Module Catalogues

Introduction to Abstract Algebra

Module Title Introduction to Abstract Algebra
Module Level Level 1
Module Credits 5.00

Aims and Fit of Module

• To introduce some commonly used mathematical structures.
• To provide knowledge about basic results in arithmetic and group theory.
• To help with the transition from concrete to abstract mathematical thinking.
• To present applications, such as data encryption, that rely heavily on abstract mathematics.
• To demonstrate how algebraic structures can be used to unify diverse mathematical topics.
• To develop the students’ skills in reading and writing mathematical proofs.
• To enrich the mathematical vocabulary of the students.

Learning outcomes

A Apply the Euclidean Algorithm to integers or polynomials.
B Work with fundamental mathematical concepts, such as relations and permutations.
C Use modular arithmetic to solve problems related to cryptography and coding theory.
D Recognise common algebraic structures, such as groups, rings or fields.
E Find the image and kernel of a homomorphism and show (in simple cases) when two structures are isomorphic.
F Apply basic results in group theory, such as Lagrange’s Theorem.

Method of teaching and learning

This module will be delivered by a combination of formal lectures and tutorials.