Matrices : Introduction – Transpose of a matrix – Inverse matrix – Symmetric and Skew –
Symmetric matrices - Hermitian and Skew-Hermitian Matrices – Orthogonal and Unitary
Matrices – Rank of a Matrix –Characteristic Roots and Characteristic Vectors of a Square
Sets – Relations and binary operations – Groups – Symmetric Group definitions and Examples –
Subgroups – Index of a group – Fermat theorem - Normal subgroups and quotient groups.
Homomorphisms – Cauchy’s theorem, Sylow’s theorem for Abelian groups
Automorphisms – permutation groups – Rings : Definition and Examples – Some special classes
Anx.18 D - B.Sc Maths (SDE) 2007-08 Page 12 of 26
Field – Integral domain - Homomorphisms of Rings. - Ideals and Quotient Rings –
Vector space: Subspace of a Vector space - Homomorphism – Isomorphism - Linear
Independence and Bases.
Dual spaces – Innerproduct spaces – Orthonormal set – Linear transformations –
Characteristic roots and characteristic vectors of a square matrix