# FOUNDATIONS OF COMPUTING - 2019/0

Module code: COM1026

## Module Overview

The course introduces the core concepts of discrete mathematics, including truth tables, propositional and predicate logic, set theory, number theory, relations, functions and mathematical proof. These concepts are useful throughout the programme.

### Module provider

Computer Science

DONGOL Brijesh (Computer Sci)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 113

Lecture Hours: 24

Tutorial Hours: 12

Laboratory Hours: 8

Semester 1

None

## Module content

Indicative content includes:

• Logic:

• Truth tables

• Propositional logic

• Quantifiers & Predicate logic

• Set theory:

• Sets: definition, union, intersection, power set, set comprehension

• Cartesian products, relations

• Elements of number theory:

• Natural numbers

• Euclidean algorithm

• Modular arithmetics

• Functions:

• Surjective, injective and bijective functions

• Periodic, logarithmic, exponential and polynomial functions

• Introduction to a programming and mathematical modelling environment, in which the following can be performed:

• Numerical calculations

• Plot graphs

• Simple programs to solve numerical problems (e.g., find zeros of a polynomial)

• Proof Methods

• Direct proofs

• Proof by induction

## Assessment pattern

Assessment type Unit of assessment Weighting
Practical based assessment Lab-Test I 20
Practical based assessment Lab-Test II 20
Examination EXAMINATION - 2 HOURS 60

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate that they have achieved the module learning outcomes.

Thus, the summative assessment for this module consists of:

·         An individual lab test on truth tables, propositional and predicate logic. This addresses LO1 and LO2.

·         An individual lab test on sets, relations,  nb. theory, functions. This addresses LO1, LO3, LO4 and LO5.

·         A 2h unseen examination on the whole course content. This addresses LO1, LO2, LO3, LO4, LO5 and LO6.

The individual lab-tests will be around week 5 and 10 respectively. The exam takes place at the end of the semester during the exam period.

Formative assessment and feedback

PollEverywhere is used  in the lectures with each lecture consisting of a number of slides explaining the theory followed by a number of slides gauging the students’ understanding. The answers are discussed when necessary, e.g., if a high proportion (more than 25%) of the students got the answer wrong.

Individual formative feedback will also be given during the lab sessions and as part of the summative assessment.

## Module aims

• This module aims to introduce students to some of the key concepts of logic, set theory, mathematical functions and proof methods in order to highlight the importance and power of abstraction within computer science. Students will also be introduced to the a programming environment capable of mathematical modelling (e.g., SAGE) to perform calculations, plot graphs, and write simple programs

## Learning outcomes

 Attributes Developed 001 Recognise the importance and role of logic in computing C 002 Understand and manipulate propositions and predicates KCT 003 Understand and manipulate set theoretic expressions including relations and functional notation KCT 004 Understand mathematical functions KPT 005 Recognise, understand and construct rigorous mathematical proofs CT 006 Use a programming environment to perform calculations, plot graphs, and write simple programs K 007 Understand elements of number theory K

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to:

• Help students recognise the importance and role of logic in computing

• Provide opportunities to manipulate propositions, predicates and set theoretic expressions including relations and functional notation

• Help students to assimilate the concept of formal proof

• Enable students to extract information about a function by sketching its graph

• Highlight the links between logic, abstraction, software specifications and programming

• Practise to perform calculations, plot graphs, and write simple programs using a mathematical modelling and/or programming environment

The learning and teaching methods include:

• Lectures (11 weeks at 2h) using PollEverywhere handsets to gauge the students’ understanding

• Tutorials (11 weeks at 1h)

• Laboratory session (4 weeks at 2h) using a mathematical modelling and/or programming environment.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.