## Algebra 2 Durham University

Please ensure you check the module availability box for each module outline, as not all modules will run each academic year.

### Department: Mathematical Sciences

#### MATH2581: ALGEBRA II

Type | Open | Level | 2 | Credits | 20 | Availability | Available in 2017/18 | Module Cap | Location | Durham |
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#### Prerequisites

- Calculus and Probability 1 (MATH1061) and Linear Algebra 1 (MATH1071).

#### Corequisites

- None.

#### Excluded Combination of Modules

- Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571)

#### Aims

- To introduce further concepts in abstract algebra and develop their theory.

#### Content

- Rings and fields.
- Examples of groups.
- Group actions.
- Homomorphisms and quotient groups.
- Finitely generated abelian groups.

#### Learning Outcomes

Subject-specific Knowledge:

- By the end of the module students will: be able to solve a range of predictable and unpredictable problems in Algebra.
- have an awareness of the abstract concepts of theoretical mathematics in the field of Algebra.
- have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas: Rings and fields, example of groups, generators, homomorphisms.
- Group actions, Equivalence relations.
- Structure of finitely generated abelian groups.
- Vector spaces over arbitrary fields.

Subject-specific Skills:

- In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Abstract reasoning.

Key Skills:

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

- Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
- Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
- Tutorials provide active engagement and feedback to the learning process.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

#### Teaching Methods and Contact Hours

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

Lectures | 42 | 2 per week | 1 Hour | 42 | |

Tutorials | 11 | Fortnightly for 20 weels | 1 Hour | 11 | ■ |

Problems Classes | 9 | Fortnightly for 20 weeks | 1 Hour | 9 | |

Preparation and Reading | 138 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

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

Written examination | 3 hours | 100% | Yes |

#### Formative Assessment:

One written assignment to be handed in every third lecture in the first 2 terms. Normally each will consist of solving problems from a Problems Sheet and typically will be about 2 pages long. Students will have about one week to complete each assignment.