Introductory description

This module introduces some of the fundamental mathematical ideas
that are used in the design and analysis of computer systems and software.
The module makes you familiar with basic concepts and notation, helps you
to develop a good understanding of mathematical proofs, and enables you
to apply mathematics to solving computer science problems. The focus in
CS130 is on discrete (i.e. not continuous) mathematics and probability.

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 axiomatic method. Basic concepts, axioms, definitions, theorems. Finite and infinite sets. Natural numbers, induction.
• Logic. Statements, truth values, Boolean operators, laws of propositional logic. Predicates, quantifiers, laws of predicate logic.
• Sets. Connection between sets and predicates. Operations on sets. Laws of set operations.
• Relations. Relation composition and inverse. Properties of relations. Equivalence relations, equivalence classes, quotient sets. Partial orders..
• Functions. Properties of functions. Equinumerous sets. Countable and uncountable sets.
• Graphs. Graph isomorphism. Graph connectivity. Eulerian and Hamiltonian graphs.
• Mathematical induction
• Basic probability

Learning outcomes

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

• -Understand and use basic mathematical terminology.
• - Understand the role of formal definitions and proofs and be able to apply them in problem solving.
• - Understand the basics of propositional and predicate logic.
• - Understand the basics of elementary set theory.
• - Understand the basics of mathematical relations and functions.
• - Understand the basics of graph theory.

Indicative reading list

Please see Talis Aspire link for most up to date list.

View reading list on Talis Aspire

Subject specific skills

Problem Solving
Understanding Abstract Concepts

Transferable skills

Critical Thinking
Creativity