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Abstract Algebra 2

Overview

  • Credit value: 15 credits at Level 6
  • Convenor and tutor: Professor Sarah Hart
  • Assessment: coursework (20%) and a two-hour examination (80%)

Module description

In this module you will learn key concepts from abstract algebra. It is part of the Graduate Certificate in Mathematics by Distance Learning, which can serve as a qualifying course for our postgraduate degrees MSc Mathematics or MSc Mathematics and Financial Modelling. This module, combined with the module Abstract Algebra 1 which precedes it, will cover material on algebraic structures such as groups, rings, fields and vector spaces, giving you a thorough grounding in these topics.

The module is studied via distance learning. Each week, you will be guided through a series of learning steps. These include short instructional videos, online quizzes to test your understanding, livestreamed face-to-face examples classes, full course notes, and exercises to try at home.

Indicative module syllabus

  • Revision of key concepts from Abstract Algebra 1, in particular the definition of groups and rings
  • Additional results and examples of groups
  • Conjugation, conjugacy classes and centralizers
  • Normal subgroups - examples and properties
  • Quotient groups
  • The Homomorphism Theorem
  • Fields: definition and examples of finite and infinite fields
  • Definition and properties of the characteristic of a field, and general results on fields
  • Vector spaces over arbitrary fields: formal axiomatic definition, properties, examples and results

Learning objectives

By the end of this module, you will:

  • knowledge and understanding of, and the ability to use, mathematical methods and techniques
  • knowledge and understanding of a range of results in mathematics
  • appreciate the need for proof in mathematics, and be able to follow and construct mathematical arguments
  • understand the importance of assumptions and have an awareness of where they are used and the possible consequences of their violation
  • appreciate the power of generalisation and abstraction in the development of mathematical theories
  • have a deeper knowledge of particular areas of mathematics.