# LINEAR ALGEBRA - 2020/1

Module code: MAT1034

Module Overview

This module is an introduction to the theory and methods of Linear Algebra.

Module provider

Mathematics

Module Leader

WOLF Martin (Maths)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 4

JACs code: G130

Module cap (Maximum number of students): N/A

Module Availability

Semester 2

Prerequisites / Co-requisites

MAT1031 Algebra

Module content

The module is divided into four main parts:

**Systems of linear equations:**rank and nullity of matrices, elementary row operations and row-echelon form, Gaussian elimination, solubility of linear equations;**Vector spaces:**axiomatic development of vector spaces, linear independence of vectors, basis representations of vectors, change of basis, dimension, vector subspaces;**Linear maps:**basic properties of linear maps, rank-nullity theorem, matrix representation, Cayley-Hamilton theorem, eigenvalues and eigenvectors, eigenspaces, algebraic and geometric multiplicities, diagonalisation;**Inner product spaces:**inner products, norms, Cauchy-Schwarz inequality, orthogonality, orthogonal complement, Gram-Schmidt process, orthogonal and unitary changes of basis, isometries, self-adjoint operators.

Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

School-timetabled exam/test | IN-SEMESTER TEST (50 MINS) | 25 |

Examination | EXAMINATION - 2 HOURS | 75 |

Alternative Assessment

None.

Assessment Strategy

__The assessment strategy is designed to provide students with the opportunity to demonstrate: __

That they have learnt the basic material in the field, and are able to apply it to examples and problems.

__The summative assessment for this module consists of: __

· In-Semester Test that constitutes 25% of the final mark;

· Final Examination that constitutes 75% of the final mark.

__Formative assessment and feedback: __

The students will be given exercise sheets every fortnight, and it will be suggested that they work through the examples as part of their independent study prior to attending the seminars. This will aid the students with the development of mathematical technique and knowledge. The students will receive feedback on their work during the seminars and office hours.

In addition, there will be four pieces of unassessed coursework as part of their independent study. This coursework will be marked and the students will receive detailed feedback on this work during the lectures, seminars, and office hours.

Module aims

- The aim of this module is to extend students' knowledge of matrices, vectors and systems of linear equations and to introduce the abstract concepts of vector spaces, linear maps and inner products.

Learning outcomes

Attributes Developed | ||
---|---|---|

001 | Students should develop an understanding of the concepts of linear algebra, and master the basic tools needed for the qualitative and quantitative description. In particular, at the end of the module the student should be able to demonstrate a proper understanding of | KCT |

002 | Whether systems of linear equations are soluble and be able to solve such systems by means of the Gaussian elimination; | KC |

003 | The concepts of vector spaces and vector subspaces; | KC |

004 | Linear (in-)dependence of vectors, basis representations of vectors, and changes of basis; | KC |

005 | The concepts of linear maps, their matrix representations, eigenvalues and eigenvectors, and carry out matrix diagonalisation; | KC |

006 | The concepts of inner products, norms, and orthogonality and be able to orthogonalise vectors by means of the Gram-Schmidt procedure; | KC |

007 | The concept of orthogonal and unitary changes of basis; | KC |

008 | The concept of self-adjoint operators; | KC |

009 | Simple proofs similar to those covered in the module. | KCT |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

Overall student workload

Independent Study Hours: 101

Lecture Hours: 44

Seminar Hours: 5

Methods of Teaching / Learning

The __learning and teaching__ strategy is designed to provide:

- A detailed introduction to linear algebra and its application in other areas
- Experience (through demonstration) of the methods used to interpret, understand and solve problems in linear algebra

The

__learning and teaching__methods include:

- 4 x 1 hour lectures per week x 11 weeks, with lecture notes provided;
- (every second week) 1 x 1 hour seminar for guided discussion of solutions to problem sheets provided to and worked on by students in advance.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Programmes this module appears in

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

Mathematics with Statistics BSc (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics with Statistics MMath | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics BSc (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics BSc (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics MPhys | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics MMath | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics MMath | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics with Music BSc (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Economics and Mathematics BSc (Hons) | 2 | Compulsory | A weighted aggregate of 40% overall and a pass on the pass/fail unit of assessment is required to pass the module |

Financial Mathematics BSc (Hons) | 2 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2020/1 academic year.