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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 differential equations, linear recurrence relations, Fourier series, least squares approximation, cryptography, coding theory, data compression.
At the end of the course, students will: be proficient 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.
This course will provide students with an opportunity to develop the Graduate Attributes specified below:
Critically competent in a core academic discipline of their award
Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.
MATH103 or EMTH119 or MATH199 or (MATH102 and MATH120)
MATH252, MATH254, EMTH203, EMTH204, EMTH211
Students must attend one activity from each section.
To obtain a clear pass in this course, you must both pass the course as a whole (≥ 50%) and also obtain at least 40% in the final examination.
General information for students
Domestic fee $749.00
International fee $3,788.00
* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.
For further information see
Mathematics and Statistics.