Unit 1……………………………………………………………………………………………………..5
Divisibility of Integers
1.1 Natural Numbers
1.2 Peano’s Axioms
1.3 Well Ordering Principle
1.4 Principle of Mathematical Induction
1.5 Divisibility
1.6 Division Algorithm
1.7 Greatest Common Divisor
1.8 Least Common Multiple
1.9 Euclidean Algorithm
1.10 Prime and Composite Numbers
1.11 Unique Factorization Theorem Unit 2……………………………………………………………………………………………………22
Polynomials
2.1 Polynomial
2.2 Horner’s Method of Synthetic Division
2.3 Greatest Common Divisor of Polynomials
2.4 Fundamental Theorem of Algebra
2.5 Method to Find Common Roots of Polynomial Equation
2.6 Descarte’s Rule of Signs
2.7 Newton’s Method of Divisors for the Integral Roots Unit 3……………………………………………………………………………………………………55 Theory of Equations – I
3.1 Relation between the roots and coefficients of general polynomial equation
3.2 Relation between the roots and coefficients of quadratic, cubic and biquadratic equation
3.3 Symmetric functions of the roots Unit 4……………………………………………………………………………………………………69
Theory of Equations – II
4.1 Transformation of Equations
4.2 Carden’s Method of solving the cubic equation
4.3 Descarte’s method of solving biquadratic equations