WM14118 Discrete Structures for Cyber Security
Introductory description
Discrete mathematics forms the mathematical foundation of computer science and cyber security. It forms the basis of how computers work, allows us to prove system correctness and security, and underlies modern cryptography. This course introduces the discrete structures used by computers, as well as how to use them to solve problems in cyber security.
Module aims
This module aims to give students an understanding of the discrete structures used in cyber security, and how to use them to solve problems in cyber security.
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.
Numbers and sets: Basic algebra: Types of numbers and their properties. Sets and their operations, set countability and power sets.
Logic and proof: Proposition and predicates. Common proof techniques including direct proof, contrapositive, exhaustion, induction and more. Common mistakes made in proofs.
Functions and relations: Functions and their inverses. Injections, surjections and bijections. Properties of relations including (anti)symmetry, reflexivity and transitivity. Partial orderings, total orderings and equivalence relations.
Number theory: Divisibility, modular arithmetic and Fermat's little theorem. The fundamental theorem of arithmetic. The GCD and LCM, and Euclid's algorithm.
Combinatorics: The multiplication and addition principles. Permutations.
Probability: Uniform distribution. Independent and mutually exclusive events.
Graph theory: Adjacency, distance and incidence matrices. Social network theory.
Learning outcomes
By the end of the module, students should be able to:
 Use a variety of techniques to prove and disprove mathematical statements
 Recognise common mistakes made in mathematical proofs
 Analyse the probabilities of random events, and use their findings to make informed recommendations
 Understand how people form social networks from a graphtheoretic perspective
 Use numbertheoretic techniques to develop simple cryptographic systems
 Use formal verification techniques to analyse the security of simple programs
Indicative reading list
Johnsonbaugh, Richard, "Discrete mathematics", 8 Ed, Pearson Education Limited (2019)
Balakrishnan, V. K., “Schaum's Outline of Combinatorics”, McGrawHill (1995)
Karumanchi, Narasimha, “Data Structures and Algorithms Made Easy: Data Structure and
Algorithmic Puzzles”, 2 Ed, CareerMonk (2011)
View reading list on Talis Aspire
Subject specific skills
This course equips students with the foundational mathematical skills necessary in computer science and cyber security, including logic and proof, functions and their inverses, graphs, and probability, and applies these skills in a cyber context.
Transferable skills
Numeracy, logical reasoning, problem solving, written communication skills, and increased numerical confidence
Study time
Type  Required 

Lectures  18 sessions of 1 hour (10%) 
Supervised practical classes  18 sessions of 2 hours (20%) 
Private study  54 hours (30%) 
Assessment  72 hours (40%) 
Total  180 hours 
Private study description
Independent activity between workshops.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D4
Weighting  Study time  

Inclass test 1  20%  18 hours 
An inclass test covering content taught in the first half of the module. 

Inclass test 2  20%  18 hours 
An inclass test covering content taught in the second half of the module. 

Endofyear exam  60%  36 hours 
An online openbook exam applying the content in the module to a cyber security context. ~Platforms  WAS

Feedback on assessment
Students will receive a perquestion breakdown of their mark along with any specific comments on their answers, and a mark scheme for each paper will be released once all submissions are marked.
Courses
This module is Core for:

UWMAH651 Undergraduate Cyber Security
 Year 1 of H651 Cyber Security
 Year 1 of H651 Cyber Security
 Year 1 of H651 Cyber Security