Software Engineering Mathematics

An essential advantage of a mathematical specification is the ability to reason about the objects it contains, and thus about the system it describes. This course is an introduction to specification using mathematics. It shows how we may reason about the objects in a specification with varying degrees of formality.

Frequency

This course normally runs twice a year.

Course dates

Objectives

At the end of the course, students will understand the mathematics required for software engineering. They will be able to reason about the mathematical objects that appear in a specification. They will also gain an appreciation for varying degrees of rigour and formality, choosing an appropriate level of detail or elaboration.

Contents

Propositional logic:

propositions; logical connectives; deductive reasoning; hypothetical reasoning

Predicate logic:

quantification; substitution; scope of variables; generalisation; specialisation

Equality:

definite description; the one-point rule; uniqueness and quantity

Sets:

membership; extension; comprehension; power sets; Cartesian products; types

Definitions:

basic types; declarations; abbreviations; axioms; generics; consistency

Relations:

domains and ranges; projections; inverses; compositions; iteration; closure

Functions:

partial functions; injections; surjections; lambda notation; overriding; enumerations

Sequences:

order and multiplicity; sequence operators; sequences as functions; structural induction; bags

Free types:

constants and constructor functions; embedding; closure; induction principles

Requirements

Although no previous experience is required, a positive attitude towards formal, mathematical notation would be an advantage. If you have any doubts as to your readiness, please feel free to contact the Programme Director before registering for the course.