Module Content

Set Theory: Operations, relations, partitions, functions, countable and uncountable. 

Logic: Propositional logic, truth tables, predicates and quantifiers, inference, proof. 

Boolean Algebra: Boolean Functions, representation, logic gates, circuits, Karnaugh Maps. 

Graphs: Graph models, representation, connectivity, Euler and Hamilton paths, shortest path, planar graphs, colouring. 

Trees: Types of tree applications, tree traversal, spanning trees, minimal spanning trees. 

Counting: Pigeonhole principle, generalizations of permutations and combinations, inclusion and exclusion principle. 

Number representation: Binary, octal, and hexadecimal number representation and conversions between different number representations. 

Teaching Methods

The module will be delivered on campus, with weekly lecture and tutorial sessions. 

Printed notes will be given ahead of time for each section of the course, to support and enhance students’ preparation and engagement during class sessions. Lectures will follow the notes, with discussions of the main theoretical topics, and study of examples of the applications of the theory. There will be a strong emphasis on student involvement in discussions in lectures, to encourage a more active approach to learning the material, and to allow the delivery to be tailored to build on the students’ current understanding. 

Regular formative work in tutorial sessions will allow students to internalise the mathematical ideas and methods developed in the lectures, and lead to the development of problem-solving skills. This formative work will also feed back into the delivery of lectures and tutorials.

Assessment Methods

This module is assessed through a Portfolio and an examination.