Introductory description

This module will primarily help students to understand and be able to use basic mathematical terminology, which they will then use to understand the format and importance of formal definitions of proofs. In addition, they will cover the basics of the axiomatic method, logic, sets, relations, and functions, as well as some of the fundamental theorems in these areas, which they will then make use of to solve related problems.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The module will comprise of 6 topics, namely:

• The role of mathematics in theoretical computer science
• The axiomatic method, including: basic concepts (axioms, definitions, theorems, proofs), finite and infinite sets, and number systems, natural numbers, and induction
• Logic, including: formal reasoning, propositions, truth values, Boolean operators, laws of propositional logic, predicates and quantifiers, and the laws of predicate logic
• Sets, including: sets and predicates, operations on sets, and the laws of set operations
• Relations, including: composition and inverse, properties, and equivalence relations
• Functions, including: the properties of functions, equinumerous sets, and countable and uncountable sets

Learning outcomes

By the end of the module, students should be able to:

• Understand the importance of mathematics in Computer Science and the role of discrete mathematics in the theory underpinning the discipline.
• Understand and use basic mathematical terminology.
• Understand the role of formal definitions and proof and be able to apply them in problem solving.
• Understand and apply basic concepts of finite and infinite sets, number systems, natural numbers, and induction.
• Understand and apply the basics of propositional and predicate logic.
• Understand and apply the basics of elementary set theory.
• Understand and apply the basics of mathematical relations and functions.

Indicative reading list

Ross and Wright, "Discrete Mathematics (5/e)", Printice Hall (2003)
Rosen, "Discrete Mathematics and its Applications (5/e)", McGraw Hill (2003)
Truss, "Discrete Mathematics for Computer Scientists (2/e)", Addison Wesley (1999)

Subject specific skills

• Able to manage data effectively and undertake data analysis
• Applies analytical and critical thinking skills to Technology Solutions development and to systematically analyse and apply structured problem solving techniques to complex systems and situations

Transferable skills

• Have demonstrated that they have mastered basic business disciplines, ethics and courtesies, demonstrating timeliness and focus when faced with distractions and the ability to complete tasks to a deadline with high quality.
• Flexible attitude
• Ability to perform under pressure
• A thorough approach to work
• Logical thinking and creative approach to problem solving