SHE Level 1
SCQF Credit Points 20.00
ECTS Credit Points 10.00
Module Code M1I322951
Module Leader Salma Mohamed
School School of Computing, Engineering and Built Environment
Subject Cyber Security and Networks
  • A (September start)-B (January start)

Summary of Content

This module introduces elements of discrete mathematics underpinning the study of both hardware and software systems. The techniques developed in this module will be practically based with an emphasis on problem solving. The material will be accessible to students with a limited mathematical background.


Solving equations: - systems of linear equation; - quadratics; - applying logarithms; - the standard functions; - the graphical method for finding roots; - interpreting equations as mathematical models. Matrices and Vectors: -Definitions, addition, multiplication, matrix inversion; -Modelling: error detection, Hill ciphers, network connectivity. Logic: -709 -Sets: union, intersection, complement, Cartesian products, Venn diagrams; -Relations: order relations, introduction to equivalence relations, composition, inversion; functions. - logic operators: and, or, not, implication and equivalence - truth tables; - examples of proof; - introduction to Formal System Specification Graphs: -Definition, Diagrams, Adjacency and Incidence Matrix, vertex degree, degree sequence, Handshaking Lemma; -Types: Bipartite, Cubic, Complete, Petersen etc.; -Paths, Cycles (including Euler and Hamilton cycles), Connectedness; -Applications: Petri Nets; Gray's codes, Compatibility graphs -709 Trees and Digraphs: - Trees: Definition, Binary, Breadth first search, Depth first search, Stacks; - Directed graphs: Definition, Representations, acyclic and weighted (networks); - In-degree, Out-degree, Handshaking Lemma, Cycles; - weighted digraphs (Networks); - Applications: tournaments, max-flow min-cut. -709 Finite State Automata: - definition; - modelling states and transitions using a digraph; - pattern recognition. Number Modular Arithmetic: the concept and basic operations, applications to cryptography. Number systems: binary, decimal, hexadecimal and changing between bases Bitwise logical operations on binary numbers

Learning Outcomes

On completion of this module, students should be able to:Use graphs and digraphs to model and solve problems;Apply simple finite state machines and simple algorithms, including recursion;Solve simple equations and carry out basic algebraic operations on matrices and vectors, simple mathematical transformations as used in elementary Cryptography;Calculate in a range of number systems associated with computer applications;Represent statements using logical operators and use them in deductive arguments and work with finite relations.

Teaching / Learning Strategy

Lectures will deliver the module syllabus. Tutorials will be used for developing basic mathematical manipulation skills, and for exploring applications (which can be expected to continue into private study). Directed study will require the undertaking of specified tutorial material; the completion or extension of the applications covered in tutorials; and the opportunity for the student to dig deeper through identified 'advanced' topics (either supplied, or obtainable from identified sources such as the World Wide Web) -'advanced' topics are not assessable. Feedback will be supplied through the marking of the class tests and their associated mocks; in tutorials - through discussion with the tutor; and through supplied solutions and commentary to SAQs.

Indicative Reading

Krantz, S., Discrete Mathematics DeMYSTiFied, McGraw-Hill Professional; 1st edition (2008); ISBN-13: 978-0071549486 Wilson R. Introduction to Graph theory R Wilson Prentice Hall, 5 th edition (2010); ISBN -13: 978-0273728894 R. Huettenmueller, College Algebra DeMYSTiFied McGraw Hill Professional 2ed. (2014); ISBN-13: 978-0071815840

Transferrable Skills

D1 Specialist knowledge and application D2 Critical thinking and problem solving D5 Numeracy D8 Self confidence, self discipline & self reliance (independent working) D12 Appreciating and desiring the need for continuing professional development D15 Ability to prioritise tasks and time management

Module Structure

Activity Total Hours
Tutorials (FT) 48.00
Assessment (FT) 18.00
Lectures (FT) 36.00
Independent Learning (FT) 98.00

Assessment Methods

Component Duration Weighting Threshold Description
Exam (Exams Office) 2.00 60.00 35% Exam (Exams Office)
Exam (School) 0.75 40.00 35% Class test