Any aspirant for the International Mathematical Olympiads such as IMO, EGMO, APMO and the domestic selection rounds (i.e RMO, INMO)
Inequalities, Progressions (A.P, G.P, H.P), Theory of indices, System of linear equations, Theory of equations, Binomial theorem and properties of binomial coefficients, Complex Numbers, Polynomials in one and two variables, Functional equations, Sequences.
Triangles, quadrilaterals, circles and their properties; standard Euclidean constructions; concurrency and collinearity (Theorems of Ceva and Menelaus); basic trigonometric identities, compound angles, multiple and submultiple angles, general solutions, sine rule, cosine rule, properties of triangles and polygons, Coordinate Geometry (straight line, circle, conics,3-D geometry), vectors.
Basic enumeration, pigeonhole principle and its applications, recursion, elementary graph theory.
Divisibility theory in the Integers (The Division Algorithm, the Greatest Common Divisor, The Euclidean Algorithm, The Diophantine Equation ax + by = c) , Fundamental Theorem of Arithmetic, Basic properties of congruence, Linear congruences, Chinese Remainder Theorem, Fermat’s Little Theorem, Wilson’s Theorem, Euler’s Phi function and Euler’s generalization of Fermat’s Theorem, Pythagorean triples (definition and properties), Diophantine equations.
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