# ALGEBRA - 2024/5

Module code: MAT1031

## Module Overview

This module combines an introduction to abstract algebra and methods of proof, with an introduction to vectors and matrices with applications to algebraic and geometric problems. This module is fundamental to subsequent modules including MAT1034 Linear Algebra and MAT2048 Groups & Rings.

### Module provider

Mathematics & Physics

### Module Leader

GRANT James (Maths & Phys)

### Number of Credits: 15

### ECTS Credits: 7.5

### Framework: FHEQ Level 4

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

## Overall student workload

Independent Learning Hours: 42

Lecture Hours: 44

Seminar Hours: 5

Guided Learning: 15

Captured Content: 44

## Module Availability

Semester 1

## Prerequisites / Co-requisites

None

## Module content

Indicative content includes:

- Methods of proof, including deduction, induction, contraposition and contradiction.
- Introduction to groups and fields.
- Equivalence relations, congruences and modular arithmetic.
- Prime numbers. Prime factorisation of integers.
- Greatest common divisors and lowest common multiples.
- Permutations. The symmetric group.
- Vectors in two and three dimensions. Scalar and vector products.
- Matrix algebra. Properties of the transpose and the trace of a matrix.
- Determinants and inverse matrices.
- Solutions of simultaneous linear equations.
- Linear transformations, including rotations in two dimensions.
- Lines in two and three dimensions. Planes in three dimensions.
- Eigenvalues and eigenvectors of 2x2 matrices.
- Polynomials and polynomial long division. The remainder theorem.

## Assessment pattern

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

Coursework | Assessed Coursework 1 | 5 |

Coursework | Assessed Coursework 2 | 10 |

Coursework | Assessed Coursework 3 | 10 |

Examination | End-of-Semester Examination (2 hrs) | 75 |

## Alternative Assessment

N/A

## Assessment Strategy

The __assessment strategy__ is designed to provide students with the opportunity to demonstrate:

- Understanding of key definitions and theory, and the ability to identify and use appropriate methods of proof in Algebra.
- The ability to identify and use the appropriate methods to solve unseen problems involving vectors and matrices.

Thus, the

__summative assessment__for this module consists of:

- Three assessed courseworks, with the first coursework worth 5%, and the second and third courseworks each worth 10% of the module mark. The first coursework will correspond to Learning Outcome 1. The second coursework will correspond to Learning Outcomes 2 and 3. The third coursework will correspond to Learning Outcomes 5 and 6.
- A synoptic examination (2 hours), worth 75% of the module mark, corresponding to all Learning Outcomes 1 to 6.

Formative assessment

Students will receive formative feedback at biweekly seminars on problem sheets, provided to students in advance and designed to consolidate student learning.

Feedback

Students will receive feedback on the three assessed courseworks. The feedback is timed such that the feedback from the three assessed courseworks assists students with preparation for the synoptic examination. This feedback is complemented by verbal feedback at biweekly seminars and at office hours.

## Module aims

- Develop students' understanding of standard methods of mathematical proof.
- Provide students with an introduction to basic definitions and theory in abstract algebra.
- Develop students¿ understanding of vectors and matrices, and enable students to solve a wide range of algebraic and geometric problems using vectors and matrices.

## Learning outcomes

Attributes Developed | ||

001 | Students will understand and be able to formulate simple algebraic proofs, selecting an appropriate method. | CT |

002 | Students will know the definitions of groups and fields, and will be able to apply these definitions to standard examples. | KC |

003 | Students will know the properties of equivalence relations, and will be able to add and multiply integers modulo n. | KC |

004 | Students will be able to determine the prime factorisation of an integer, and the greatest common divisor and lowest common multiple of integers. | KC |

005 | Students will be able to solve problems involving vectors. | KC |

006 | Students will be able to solve problems involving matrices, determinants and linear systems of equations. | KCT |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

## Methods of Teaching / Learning

The __learning and teaching__ strategy is designed to:

- Provide students with an introduction to abstract algebra and methods of proof.
- Provide students with experience of methods used to understand and solve problems involving vectors and matrices.

The learning and teaching methods include:

- Four one-hour lectures for eleven weeks, with module notes provided to complement the lectures. These lectures provide a structured learning environment and opportunities for students to ask questions and to practice methods taught.
- Five seminars for guided discussion of solutions to problem sheets (provided to students in advance) to reinforce their understanding and guide their learning.
- Three assessed courseworks to provide students with further opportunity to consolidate learning. Students receive feedback on these courseworks as guidance on their progress and understanding.

Lectures may be recorded or equivalent recordings of lecture material provided. These recordings are intended to give students an opportunity to review parts of lectures which they may not fully have understood and should not be seen as an alternative to attending lectures

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.

## Reading list

https://readinglists.surrey.ac.uk

Upon accessing the reading list, please search for the module using the module code: **MAT1031**

## Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourceness and Resilience, and Sustainability. This module is designed to allow students to develop knowledge, skills and capabilities in the following areas:

**Digital Capabilities**: The SurreyLearn page for MAT1031 features a dynamic discussion forum where students can pose questions and engage with others using e.g. LaTeX and MathML tools. This enhances their digital competencies while facilitating collaborative learning and information sharing.

**Employability: **The module MAT1031 equips students with skills which significantly enhance their employability. The mathematical proficiency gained hones critical thinking and problem-solving abilities. Students learn to evaluate complex algebraic problems, break them into manageable components, and apply logical reasoning to arrive at solutions — these are highly sought after skills in any profession.

**Global and Cultural Capabilities:** Student enrolled in MAT1031 originate from a variety of countries and have a wide range of cultural backgrounds. Students are encouraged to work together during problem-solving teaching activities in seminars and lectures, which naturally facilitates the sharing of different cultures.

**Resourcefulness and Resilience**: MAT1031 is a module which demands a rigorous approach to abstract algebra as well as the ability to perform calculations with vectors and matrices. Students will gain skills in analysing problems and lateral thinking, and will complete assessments which challenge them and build resilience.

## Programmes this module appears in

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

Mathematics with Statistics BSc (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics BSc (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics BSc (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Economics and Mathematics BSc (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics MPhys | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics and Physics MMath | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Financial Mathematics BSc (Hons) | 1 | Compulsory | A weighted aggregate mark of 40% is required to pass the module |

Mathematics MMath | 1 | 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 2024/5 academic year.