About the Book
Algebra (Not Revised in 2017): Union, Intersection, Difference, Complement of Sets, Algebra of Statements, Tautology, Cartesian Product, Binary Relations & Operations, Equivalence Relations & Classes, Order Relations on Integers, Division Algorithm, Unique Factorization Theorem, Modulo, Linear Congruence, Residue Classes| Manipulation of Inequalities, Factorization, Arithmetic, Geometric, Weighted Means, Mean of mth powers, Cauchy – Schwarz, Tchebychef, Holder, Minkowski’s Inequality| Infinite Series, Theorems on Convergence, Ratio, Root & 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 & Properties, Multiplying Determinants, Minors, Cofactors, Solution of Simultaneous Equations, Addition, Multiplication of Matrices, Types of Matrices – Symmetric, Skew Symmetric, Reciprocal, Orthogonal, Hermitian, Transpose & Adjoint of a Matrix, Solution of Simultaneous Equations, Rank of a Matrix, Linear Dependence, Characteristic Equation, Eigen Vectors, Cayley Hamilton Theorem| Groups & Properties, Residue Classes, Abelian, Cyclic, Permutation Groups, Normal Subgroup, Isomorphism, Homomorphism, Cosets| Rings, Fields, Integral Domain, Isomorphism, Homomorphism, Ideals| Vector Spaces, Linear Combinations, Linear Dependence, Basis, Dimension, Sum of Subspaces, Homomorphism, Inner Product of Vectors| Theory of Equations (Revised 2017): Polynomials, Division Algorithm & Remainder Theorems, Synthetic Division, Zeroes of Polynomials, Fundamental Theorem of Algebra, Properties of Equations, Descarte’s Rule of Signs, Relations Between Roots & Coefficients, Transformation of Equations, Multiple Roots, Reciprocal Equations|Cubic & Quartic Equations – Cardan’s, Descarte’s, Ferrari’s Methods of Solving Equations| Numerical Solution of Equations – Limits of Roots, Integer Roots, Newton’s, Horner’s Methods
