Mathematics Optional Algebra Module

Vector spaces over R and C, linear dependence and independence; subspaces, bases, dimension; linear transformations, rank and nullity; matrix of a linear transformation, algebra of matrices; row and column reduction, echelon form, congruence and similarity; rank and inverse of a matrix; solving linear systems; eigenvalues, eigenvectors, characteristic polynomial; Cayley-Hamilton theorem; symmetric, Hermitian, orthogonal and unitary matrices.

Groups, subgroups, cyclic groups, cosets, Lagrange's theorem; normal subgroups, quotient groups, homomorphism of groups; basic isomorphism theorems, permutation groups, Cayley's theorem; rings, subrings, ideals, homomorphisms of rings; integral domains, principal ideal domains, Euclidean domains and UFDs; fields and quotient fields.

Linear programming problems; basic solution, basic feasible solution and optimal solution; graphical and simplex methods of solution; duality; transportation problems; assignment problems.