Lecturer	David Kay
Degrees	Preliminary Examinations — Computer Science
Term	Michaelmas Term 2015  (24 lectures)

Overview

This is a first course in linear algebra. The course will lay down the basic concepts and techniques of linear algebra needed for subsequent study. At the same time, it will provide an appreciation of the wide application of this discipline within the scientific field.

The course will require development of theoretical results. Proofs and consequences of such results will require the use of mathematical rigour, algebraic manipulation, geometry and numerics.

A goal of the course is to provide insight into how linear algebra theorems and results, sometimes quite abstract, impinge on everyday life. This will be illustrated with detailed examples.

Learning outcomes

At the end of this course the student will be capable of gained the ability to:

• Comprehend vector spaces (subspaces).
• Understand fundamental properties of matrices including inverse matrices, eigenvalues and linear transformations. 
• Be able to solve linear systems of equations.
• Have an insight into the applicability of linear algebra.

Synopsis

• Lectures 1-3 Vectors: Vectors and geometry in two and three space dimensions, Algebraic properties, Dot products and orthogonality, Linear independence, Basis, Dimension, Vector spaces and subspaces. 
• Lectures 4-6 Matrices: Matrix operations, Column and row space, Null and range space, rank, Determinants, Inverse matrices, Population growth, Error correcting codes. 
• Lectures 7-13 Solution of linear systems: Examples of linear systems, Problems arising from solving on a Computer, Row echelon form, Gaussian elimination, Pivoting, Network analysis, Global positioning system.
• Lectures 14-15 Iterative methods:  Jacobi, Gauss-Seide and steepest descent.

• Lectures 16-19 Linear transformations: Definition and examples, Properties, Composition, Rotations and reflections, Matrices, One-to-one and onto, Robotics.

• Lectures 20-24 Eigenvalues and eigenvectors: Definition, Similarity and diagonalization, Population growth revisited, Systems of linear differential equations.

Syllabus

• Vector spaces and subspaces 
• Matrices
• Inverse matrices
• Iterative methods
• Linear transformations 
• Solution of linear systems 
• Eigenvalues and eigenvectors

Reading list

• Introduction to linear algebra (3rd Edition), Gilbert Strang, Wellesley-Cambridge press.

Feedback

Students are formally asked for feedback at the end of the course. Students can also submit feedback at any point here. Feedback received here will go to the Head of Academic Administration, and will be dealt with confidentially when being passed on further. All feedback is welcome.

Taking our courses

This form is not to be used by students studying for a degree in the Department of Computer Science, or for Visiting Students who are registered for Computer Science courses

Other matriculated University of Oxford students who are interested in taking this, or other, courses in the Department of Computer Science, must complete this online form by 17.00 on Friday of 0th week of term in which the course is taught. Late requests, and requests sent by email, will not be considered. All requests must be approved by the relevant Computer Science departmental committee and can only be submitted using this form.