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Algebra 2


  • Credit value: 30 credits at Level 5
  • Convenor and tutor: Steven Noble
  • Assessment: short, problem-based assignments (20%) and a three-hour examination (80%)

Module description

This module will give you a thorough grounding in the concepts and techniques of linear algebra, in a more general context than in first-year undergraduate modules. You’ll also gain an understanding of the key definitions and results of group theory. It will also prepare you for the Level 6 option Algebra 3.

Indicative module syllabus

Linear Algebra

  • Vector spaces and subspaces
  • Linear independence, spanning sets, basis and dimension
  • Linear transformations and matrices
  • Image, kernel and the rank-nullity formula


  • Revision of binary operations
  • Definition of a group with examples from geometry, permutations, matrices and number sets
  • Homomorphisms and isomorphisms
  • Cyclic groups and abelian groups
  • Subgroups and Lagrange’s Theorem


  • Definitions of graphs and classes of graphs
  • Trees, Cayley’s theorem and finding minimum weight spanning trees
  • Eulerian and Hamiltonian graphs
  • The Travelling Salesman Problem
  • Connectedness and Menger’s Theorem
  • Flows in networks
  • Matchings in graphs and Hall’s Theorem
  • Stable matchings, optimal assignments and the Hungarian algorithm

Learning objectives

By the end of this module, you will have:

  • knowledge and understanding of, and the ability to use, mathematical techniques
  • knowledge and understanding of a range of results in mathematics
  • an appreciation of the need for proof in mathematics, and the ability to follow and construct mathematical arguments
  • an understanding of the importance of assumptions and an awareness of where they are used and the possible consequences of their violation
  • an appreciation of the power of generalisation and abstraction in the development of mathematical theories
  • a deeper knowledge of some particular areas of mathematics, in particular, linear algebra and group theory.