# MAS2703 : Algebra

• Offered for Year: 2024/25
• Module Leader(s): Dr John Britnell
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters

Your programme is made up of credits, the total differs on programme to programme.

 Semester 2 Credit Value: 10 ECTS Credits: 5.0 European Credit Transfer System

#### Aims

To introduce the viewpoint of modern algebra by extending the work of earlier modules and to provide a basis for further study of algebra.

Module summary

Modern algebra deals with sets equipped with operations resembling some or all of addition, subtraction, multiplication and division. One example of such a system is a field. The concept of a field is a natural one since we have a familiar structure with two operations which mimic addition and multiplication of numbers. We study examples of finite fields. We consider polynomials defined over a field and means of determining reducibility or irreducibility in some cases. We find that polynomials over a field form a system known as a ring and we consider the possibility of factorisation in a ring. In particular, we study rings consisting of complex numbers and see examples of such rings in which some numbers have more than one irreducible factorisation.

#### Outline Of Syllabus

Multiple examples of rings and fields, including polynomial rings, Zn, and complex number rings. Applications to the study of polynomials, their roots and their factorisation. Factorisation in rings.

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessments
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Scheduled Learning And Teaching ActivitiesDrop-in/surgery51:005:00Drop-in classes
Guided Independent StudyIndependent study531:0053:00Preparation time for lectures, background reading, coursework review
Total100:00
##### Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher order thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A80N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
##### Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.