Transcript Dr. Andreescu CIE Presentation

2010 MathComp/MathFun
FOCUSING ON PROBLEM SOLVING HELPS
MOTIVATE OUR TALENTED YOUTH
DR. TITU ANDREESCU
UNIVERSITY OF TEXAS AT DALLAS
[email protected]
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 eventually 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 1974
 More 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 IberoAmerican Mathematics Olympiad, or the AsianPacific 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
 MATHCOUNTS
 American Mathematics Competitions
 The W.L. Putnam Mathematics Competitions
American Mathematics Competitions
 AMC 8
 AMC 10
 AMC 12
 AIME
 USAJMO
 USAMO (leading to MOSP and IMO)
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
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
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
Solution:

B) 1053 C) 1103.3 D) 1504.5 E) 2006
50
2006
 2006
 50  2006
100
100

What is an exercise and what is a problem?
 If
5 32 32 5 is written in decimal form, find the sum of
its digits.
 Solution.
Because 5 32  5 75 25 and 32 5  (2 5 ) 5  225, the given number
can be written as 57 (5  2)25  78125 10 25 = 781250 . . . 0
(25 zeros). The sum of the digits for the decimal
 is 7 + 8 + 1 + 2 + 5 = 23.
representation

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
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 sets
Expands mathematical horizons of participants
Deepens their understanding of mathematics
Develops 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