Syllabus
No special knowledge of curriculum material is required. Good knowledge of curriculum at the next lower level would be helpful. The syllabus for Mathematics Olympiad (Regional, National and International) is pre-degree college mathematics. The areas covered are, mainly –
a)Algebra, b) Geometry, c) Number theory and d) Graph theory & combinatorics.
Algebra: Polynomials, Solving equations, inequalities, and complex numbers.
Geometry: Geometry of triangles and circles.
(Trigonometric methods, vector methods, complex number methods, transformation geometry methods can also be used to solve problems)
Number Theory: Divisibility, Diophantine equations, congruence relations, prime numbers and elementary results on prime numbers.
Combinatorics & Graph Theory: Counting techniques, pigeon hole principle, the principle of inclusion and exclusion, basic graph theory.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics".
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics, therefore, excludes topics in "continuous mathematics" such as calculus and analysis.
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object.
Lists of mathematics topics cover a variety of topics related to mathematics. Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing. Lists cover aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects, and reference tables. They also cover equations named after people, societies, mathematicians, journals, and meta-lists.
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 American Mathematics Competitions. In 2010, it split into the USAMO and the United States of America Junior Mathematical Olympiad (USAJMO).
The Cyprus Mathematical Society (CMS) aims to promote the mathematical education and science. It was founded in 1983. The C.M.S. is a non-profit organization supported by the voluntary work of its members. The C.M.S. counts over 600 members. In order to promote its aims, C.M.S. organizes Mathematical competition between students all over Cyprus, and takes part in international mathematics competitions. CMS organize a series of mathematics competitions as part of the selection process of the national teams in the international mathematics competitions and the Cyprus Mathematical Olympiad. The new selection process in described below.
Mathematics education in New York in regard to both content and teaching method can vary depending on the type of school a person attends. Private school math education varies between schools whereas New York has statewide public school requirements where standardized tests are used to determine if the teaching method and educator are effective in transmitting content to the students. While an individual private school can choose the content and educational method to use, New York State mandates content and methods statewide. Some public schools have and continue to use established methods, such as Montessori for teaching such required content. New York State has used various foci of content and methods of teaching math including New Math (1960s), 'back to the basics' (1970s), Whole Math (1990s), Integrated Math, and Everyday Mathematics.
The Indian National Mathematical Olympiad (INMO) is a high school mathematics competition held annually in India since 1989. It is the third tier in the Indian team selection procedure for the International Mathematical Olympiad and is conducted by the Homi Bhabha Centre for Science Education (HBCSE) under the aegis of the National Board of Higher Mathematics (NBHM).
The Singapore Mathematical Olympiad (SMO) is a mathematics competition organised by the Singapore Mathematical Society. It comprises three sections, Junior, Senior and Open, each of which is open to all pre-university students studying in Singapore who meet the age requirements for the particular section. The competition is held annually, and the first round of each section is usually held in late May or early June. The second round is usually held in late June or early July.
This article describes the selection process, by country, for entrance into the International Mathematical Olympiad.
The Association of Mathematics Teachers of India or AMTI is an academically oriented body of professionals and students interested in the fields of mathematics and mathematics education.
Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.
Mathematics education in the United States varies considerably from one state to the next, and even within a single state. However, with the adoption of the Common Core Standards in most states and the District of Columbia beginning in 2010, mathematics content across the country has moved into closer agreement for each grade level. The SAT, a standardized university entrance exam, has been reformed to better reflect the contents of the Common Core. However, many students take alternatives to the traditional pathways, including accelerated tracks. As of 2023, twenty-seven states require students to pass three math courses before graduation from high school, and seventeen states and the District of Columbia require four.
Lisa Sauermann is a mathematician from Germany known for her performance in the International Mathematical Olympiad, where in 2011 she had the single highest score. She won four gold medals (2008–2011) and one silver medal (2007) at the olympiad, representing Germany.
Mathematics is a field of study that investigates topics such as number, space, structure, and change.
Mathematics is a broad subject that is commonly divided in many areas that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers.
