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Group Theory: Groups, subgroups, Abelian groups, non-Abelian groups, cyclic groups, permutation groups, normal subgroups, Lagrange's Theorem for finite groups, group homomorphism, and basic concepts of quotient groups.

Syllabus of Linear Algebra- Vector space, Linear dependence of vectors, Basis, Dimension, Linear transformations, Matrix representation with respect to an ordered basis, Range space and null space, Rank-nullity theorem, Rank and inverse of a matrix, Determinant, Solutions of system of linear equations, Consistency conditions, Eigenvalues and eigenvectors, Cayley-Hamilton theorem, Symmetric, Skew-symmetric, Hermitian, Skew-Hermitian, Orthogonal and unitary matrices.

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