Text Book on Algebra and Theory of Equations

Contents: Theory of Equations (Revised 2017) Polynomials, Division Algorithm and Remainder Theorems, Synthetic Division, Zeroes of Polynomials, Fundamental Theorem of Algebra | Properties of Equations, Descarte's Rule of Signs, Relations Between Roots and Equations, Transformation of Equations, Multiple Roots, Reciprocal Equations Cubic and Quartic Equations - Cardan's, Descarte's, Ferrari's Methods of Solving Equations | Numerical Solution of Equations - Limits of Roots, Integer Roots of an Equation | Newton's, Horner's Methods | Algebra (Not Revised in 2017) Difference, Complement of Sets, Algebra of Statements, Tautology, Cartesian Product of sets, Binary Relations, Operations, Equivalence Relations, Classes, Order Relations on Integers, Division Algorithm, Unique Factorization Theorem, Modulo, Linear Congruence, Residue Classes | Manipulation of Inequalities, Arithmetic, Geometric, Weighted Means, Mean of mth powers, Cauchy - Schwarz, Tchebychef, Holder, Minkowski's Inequality Definition, Theorems on Convergence, Ratio, Root and Comparison Tests, Higher Risk Ratio Test, Logarithmic Ratio Test, Cauchy's Condensation Test, Test for Alternating Series, Absolute Convergence, Addition, Subtraction, Multiplication of Series, Weirstrass's M Test Determinants and Properties, Multiplying Determinants, Minors, Cofactors, Solution of Simultaneous Equations, Addition, Multiplication of Matrices, Types of Matrices - Symmetric, Skew Symmetric, Reciprocal, Transpose and Adjoint Matrix, Solution of Simultaneous Equations, Rank of a Matrix, Linear Dependence, Characteristic Equation, Eigen Vectors, Cayley Hamilton Theorem, Groups and Properties, Residue Classes, Abelian, Cyclic, Permutation Groups, Normal Subgroup, Isomorphism, Homomorphism, Cosets | Rings, Fields, Integral Domain, Isomorphism, Homomorphism, Ideals | Vector Spaces, Linear Combinations, Basis, Linear Dependence, Dimension, Homomorphism, Inner Product