# Unit information: Linear Algebra in 2021/22

Unit name Linear Algebra MATH10015 20 C/4 Teaching Block 4 (weeks 1-24) Dr. Carey Not open A in A Level Mathematics or equivalent None School of Mathematics Faculty of Science

## Description including Unit Aims

Lecturers: Rachael Carey and Farhad Babaee

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

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

## Assessment Information

Assessment for learning/Formative assessment:

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

Assessment of learning/Summative assessment:

• Two timed, open-book examinations (each worth 45%) after each teaching block
• Coursework (10%)

## Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH10015).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.