MATH203-17S1 (C) Semester One 2017 Linear Algebra 15 points, 0.1250 EFTS 20 Feb 2017 - 25 Jun 2017 Description Linear algebra is a key part of the mathematician's toolkit and has applications to many areas in science, commerce and engineering. This course develops the fundamental concepts of linear algebra, including vector spaces, linear transformations, eigenvalues, and orthogonality. Emphasis is placed on understanding both abstract mathematical structures and their concrete applications. Course Information: Linear algebra is a key part of the mathematician's toolkit and has applications to many areas in science, commerce and engineering. This course develops the fundamental concepts of linear algebra, including vector spaces, linear transformations, eigenvalues, and orthogonality. Emphasis is placed on understanding both abstract mathematical structures and their concrete applications. Topics Covered: Vector spaces; Linear independence, bases and coordinate systems; Linear transformations, matrices, rank, nullity, and relationships between the fundamental matrix spaces; Eigenvalues, eigenvectors, diagonalisation and canonical forms of a matrix; Inner products and orthogonality; Gram-Schmidt process, QR-decomposition and orthogonal projections; Orthogonal diagonalization and the spectral theorem; Vector and matrix norms and condition numbers; LU-decompositions. Applications: Markov chains, population and economic models, coupled systems of linear ordinary dierential equations, linear recurrence relations, Fourier series, least squares approximation, cryptography, coding theory, data compression. Learning Outcomes At the end of the course, students will: be procient in the standard techniques of linear algebra; understand why these techniques work; be able to use these techniques in a variety of applications, including using MATLAB to solve standard problems; have developed problem solving skills both as part of a team and as an individual; have developed written and oral communications skills, emphasizing the ability to explain what the mathematics means.