ISI and CMI Entrance Program curriculum consists of advanced high school mathematics and additional topics such as geometry, number theory and combinatorics.
Book: Elementary Number Theory by David Burton
Arithmetic of Remainder, Theory of Congruence, Divisibility, Theorems of Fermat, Euler, Wilson, Pythagorean Triples, Euclidean Algorithm.
Book: Challenges and Thrills of Pre College Mathematics by Venkatchala et al
Geometry of straight lines, triangles and circles. Advanced topics such as geometric transformations, complex numbers in geometry, mass point geometry, coordinate Geometry and trigonometry.
Book: Principles and Techniques in Combinatorics by Chuang Chong Chen and Koh Khee Meng
Bijection Principle, Principle of Inclusion and Exclusion, Recurrence Relation, Pigeon Hole Principle, Permutation and Combination, Combinatorial Identitites.
Book: Excursion in Mathematics published by Bhaskaracharya Pratisthana
AM - GM and Cauchy Schwarz Inequality, Complex Numbers, Theory of Equation, Functional Equation, Sequences and Series.
Book: Single Variable Calculus by Maron
Real numbers, Limit, Continuity, Differential Calculus, Rolle's Theorem, Integral Calculus, Fundamental Theorem of Calculus, Graphing Techniques.
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