## 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.

■ 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