A mathematical olympiad is a mathematical competition where participants are examined by

problem solving Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business an ...

and may win medals depending on their performance. Usually aimed at pre-university students, much of olympiad mathematics consists of

elementary mathematics Elementary mathematics, also known as primary or secondary school mathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical c ...

, though solutions may involve the use of

calculus Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

or higher-level mathematics. The biggest mathematics olympiad is the

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is widely regarded as the most prestigious mathematical competition in the wor ...

. Among their objectives, they serve the purpose of identifying talented or gifted students in mathematics, who often receive opportunities for scholarships at universities.https://unesdoc.unesco.org/ark:/48223/pf0000110203 In a sense, they measure some mathematical abilities of the students.

History

The concept of mathematics competitions dates back to the late 19th century. A one-off competition for 70 primary school students was held in

Bucharest Bucharest ( , ; ) is the capital and largest city of Romania. The metropolis stands on the River Dâmbovița (river), Dâmbovița in south-eastern Romania. Its population is officially estimated at 1.76 million residents within a greater Buc ...

in May 1885, but little is known about it. A better-documented Eötvös Competition in

Hungary Hungary is a landlocked country in Central Europe. Spanning much of the Pannonian Basin, Carpathian Basin, it is bordered by Slovakia to the north, Ukraine to the northeast, Romania to the east and southeast, Serbia to the south, Croatia and ...

became one of the earliest organized contests in 1894. Romania followed with another competition, this time for secondary school students, in June 1898.

USSR The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

introduced regular math olympiads in the 1930s, and the predecessor of the Putnam Competition started in 1938 in the US. The success of these national competitions eventually led to the establishment of the International Mathematics Olympiad, which has grown from 7 participating countries in 1959 to over 100 countries in recent years.

Curriculum

Modern olympiad mathematics can be split into four categories:

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, and

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

. Algebra is restricted to

elementary algebra Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra introduces variable (mathematics ...

, number theory is restricted to

elementary number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for exampl ...

, and geometry is usually restricted to

Euclidean plane geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (pos ...

. While never required, the use of non-elementary techniques like

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

and

projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (''p ...

is allowed, and can often lead to more

elegant Elegance is beauty that shows unusual effectiveness and simplicity. Elegance is frequently used as a standard of tastefulness, particularly in visual design, decorative arts, literature, science, and the aesthetics of mathematics. Elegant t ...

History

Curriculum

List of mathematics olympiads

See also

References

Further reading

External link