Module Title
Introduction to Abstract Algebra

Module Level
Level 1

Module Credits
5.00

Academic Year
2024/25

Semester
SEM2

• 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.

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.

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