Mathematics I

Module overview

This module aims to: - Introduce the logical and mathematical foundations of computer science. - Illustrate the use of formal languages in computer science, including in algorithms and programming. - Extend students' mathematical sophistication and skills. - Present basic concepts and techniques of combinatorics, statistics and probability. - Give mathematical background necessary for other compulsory modules. - Develop the study skills necessary for students to learn new concepts of mathematics and programming (including those we do not cover in the degree). - Instill a range of useful problem solving skills.

Aims and Objectives

Learning Outcomes

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

Use the language of logic and set theory in order to make precise formal statements
Critically analyse and solve counting problems on finite, discrete structures
Calculate probabilities of events and recognise discrete probability distributions
Recognise, understand and construct rigorous mathematical proofs

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

Logical systems and the concept of formal proof
Functions and relations as fundamental structures in computer science
Elementary ideas of probability theory
Basic counting techniques and their applications to common data structures
The interplay of syntax and semantics in mathematics, logic and computer science
Principles of mathematical proof and sound logical reasoning
The language of set theory and common operations on sets, including infinite sets

Learning and Teaching

Teaching and learning methods

The content of this module is delivered through lectures, the module website, directed reading, pre-recorded materials and tutorials. Students work on their understanding through a combination of independent study, preparation for timetabled activities, tutorials, and problem classes, along with formative assessments in the form of problem sheets.

Study time
Type	Hours
Preparation for scheduled sessions	6
Follow-up work	18
Completion of assessment task	10
Lecture	36
Tutorial	12
Wider reading or practice	50
Revision	18
Total study time	150

Assessment

Assessment strategy

This module is assessed by a combination of problem sheets and a final assessment in the form of a written examination.

Summative

This is how we’ll formally assess what you have learned in this module.

Breakdown
Method	Percentage contribution
Problem Sheets	10%
Written exam	90%