2010 mathcomp/mathfun
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FOCUSING ON PROBLEM SOLVING HELPS MOTIVATE OUR TALENTED YOUTH
DR. TITU ANDREESCUUNIVERSITY OF TEXAS AT DALLAS
TANDREESCU@GMAIL .COM
2010 MathComp/MathFun
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
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
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
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
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 1974More than 100 countries participate in the
IMO today
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
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
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
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.
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
Math competitions in the U.S.
Competitions for elementary and middle school students such as CIE MathComp
MATHCOUNTSAmerican Mathematics CompetitionsThe W.L. Putnam Mathematics Competitions
American Mathematics Competitions
AMC 8AMC 10AMC 12AIMEUSAJMOUSAMO (leading to MOSP and IMO)
Math Competitions are needed
Creates ways to identify mathematical talent Typical school curriculum is aimed towards the
average studentWhat takes place before and after a
competition is meaningful for math education Preparation that takes place and discussions after the
competition ends is importantStudents who take part in math competitions
are steered towards science careers
Olympiad style problems
They are challenging essay-type problemsTo provide correct and complete solutions
require deep analysis and careful argumentThey might seem impenetrable to the novice,
but they can be solved using elementary high school mathematics
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
What is an exercise and what is a problem?
The difference between exercises and problems
What is 50% of 2006 plus 2006% of 50?A) 1013.5 B) 1053 C) 1103.3 D) 1504.5
E) 2006
Solution:
€
50
100×2006 +
2006
100×50 = 2006
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.
€
532325
€
532 = 57525
€
325 = (25)5 = 225
€
57(5 ⋅2)25 = 78125 ⋅1025
Resources available to talented math kids
Participate in competitionsTake on-line classesAttend Math Circles or Math ClubsTake part in Summer ProgramsWork on problems from several books
available for Olympiad training
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.
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
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 setsExpands mathematical horizons of
participantsDeepens their understanding of mathematicsDevelops important problem solving skills
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.
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. Zumin Feng, Dr. Jonathan Kane, etc
Books
“Mathematical Olympiad Challenges” by Titu Andreescu and Razvan Gelca
“Mathematical Olympiad Treasures” by Titu Andreescu and Bogdan Enescu
“Number Theory: Structures, Examples, and Problems” by Titu Andreescu and Dorin Andrica
“Problems from the Book”, by Titu Andreescu and Gabriel Dospinescu
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