Higher Algebra

Content1. Theory of Numbers

Division, G.C.M. Numbers Prime to each other, Prime and Composite Numbers . The Divisors of a Number.Product of n Consecutive Integers (6).Residues of Terms of an

A.P. .Induction .

EXERCISE I

2. Rationals and Irrationals.

Rationals, Fundamental Laws of Order and of Arithmetic, Representation by Points on a Line Absolute Values, Large and Small Numbers, Meaning of ‘Tends,’ Aggregate, Sequence Approximate Values, Fundamental Inequalities Irrationals, Meaning of Representation of a Number by an Endless Decimal Real Numbers, the Function ax EXERCISE II

3. Polynomials

Notation Division, Synthetic Division.Remainder Theorem and Applications, Equating Coefficients . Quadratic Functions of x and y

EXERCISE III

Expansion of Products, Binomial Theorem for Positive Integral Index . Expansion of f(x + h), where f(x) = (a0, a1, a2,…..an) (x, 1)n. Multinomial Theorem, Greatest Coefficient in

(a + b + c + …… + k)n

EXERCISE IV

H.C.F., Prime and Composite Functions .

EXERCISE V