The document discusses several prominent mathematical olympiads from around the world, including the International Mathematical Olympiad (IMO), the Indian National Mathematical Olympiad (INMO), the United States of America Mathematical Olympiad (USAMO), the British Mathematical Olympiad, the Asian Pacific Mathematics Olympiad (APMO), the Southeast Asian Mathematics Olympiad, and the William Lowell Putnam Mathematical Competition. It provides details on the history, structure, selection process, awards, and goals of each competition.

1. Mathematical Olympiads
throughout the world
Prepared by – Shreet Mishra ( class – XI)
roll no. - 47

2. INTRODUCTION
• A general Mathematical Olympiad is an
exam in which questions of only
mathematics is asked. The person who
scores first rank gets gold medal, the
person who scores second position gets
silver medal and the person who scores
third rank gets bronze medal. Today,
there are thousands of mathematical
Olympiads going throughout the world.

3. INTRODUCTION
Today, there are thousands of mathematical Olympiads going throughout the
world some of them are -:
• International Mathematical Olympiad (IMO)
• AITMO (Asian Inter-city Teenagers Mathematics Olympiad) — for junior
secondary students around the Eastern Asian region
• APMO (Asian Pacific Mathematics Olympiad) — Pacific rim
• APMCM (Asian Pacific Mathematics Contest in Modeling)
• The Indian National Mathematical Olympiad (INMO)
• The United States of America Mathematical Olympiad (USAMO)
• The British Mathematical Olympiad
• William Lowell Putnam Mathematical Competition — USA and Canada

4. The International Mathematical
Olympiad (IMO)
• The International Mathematical Olympiad (IMO) is an
annual six-problem, 42-point mathematical
Olympiad for pre-collegiate students and is the oldest
of the International Science Olympiads. The first IMO
was held in Romania in 1959. It has since been held
annually, except in 1980. About 100 countries send
teams of up to six students plus one team leader, one
deputy leader, and observers. Ever since its inception
in 1959, the Olympiad has developed a rich legacy and
has established itself as the pinnacle of mathematical
competition among high school students.

5. The International Mathematical
Olympiad (IMO)

6. The International Mathematical
Olympiad (IMO)
• The content ranges from precalculus problems that are
extremely difficult to problems on branches of mathematics
not conventionally covered at school and often not at
university level either, such
as projective and complex geometry, functional
equations and well-grounded number theory, of which
extensive knowledge of theorems is required. Calculus,
though allowed in solutions, is never required, as there is a
principle at play that anyone with a basic understanding of
mathematics should understand the problems, even if the
solutions require a great deal more knowledge. Supporters
of this principle claim that this allows more universality
and creates an incentive to find elegant, deceptively simple-looking
problems which nevertheless require a certain level
of ingenuity.

7. The International Mathematical
Olympiad (IMO)
• The selection process differs by country, but it often
consists of a series of tests which admit fewer students
at each progressing test. Awards are given to a top
percentage of the individual contestants. Teams are
not officially recognized—all scores are given only to
individual contestants, but team scoring is unofficially
compared more so than individual scores. Contestants
must be under the age of 20 and must not be
registered at any tertiary institution. Subject to these
conditions, an individual may participate any number
of times in the IMO.

8. The Indian National Mathematical
Olympiad (INMO)
• The Indian National Mathematical Olympiad
(INMO) is a high school
mathematics competition held annually
in India since 1989. It is the second tier in the
Indian team selection procedure for
the International Mathematical Olympiad and
is conducted by the Homi Bhaba Centre for
Science Education (HBCSE) under the aegis of
the National Board of Higher Mathematics
(NBHM).

9. The Indian National Mathematical
Olympiad (INMO)
• The INMO is conducted by the MO Cell in February of every
year. Prospective candidates first need to write the Regional
Mathematical Olympiad of their respective state or region,
usually held on the first Sunday of December of the
previous year. Around thirty students are selected from
each region, to write the INMO, which is usually held on the
first Sunday of February. Among these 500 or more
students, a total of around thirty qualify the INMO. Students
qualifying the INMO are automatically eligible for
admission to the B.Sc. (Hons) Mathematics course in the
[Chennai Mathematical Institute]. Since 2008, INMO
awardees applying for B. Stat or B. Math courses of the
Indian Statistical Institute are directly called for the
interview without having to write the written test.

10. The United States of America
Mathematical Olympiad (USAMO)
• The United States of America Mathematical
Olympiad (USAMO) is a highly selective high
school mathematics competition held annually in
the United States. Since its debut in 1972, it has served as
the final round of the AMC series of contests. The United
States of America Junior Mathematical Olympiad (USAJMO)
was introduced in 2010 to recognize top scorers based on
their AMC10-based index. Qualifying for the USAMO is
considered one of the most prestigious awards for high
school students in the United States, with only 264 students
qualifying in 2013 out of over 350,000 students
competing. Top scorers on the USAMO are invited to
the Mathematical Olympiad Summer Program and
represent the United States at the International
Mathematical Olympiad.

11. The United States of America
Mathematical Olympiad (USAMO)
• In 2011 we will have slightly revised
qualification rules for the USA
Mathematical Olympiad and USA Junior
Mathematical Olympiad. The goal is to
select approximately 500 students total
for the two Olympiads, split
approximately 270 for the USAMO and
230 for the USAJMO respectively.

12. The British Mathematical Olympiad
• The British Mathematical Olympiad forms part of the
selection process for the UK International Mathematical
Olympiad team. It is organised by the British Mathematical
Olympiad Sub trust, which is part of the United Kingdom
Mathematics Trust. There are two rounds, the BMO1 and
the BMO2.
• The first round of the BMO is held in December, and from
2006 is an open entry competition, costing £17 to
enter. However, this fee is waived for those who (1) achieve
the qualifying mark in the Senior Mathematical
Challenge and (2) are British citizens, or will have studied
for 3 full years of full-time secondary education in the UK
by the time they leave school. The paper lasts 3½ hours,
and consists of six questions (from 2005), each worth 10
marks.

13. The British Mathematical Olympiad
• Candidates are encouraged to write full proofs to the
questions they attempt, as a full answer to a question
is worth many more marks than incomplete answers
to several questions. This is because of the marking
scheme: an answer is marked on either a "0+" or a "10-
" mark scheme, depending on whether the answer
looks generally complete or not. So if an answer is
judged incomplete or unfinished, it is awarded a few
marks for progress and relevant observations,
whereas if it is presented as complete and correct,
marks are deducted for faults, poor reasoning, or
unproven assumptions. As a result, it is quite
uncommon for an answer to score a middling mark
(e.g. 4–6).

14. The Asian Pacific Mathematics
Olympiad (APMO)
• The Asian Pacific Mathematics Olympiad (APMO)
starting from 1989 is a regional mathematics
competition which involves countries from the Asian
Pacific region. The USA also takes part in the APMO.
Every year, APMO is held in the afternoon of the
second Monday of March for participating countries in
the North and South Americas, and in the morning of
the second Tuesday of March for participating
countries on the Western Pacific and in Asia.

15. APMO's Aims -:
• the discovering, encouraging and challenging of
mathematically gifted school students in all Pacific-Rim
countries
• the fostering of friendly international relations and
cooperation between students and teachers in the Pacific-
Rim Region
• the creating of an opportunity for the exchange of
information on school syllabi and practice throughout the
Pacific Region
• The encouragement and support of mathematical
involvement with Olympiad type activities, not only in the
APMO participating countries, but also in other Pacific-Rim
countries.

16. The Southeast Asian Mathematics
Olympiad
• The Southeast Asian Mathematics Olympiad, or SEA-MO,
is the Regional Mathematics
Competition in Southeast Asia. This competition is
organised by the Southeast Asian Ministers of
Education Organization Regional Centre for Education
in Science and Mathematics (SEAMEO RECSAM),
which bases its operations in Penang, Malaysia. Unlike
the International Mathematical Olympiad, the venue
for this competition is not rotated from country to
country and it has been held in Penang, Malaysia since
its conception.

17. The Southeast Asian Mathematics
Olympiad
• Each participating country is represented by four
participants, a team leader and deputy leader.
Participation in this event is strictly by invitation only.
Competitors have to sit for three papers: the Short
Answer test consisting of twenty questions;
the Individual Power Test which spans three hours and
comprises five questions; and the Team Test.

18. The William Lowell Putnam
Mathematical Competition
• The William Lowell Putnam Mathematical Competition,
often abbreviated to the Putnam Competition, is an
annual mathematics
competition for undergraduate college students enrolled at
institutions of higher learning in the United
States and Canada (regardless of the students'
nationalities). It awards a scholarship and cash prizes
ranging from $250 to $2,500 for the top students and
$5,000 to $25,000 for the top schools, plus one of the top
five individual scorers (designated as Putnam Fellows) gets
graduate tuition waived at Harvard (Putnam Fellow Prize
Fellowship), and the top 100 individual scorers have their
names mentioned in the American Mathematical Monthly's
October issue (alphabetically ordered within rank).

19. The William Lowell Putnam
Mathematical Competition
• It is considered by many to be the most prestigious
university-level mathematics examination in the
world, and its difficulty is such that the median score is
often zero or one (out of 120) despite being attempted
by students specializing in mathematics.

20. Thank
you