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The Universities / Institutes mainly takes the following syllabus :
Mathematics
Algebra
Sets, 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, Demoivre’s theorem and its simple application
Matrics & Determinants
Matrix 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 Equations.
Theory Of Equations
Polynomials and their charcteristics, Roots of an equation, Relations between Roots and Coefficients,Transformation of Equations, Symmetric function etc.
Abstracy Algebra
Groups, Cyclic groups, Subgroups, Normal Groups, Lagrange’s theorem, Homomorphism, Isomorphism, Ring, Field, Vector Spaces, Linear Independence of Vectors, Basis, Dimension, Linear Transformation and diagonalisation of Matrices etc.
Vector Algebra
Scalar and Vector quantities their representation, Addition and subtraction of vectors, Scalar and vector product of two vectors, Scalar triple product, Expansion formula of Vector triple product.
Trigonometry
Simple identities, trignometric equations, Properties of triangles, Solution of triangle, Height and distance, Inverse function.
Calculas & Real