Algebra Fundamentals

• Credit value: 15 credits at Level 4
• Convenor: Dan McVeagh
• Assessment: a short-problem set (20%), online quiz (10%) and two-hour examination (70%)

In this module we introduce you to key algebraic concepts, including set theory, functions and permutations. You will learn to work with sets, explore the properties of various types of mappings, and examine the theory of permutations.

Indicative syllabus

• Set Theory: subsets, power sets, complements, intersection, union and difference of two sets, Venn diagrams, partitions
• Mappings: domain, codomain, range, injective, surjective and bijective mappings, composition of mappings, invertible mappings, induced mappings and restrictions
• Permutations: composition of permutations, inverses, cycles notation, disjoint cycles, cycle decomposition, order of a permutation, transpositions, even and odd permutations

By the end of this module you will be able to:

• combine mappings and permutations
• demonstrate knowledge of the basic notation and terminology of Set Theory
• use a mathematical computer package to investigate and find solutions to the problems considered in the module.