May 28th, 2015
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ALGEBRASets, Relations, Functions, Elementary Number Theory Including the relation of congruence Modulo, Simultaneous linear / quadratic equations, Indices, Logarithms, Arithmetic, Geometric and Harmonic progressions, Binomial theorem, Surds, Complex numbers, Demoivres theorem and its simple applicationMATRICES AND DETERMINANTSMatrix operations, Definition and properties of determinats, Cofactors, Adjoint, Elementry Transformations, Rank and inverse of a Matrix, Matrix Polynomial, Characteristic Equations,Eigen Values, Latent Vectors, Caylay Hamilton theorem, Linear system of EquationsTHEORY OF EQUATIONSPolynomials and their charcteristics, Roots of an equation, Relations between Roots and Coefficients,Transformation of Equations, Symmetric function etc.ABSTRACT ALGEBRAGroups, Cyclic groups, Subgroups, Normal Groups, Lagranges theorem, Homomorphism, Isomorphism, Ring, Field, Vector Spaces, Linear Independence of Vectors, Basis, Dimension, Linear Transformation and diagonalisation of Matrices etcVECTOR ALGEBRAScalar and Vector quantities their representation, Addition and subtraction of vectors, Scalar and vector product of two vectors, Scalar triple product, Expa

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