Unit information: Linear Algebra in 2019/20

Unit name	Linear Algebra
Unit code	MATH10015
Credit points	20
Level of study	C/4
Teaching block(s)	Teaching Block 4 (weeks 1-24)
Unit director	Dr. Mackay
Open unit status	Not open
Pre-requisites	A in A Level Mathematics or equivalent
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Unit Aims

Linear Algebra constitutes the bedrock of higher mathematics. It is indispensable and used in one form or another throughout every mathematical discipline.

This unit aims to lay down foundational concepts for studying maths at the undergraduate level and enable students to develop clear mathematical thinking.

Unit Description

Linear Algebra begins with the Euclidean plane, complex numbers and n-dimensional Euclidean space, which leads to the ideas of vectors and matrices, which also arise naturally from the study of systems of linear equations. These objects behave linearly, and this helps us understand their properties. In the second half of the course we develop the abstract notion of a vector space. This is one of the basic structures of pure mathematics; yet the methods of the course are also fundamental for applied mathematics and statistics.

This course carefully defines the objects and ideas we work with, and rigorously demonstrates their properties, as well as teaching the tools required for practical computation of examples.

Intended Learning Outcomes

At the end of the unit, the students should:

• have developed some familiarity with abstract mathematical thinking;
• be familiar with geometric objects like lines, planes and hyperplanes, and their axiomatic generalisation into vector spaces and linear maps;
• be able to solve linear equations using elementary operations;
• be able to work with matrix algebra, including matrix inverses, determinants, and eigenvalues and eigenvectors.

Teaching Information

Lectures, supported by lecture notes with problem sets and model solutions, problems classes and small group tutorials.

Assessment Information

Formative assessment:

• problem sheets set by the lecturer and marked by the students’ tutors.

Summative assessment:

• Two 1.5h exams (45%) after each teaching block
• Coursework (10%)

Reading and References

Recommended

• Gilbert Strang, Linear Algebra and its Applications, Thomson Brooks/Cole, 2006
• R. Allenby, Linear Algebra, E. Arnold, 1995
• Howard Anton and Chris Rorres, Elementary Linear Algebra, John Wiley & Sons, 2014
• Serge Lang, Linear Algebra, Springer, 2010
• Seymour Lipschutz and Marc Lipson, Linear Algebra, McGraw-Hill, 2013