## 3H: Algebra MATHS4072

• School: School of Mathematics and Statistics
• Credits: 20
• Level: Level 4 (SCQF level 10)
• Typically Offered: Semester 1
• Available to Visiting Students: Yes

### Short Description

This course will provide an introduction to the basics of group theory, ring theory and field theory. It will provide a good grounding in algebraic structures including the construction and application of quotient or factor groups, factor rings and of homomorphisms between rings and groups.

### Timetable

34 x 1hr lectures and 12 x 1hr tutorials in a semester.

None

### Excluded Courses

Algebra I (86PG)

Algebra II (86PH)

None

### Assessment

90% Examination, 10% Coursework.

Main Assessment In: April/May

Are reassessment opportunities available for all summative assessments? Not applicable

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below.

### Course Aims

The basics of group theory, ring theory and field theory will be covered. The intention is to provide a good grounding in algebraic structures including the construction and application of quotient or factor groups, factor rings and the uses of homomorphisms between rings and groups.

### Intended Learning Outcomes of Course

By the end of this course students will be able to:

■ write coherent statements of definitions and results covered in the course;

■ recognise situations in which it is appropriate to apply key theorems including the isomorphism theorems for groups and ring;

■ carry out simple computations using groups, rings, and fields;

■ illustrate concepts by the use of examples;

■ reproduce key proofs;

■ solve problems in group ring and field theory, including both problems that are similar to problems recommended for formative assessment as well as unseen and more challenging problems.

None