The University of Southampton
Courses

# COMP1217 Foundations of IT

## Module Overview

The module is about equipping students with the tools and techniques required to describe system or algorithm formally. This will allow the students to apply these techniques and skills in future modules.

### Aims and Objectives

#### Module Aims

This module aims to equip students with the tools and techniques required to formally describe systems or algorithms.

#### Learning Outcomes

##### Knowledge and Understanding

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

• Define the language of set theory and common operations on sets
• Describe the interplay of syntax and semantics in mathematics, logic and computer science
##### Subject Specific Practical 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
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Describe functions and relations as fundamental structures in computer science
• Describe the logical systems and the concept of formal proof
• Recognise, understand and construct rigorous mathematical proofs

### Syllabus

Mathematical proof - Proof by case analysis, proof by contradiction. - Induction and recursion. - Universal properties. Sets, functions and relations - Basic notation, representations and examples. Membership and subsets. - Operations on sets: union, sum, intersection and complement. - Pairs, tuples, cartesian products, powersets. - Relations, equivalence relations and partial orders. - Functions: injections, surjections, bijections. - Cardinality, infinite sets. Logic - Propositional logic. Logical connectives. - Syntax and semantics. - Natural deduction, soundness and completeness. - Quantifiers and predicate logic.

### Learning and Teaching

TypeHours
Revision10
Lecture24
Follow-up work12
Tutorial12
Preparation for scheduled sessions12
Total study time150

Schaum's Outline of Discrete Mathematics.

Textbook. The subject matter of this module is normally found in the first few chapters in any book on Discrete mathematics, and there are copious text books in the library on the subject.

### Assessment

#### Summative

MethodPercentage contribution
Exam  (2 hours) 80%
Tutorial Exam 20%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External