Course Catalogue

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This course introduces the fundamental concepts, methods and theories of linear algebra, vector spaces and quadratic forms.

Course will be delivered continuously in the traditional manner at UESTC.

Mandatory Entry Requirements

None

Recommended Entry Requirements

None

None

None

Assessment

Examination 75% - closed book mid term 20%/ closed book final exam55%

Project work 25%

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below.

Due to the nature of the coursework and sequencing of courses, it is not possible to reassess the coursework project and laboratory.

The initial grade on coursework project and laboratory will be used when calculating the resit grade.

This course aims to provide a foundation in linear algebra, including basic understanding of linear systems, matrix algebra, determinants, vector spaces, eigenvalue problems, orthogonality and quadratic forms, to prepare the students for their future study and research.

By the end of this course students will be able to:

■ Apply Gaussian elimination solve linear systems and perform matrix algebra;

■ Apply the properties of determinants to evaluate the determinant of a matrix, and apply Cramer's rule to solve linear systems;

■ Evaluate linear dependence of a vector set, establish a basis, evaluate the dimension and coordinates for an n-dimensional vector space, apply basis and dimension evaluation to the fundamental subspaces of a matrix;

■ Apply characteristic polynomial to solve the eigenvalue problem and diagonalization;

■ Formulate inner products, orthogonality and apply the Gram-Schmidt process to construct an orthogonal basis, apply orthogonal projection to find the best approximation;

■ Apply change of variable to transform a quadratic form into one with no cross-product term and orthogonally diagonalize a symmetric matrix.

Students must attend the degree examination and submit at least 75% by weight of the other components of the course's summative assessment.

Students should attend at least 75% of the timetabled classes of the course.

Note that these are minimum requirements: good students will achieve far higher participation/submission rates. Any student who misses an assessment or a significant number of classes because of illness or other good cause should report this by completing a MyCampus absence report.