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. Babaee |

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 |

**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.

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.

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 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%)

The lectures will present the material in a different order from most textbooks. There is no required text. Notes taken by students of mostly theoretical material taught during lectures and examples from homework and problem classes should suffice to master the material. Attendance of all contact hours is mandatory.

There are many good linear algebra texts. They come in different styles, some follow a more abstract approach, others emphasise applications and computational aspects. Some students may prefer the style of one book more than another.

**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

Lectures aim to give a broader and more creative perspective of the material, focusing on the depth and meaning of studied concepts. Therefore, even though there is a natural correlation between lectures and written notes, it will be somewhat approximate and not without occasional deviation.