Syllabus for International Mathematics Olympiad (regional, national and international)

Olympiad 2nd Round Qualifying Examination Holds On the 19th of January, 2018. Kindly get in touch with Olympiad State Coordinators at the State Ministry of Education for State Venue.

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Syllabus for International Mathematics Olympiad (regional, national and international)

The syllabus for Mathematics Olympiad (regional, national and international) is pre-degree college mathematics.

The areas covered are:
Number Theory –
Arithmetic of integers
Divisibility ( primes, gcd, lcm, Euclidean Algorithm)
Congruence (Fermat Little Theorem, Chinese Remainder Theorem, Wilson’s Theorem ,  Euler’s Toutient Theorem etc)
Number Theoretic functions ( Ceiling and floor functions
p- adic evaluation
Diophantine Equation (Pell’s equation)

Geometry –
Points, lines and polygons
Trigonometry
Circumcentre, Incentre, Orthocentre, Centroid
Theorems of Ceva and Menalaus
Quadrilaterals
Circle Geometry
Other Theorems ( Nine-point circle, Stewart’s theorem, Ptolemy’s theorem, Simpson’s line, Euler’s line etc)
Coordinate geometry Complex Geometry Baricentric Geometry Inversion Geometry Projective Geometry

Algebra  –
Sequence and series  ( A.P, G.P, Harmonic sequence, Fibonacci sequence) Functional Equations
Polynomials (systems of equations, Viete’s functions, factorizations etc)
Inequalities (AM-GM inequality, Cauchy- Swartz inequality, Chebychev’ s inequality, Holder’s inequality, Minkowski’s inequality , Jensen’s inequality, Schur’s inequality, Muirhead’s inequality , Trigonometric inequality, etc)

Combinatorics
Principle of Counting (Permutation and combinations) Principle of Mathematical Induction (PMI)
Inclusion- Exclusion Principle (Derangement) Pigeon-hole  Principle
Invariant Principle
Graph Theory

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