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. 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 Recognize and work with common algebraic structures (such as groups, subgroups, and homomorphisms) and constructions (such as the Cartesian product of groups). E Find the image and kernel of a homomorphism and show (in simple cases) whether 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.