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Abstract Algebra 1

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 2, 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 prerequisite material on sets, functions and matrices
  • Binary relations and equivalence relations
  • Binary operations - definition, properties and examples
  • Definition of a group - first examples and properties
  • Subgroups, the subgroup test, further examples
  • Cosets and Lagrange’s Theorem
  • Linear congruences and the integers modulo n
  • Definition of rings - key examples including number rings and matrix rings
  • Subrings and the Subring Test
  • Zero divisors, units and integral domains
  • Factorisation and irreducibility

Learning objectives

By the end of this module, you will:

  • have knowledge and understanding of, and the ability to use, mathematical methods and techniques
  • have 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.