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Semester 1

Introduction to Linear Algebra (MATH08057)







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Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.

Course Summary

An introduction to linear algebra, mainly in R^n but concluding with an introduction to abstract vector spaces. The principal topics are vectors, systems of linear equations, matrices, eigenvalues and eigenvectors and orthogonality. The important notions of linear independence, span and bases are introduced. This course is both a preparation for the practical use of vectors, matrices and systems of equations and also lays the groundwork for a more abstract, pure-mathematical treatment of vector spaces.Students will learn how to use a computer to calculate the results of some simple matrix operations and to visualise vectors.

Course Description

This syllabus is for guidance purposes only:The course will have a range of student-focused activities equivalent to approximately three lecture-theatre-hours and a 90 minute Example Class per week. The course contents are given in the course textbook, Nicholson, predominantly Chapters 1 to Chapter 5, and the start of Chapter 8, with a selection (not all) of the applications covered and selected topics omitted.- Vectors in R^n, and in general. Vectors and geometry- Systems of linear equations, echelon form, Gaussian elimination, intro to span and linear independence.- Matrices, multiplication, transpose, inverses, linear maps. Intro to subspaces and bases. Rank. - Eigenvalues and eigenvectors. Determinants- Orthogonality, Gram-Schmidt, orthogonal Diagonalization.- Introduction to abstract vector spaces and subspaces. - Selected applications (taught in sequence where appropriate)

Assessment Information

Written Exam 0%, Coursework 100%, Practical Exam 0%

Additional Assessment Information

Coursework 100% Examination 0%The assessment for this course will involve regular coursework throughout the assessment (probably weekly) with a combination of online assessments, written hand-in assessments, and synoptic coursework to be completed at the end of the semester.

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