Dr Titu Andreescu University of Texas at Dallas tandreescugmailcom 2010 MathCompMathFun About the presenter Since an early age I had a high interest in mathematics competitions 1973 1974 1975 I won the Romanian ID: 813565
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Slide1
Focusing on problem solving helps motivate our talented youthDr. Titu AndreescuUniversity of Texas at Dallastandreescu@gmail.com
2010 MathComp/MathFun
Slide2About the presenterSince an early age I had a high interest in mathematics competitions1973, 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
Slide3About the presenterUS 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
Slide4History of math competitionsprimary 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
Slide5History of math competitionsThe 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
Matematic
a
,
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
Slide6History of math competitionsThe 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
Slide7About the IMOEach 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
Slide8About the IMOthe 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
s
cores
of participants from each country are totaled and the countries are unofficially ranked, providing grounds for comparison between countries
Slide9How 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
Slide10Types of contest problemsMultiple-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
C
lassical style
competitions
(such as
the IMO)
require
students to present arguments (proofs) in written form
.
Slide11Types of competitionsNational competitions, such as USAMO, or the Chinese Mathematical OlympiadRegional 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
Slide12Math competitions in the U.S.Competitions for elementary and middle school students such as CIE MathCompMATHCOUNTSAmerican Mathematics CompetitionsThe W.L. Putnam Mathematics Competitions
Slide13American Mathematics CompetitionsAMC 8AMC 10AMC 12AIMEUSAJMOUSAMO (leading to MOSP and IMO)
Slide14Math Competitions are neededCreates ways to identify mathematical talentTypical school curriculum is aimed towards the average studentWhat takes place before and after a competition is meaningful for math educationPreparation that takes place and discussions after the competition ends is important
Students who take part in math competitions are steered towards science careers
Slide15Olympiad style problemsThey 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
Slide16Hints for advanced problem solversDo not be intimidated! Some of the problems involve complex mathematical ideas, but they can attacked by using elementary techniques, admittedly combined in clever waysBe patient and persistent! Learning comes more from struggling with problems than from solving them.Problem solving becomes easier with experienceSuccess is not a function of cleverness alone
Slide17What is an exercise and what is a problem?The difference between exercises and problemsWhat is 50% of 2006 plus 2006% of 50?1013.5 B) 1053 C) 1103.3 D) 1504.5 E) 2006
Solution:
Slide18What 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.
Slide19Resources available to talented math kidsParticipate in competitionsTake on-line classesAttend Math Circles or Math ClubsTake part in Summer ProgramsWork on problems from several books available for Olympiad training
Slide20Mathematical ReflectionsFree 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.
Slide21AwesomeMath Summer Program (AMSP) www.awesomemath.orgA 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
Slide22Math Rocks!Available to exceptional Plano ISD students, grades 4 to 7Will expand from 4 to 8 elementary schools in 2010/2011Features challenging topics and problem setsExpands mathematical horizons of participantsDeepens their understanding of mathematics
Develops important problem solving skills
Slide23Metroplex 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 curriculumThey 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.
Slide24Metroplex Math CircleMeets in room 2.410 of the Engineering and Computer Sciences building on the campus of the University of Texas at DallasRegular sessions are held Saturday afternoons from 2:00 to 4:00 while the university is in sessionsSpeakers from all over the country, such as: Richard Rusczyk
, Dr. Art Benjamin, Dr.
Zumin
Feng
, Dr. Jonathan Kane, etc
Slide25Books“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