WM181-15 Discrete Mathematics
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. Minimum spanning trees.
Learning outcomes
By the end of the module, students should be able to:
- Reason mathematically about the discrete structures used in cyber security
- Use a variety of techniques to prove and disprove mathematical statements
- Recognise common mistakes made in mathematical proofs
- Apply a variety of proof techniques to solve cyber security problems
Indicative reading list
Johnsonbaugh, R., 2019. Discrete Mathematics, 8th Edition. Pearson Education.
Balakrishnan, V. K., 1995. Schaum's Outline of Combinatorics. McGraw-Hill.
Karumanchi, N., 2011. Data Structures and Algorithms Made Easy: Data Structure and Algorithmic Puzzles, 2 Ed. CareerMonk.
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 (12%) |
| Tutorials | 18 sessions of 1 hour (12%) |
| Private study | 54 hours (36%) |
| Assessment | 60 hours (40%) |
| Total | 150 hours |
Private study description
Time spent doing the weekly example sheets and revising the course content
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 D
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| In-class test 1 | 20% | 15 hours | No |
|
An in-class test covering content taught in the first half of the module. |
|||
| In-class test 2 | 20% | 15 hours | No |
|
An in-class test covering content taught in the second half of the module. |
|||
| End-of-module exam | 60% | 30 hours | No |
|
An online open-book exam covering all content in the syllabus. The exam may also apply the material covered to a cyber security scenario. ~Platforms - WAS
|
|||
Assessment group R
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Reassessment exam | 100% | No | |
|
An online open-book exam covering all content in the syllabus. The exam may also apply the material covered to a cyber security scenario. ~Platforms - WAS
|
|||
Feedback on assessment
Students will receive a per-question 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:
-
UWMA-H651 Undergraduate Cyber Security
- Year 1 of H651 Cyber Security
- Year 1 of H651 Cyber Security
- Year 1 of H651 Cyber Security