Handbook

Linear algebra is a critical tool in all mathematics and its applications. For example, the output of many electrical circuits depends linearly on the input (over moderate ranges of input), and successfully correcting the trajectory of a space probe involves repeatedly solving systems of linear equations in hundreds of variables. Linear methods are vital in ecological population models and in mathematics itself. Students have been introduced to systems of linear equations and matrices, vector spaces and linear transformations in first-year Mathematics courses without understanding all the subtleties involved.

MATH2501will review material from first year (MATH1231, MATH1241 or MATH1251) so that vector spaces and linear transformations become familiar friends rather than uneasy acquaintances. Students will learn about important geometric transformations: projections, rotations, and reflections. Students will see their applications, such as the least squares approximations, and will learn how to view many linear transformations as being made up of “stretches”; in various directions, the so-called diagonalisation process, and the more general Jordan form. The course will also introduce Jordan forms, which are used to calculate functions of matrices, such as the exponential of a matrix and hence to solve systems of linear differential equations.

The course is delivered through lectures and tutorials, which provide guidance and activities to help students refine and apply the knowledge gained in lectures.

Note: MATH2601 is the higher level version of this course, which is primarily but not exclusively intended for students aiming to complete honours in applied mathematics, pure mathematics, statistics or data science, and so aims to give students a deeper level of understanding of the course content.