Undergraduate Programme and Module Handbook 2024-2025

# Module MATH1071: Linear Algebra I

## Department: Mathematical Sciences

### MATH1071: Linear Algebra I

Type | Open | Level | 1 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | Location | Durham |
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#### Prerequisites

- Normally, A level Mathematics at grade A or better and AS level Further Mathematics at grade A or better, or equivalent.

#### Corequisites

- Calculus I (MATH1061)

#### Excluded Combination of Modules

- Calculus I (Maths Hons) (MATH1081), Linear Algebra I (Maths Hons) (MATH1091), Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571) may not be taken with or after this module.

#### Aims

- This module is designed to follow on from, and reinforce, A level mathematics.
- It will present students with a wide range of mathematics ideas in preparation for more demanding material later.
- Aim: to give a utilitarian treatment of some important mathematical techniques in linear algebra.
- Aim: to develop geometric awareness and familiarity with vector methods.

#### Content

- A range of topics are treated each at an elementary level to give a foundation of basic definitions, theorems and computational techniques.
- A rigorous approach is expected.
- Linear Algebra in n dimensions with concrete illustrations in 2 and 3 dimensions.
- Vectors, matrices and determinants.
- Vector spaces and linear mappings.
- Diagonalisation, inner-product spaces and special polynomials.
- Introduction to group theory.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve a range of predictable or less predictable problems in Linear Algebra.
- have an awareness of the basic concepts of theoretical mathematics in Linear Algebra.
- have a broad knowledge and basic understanding of these subjects demonstrated through one of the following topic areas:
- Vectors in Rn, matrices and determinants.
- Vector spaces over R and linear mappings.
- Diagonalisation and Jordan normal form.
- Inner product spaces.
- Introduction to groups.
- Special polynomials.

Subject-specific Skills:

- Students will have basic mathematical skills in the following areas: Modelling, Spatial awareness, Abstract reasoning, Numeracy.

Key Skills:

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Tutorials provide active engagement and feedback to the learning process.
- Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills. They are also an aid in developing students' awareness of standards required.
- Initial diagnostic testing and associated supplementary support classes fill in gaps related to the wide variety of syllabuses available at Mathematics A-level.
- The examination provides a final assessment of the achievement of the student.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 58 | 3 per week in terms 1, 2 or 3 per week in term 2 (alternating fortnightly with Problems Classes), 2 revision lectures in term 3. | 1 Hour | 58 | |

Tutorials | 9 | Weeks 4, 6, 8, 10 (Term 1) and 14, 16, 18, 20 (Term 2), plus 1 revision tutorial in Easter term. | 1 Hour | 9 | ■ |

Problems Classes | 4 | Fortnightly in weeks 13-19 | 1 Hour | 4 | |

Support classes | 18 | Weekly in weeks 2-10 and 12-20 | 1 Hour | 18 | |

Preparation and Reading | 111 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 90% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Written examination | 3 hours | 100% | Yes |

Component: Continuous Assessment | Component Weighting: 10% | ||

Element | Length / duration | Element Weighting | Resit Opportunity |

Fortnightly assessments during the first 2 terms. Normally, each will consist of solving problems. Students will have about one week to complete each assignment. | 100% |

#### Formative Assessment:

40 minute collection paper in the beginning of Epiphany term. Fortnightly formative assessment.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University