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Module ABSTRACT ALGEBRA

Module code: MT242P
Credits: 5
Semester: 2
Department: MATHEMATICS AND STATISTICS
International: Yes
Overview Overview
 

Module Objective: To introduce the student to abstract algebra, with a firm emphasis on linear algebra over R and C.

The rationals, reals and complex numbers as examples of fields, the field with 2 elements and field of rational functions; Rn and Cn as vector spaces, vector spaces of functions; the axioms of a vector space; subspace, direct sums, linear maps; kernel, image and quotient spaces; span, linear independence, basis and dimension; linear maps and matrices, change of basis, rank and nullity; normed vector spaces, orthonormal bases, orthogonal projection, Gram-Schmidt process; eigenvalues and eigenvectors, diagonalisation; dual spaces, tensor products, endomorphism algebras; other topics may include exterior algebra and determinants.

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