMO Advisory Board (2002 – 2006) Chair of the USAMO Committee (1996 – 2004) MAA Sliffe Award winner for Distinguished Teaching

  4. History of math competitions primary school math competition with 70 participants was held in Bucharest, Romania, as early as 1885 the 1894 Eötvös competition in Hungary is widely credited as the forerunner of contemporary mathematics (and physics) competitions for secondary school students

  5. History of math competitions The year 1894 is notable also for the birth of the famous mathematics journal KöMaL (an acronym of the Hungarian name of the journal, which translates to High School Mathematics and Physics Journal ) similar development occurred in Hungary’s neighbor, Romania. The first issue of the monthly Gazeta Matematica, was published in September 1895. The journal organized a competition for school students, which improved in format over the years and eventu- ally gave birth to the National Mathematical Olympiad in Romania

  6. History of math competitions The first International Mathematics Olympiad (IMO) was organized by Romania in 1959. The following countries took part: Bulgaria, Czechoslovakia, German Democratic Republic, Hungary, Poland, Romania, and the Soviet Union (USSR). USA first participated in 1974 More than 100 countries participate in the IMO today

  7. About the IMO Each country sends a team of up to six middle school or high-school students, chaperoned by a team leader and a deputy team leader. The competition is held on two consecutive days; each day, the students have four and a half hours to solve three problems the six problems are selected by an international jury formed by the national team leaders and representatives of the host country

  8. About the IMO the problems are rather difficult and solving them requires a significant degree of inventiveness ingenuity, and creativity each problem is worth seven points (the perfect score is 42 points-see year 1994) the IMO is a competition for individuals; participants are ranked according to their score and (multiple) individual medals are awarded scores of participants from each country are totaled and the countries are unofficially ranked, providing grounds for comparison between countries

  9. How does the IMO impact the educational system in a country IMO imposes high standards, therefore each participating country is trying to constantly improve their mathematics education, the process of selecting and preparing their students As a consequence, a variety of mathematics competitions and enrichment programs have been developed around the world

  10. Types of contest problems Multiple-choice, where each problem is supplied with several answers, from which the competitor has to find (or guess, as no justification is required) the correct one Classical style competitions (such as the IMO) require students to present arguments (proofs) in written form.

  11. Types of competitions National competitions, such as USAMO, or the Chinese Mathematical Olympiad Regional Mathematical Olympiads such as the Ibero-American Mathematics Olympiad, or the Asian-Pacific Mathematics Olympiad Correspondence Exams, such as USAMTS, Tournament of Towns Competitions ran through the internet, such as Purple Comet Other team competitions such as Baltic Way

  12. Math competitions in the U.S. Competitions for elementary and middle school students such as CIE MathComp MATHCOUNTS American Mathematics Competitions The W.L. Putnam Mathematics Competitions

  13. American Mathematics Competitions AMC 8 AMC 10 AMC 12 AIME USAJMO USAMO (leading to MOSP and IMO)

  14. Math Competitions are needed • Creates ways to identify mathematical talent • Typical school curriculum is aimed towards the average student • What takes place before and after a competition is meaningful for math education • Preparation that takes place and discussions after the competition ends is important • Students who take part in math competitions are steered towards science careers

  15. Olympiad style problems They are challenging essay-type problems To provide correct and complete solutions require deep analysis and careful argument They might seem impenetrable to the novice, but they can be solved using elementary high school mathematics

  16. Hints for advanced problem solvers Do not be intimidated! Some of the problems involve complex mathematical ideas, but they can attacked by using elementary techniques, admittedly combined in clever ways Be patient and persistent! Learning comes more from struggling with problems than from solving them. Problem solving becomes easier with experience Success is not a function of cleverness alone

  17. What is an exercise and what is a problem? The difference between exercises and problems What is 50% of 2006 plus 2006% of 50? 1013.5 B) 1053 C) 1103.3 D) 1504.5 E) 2006 Solution:

  18. What is an exercise and what is a problem? If is written in decimal form, find the sum of its digits. Solution. Because and , the given number can be written as = 781250 . . . 0 (25 zeros). The sum of the digits for the decimal representation is 7 + 8 + 1 + 2 + 5 = 23.

  19. Resources available to talented math kids Participate in competitions Take on-line classes Attend Math Circles or Math Clubs Take part in Summer Programs Work on problems from several books available for Olympiad training

  20. Mathematical Reflections Free on-line journal aimed primarily at high school students, undergraduates, and everyone interested in mathematics. Through articles and problems, we seek to expose readers to a variety of interesting topics that are fully accessible to the target audience.

  21. AwesomeMath Summer Program (AMSP) www.awesomemath.org A three-week intensive summer camp for mathematically gifted students from around the globe Targeted to 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 other programs It hones 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 Dates: July 6 – 27 and July 30 – August 20, 2010

  22. Math Rocks! Available to exceptional Plano ISD students, grades 4 to 7 Will expand from 4 to 8 elementary schools in 2010/2011 Features challenging topics and problem sets Expands mathematical horizons of participants Deepens their understanding of mathematics Develops important problem solving skills

  23. Metroplex Math Circle (MMC) metroplexmathcircle.wordpress.com Intended for students who are 14 and older and show a strong desire to go beyond a standard high school curriculum They can use their experience at MMC to excel in national math competitions or to better prepare them for work at elite universities Younger students with demonstrated mathematical talents are also welcome to participate in the MMC lectures.

  24. Metroplex Math Circle Meets in room 2.410 of the Engineering and Computer Sciences building on the campus of the University of Texas at Dallas Regular sessions are held Saturday afternoons from 2:00 to 4:00 while the university is in sessions Speakers from all over the country, such as: Richard Rusczyk, Dr. Art Benjamin, Dr. ZuminFeng, Dr. Jonathan Kane, etc

  25. Books “Mathematical Olympiad Challenges” by Titu Andreescu and RazvanGelca “Mathematical Olympiad Treasures” by Titu Andreescu and BogdanEnescu “Number Theory: Structures, Examples, and Problems” by Titu Andreescu and DorinAndrica “Problems from the Book”, by Titu Andreescu and Gabriel Dospinescu

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