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Abstract Algebra 2

Overview

  • Credit value: 15 credits at Level 6
  • Convenor: Mr Dan Mcveagh
  • Assessment: coursework (20%) and a two-hour examination (80%)

Module description

In this module you will learn key concepts from abstract algebra. Combined with the module Abstract Algebra 1 which precedes it, this module will cover material on algebraic structures such as groups, rings, fields and vector spaces, giving you a thorough grounding in these topics.

This module is offered in hyflex format, allowing you to choose how you want to learn. Each week, you will be guided through a series of learning steps. These include short instructional videos, online quizzes to test your understanding, examples classes that you can attend either in person or via livestream, full course notes, and exercises to try at home.

Indicative syllabus

  • Revision of key concepts from Abstract Algebra 1, in particular the definition of groups
  • Additional results and examples of groups
  • Conjugation, conjugacy classes and centralizers
  • Normal subgroups - examples and properties
  • Quotient groups
  • The Homomorphism Theorem
  • 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:

  • 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.