Theory 1: Mathematical Foundations of Computer Science - COM00013C

Department: Computer Science
Credit value: 20 credits
Credit level: C
Academic year of delivery: 2025-26
- See module specification for other years: 2022-23 2023-24 2024-25

Module summary

Mathematical Foundations of Computer Science

Module will run

Occurrence	Teaching period
A	Semester 1 2025-26

Module aims

Students will be introduced to the key discrete mathematics concepts that are the foundation of computer science. Seven topics are covered as follows: i) counting (combinatorics), ii) discrete probability, iii) graphs, iv) propositional and predicate logic, v) proofs and sets, vi) relations on sets, and vii) relations on a single set. After studying the module, students will be able to apply the learnt concepts, theories and formulae in real-world examples of computational problems.

Module learning outcomes

T101 Define, read and apply mathematical notations for the purpose of describing mathematical concepts from across discrete mathematics.

T102 Select appropriate techniques to prove properties related to discrete mathematics concepts.

T103 Understand how to construct sets of elements with certain properties and determine their cardinality using counting formulae from combinatorics.

T104 Understand and apply basic set theory, including formally defining set relations and operations.

T105 Describe and use the basic concepts of discrete probability to describe events, with an understanding of joint, conditional and marginal probabilities, Bayes’ theorem, expectation, covariance and correlation.

T106 Formally define and illustrate by example graphs of different graph classes, such as simple, undirected, directed, weighted, directed acyclic, connected, disconnected and trees - with an understanding of how they may be used in real-world computational problems.

T107 Apply a variety of techniques to identify whether logical expressions are true or false, valid or invalid or equivalent to one another, and be able to apply logical statements to describe real-world logical problems.

Indicative assessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	100

Special assessment rules

None

Indicative reassessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	100

Module feedback

Feedback is provided through work in practical sessions, and after the final assessment as per normal University guidelines.

Indicative reading

** Dean N., The Essence of Discrete Mathematics, Prentice Hall, 1997

** Haggarty R., Discrete Mathematics for Computing, Addison Wesley, 2002

** Truss J., Discrete Mathematics for Computer Scientists, Addison Wesley, 1999

** Gordon H., Discrete Probability, Springer, 1997

* Solow D., How to Read and Do Proofs, Wiley, 2005

T101	Define, read and apply mathematical notations for the purpose of describing mathematical concepts from across discrete mathematics.
T102	Select appropriate techniques to prove properties related to discrete mathematics concepts.
T103	Understand how to construct sets of elements with certain properties and determine their cardinality using counting formulae from combinatorics.
T104	Understand and apply basic set theory, including formally defining set relations and operations.
T105	Describe and use the basic concepts of discrete probability to describe events, with an understanding of joint, conditional and marginal probabilities, Bayes’ theorem, expectation, covariance and correlation.
T106	Formally define and illustrate by example graphs of different graph classes, such as simple, undirected, directed, weighted, directed acyclic, connected, disconnected and trees - with an understanding of how they may be used in real-world computational problems.
T107	Apply a variety of techniques to identify whether logical expressions are true or false, valid or invalid or equivalent to one another, and be able to apply logical statements to describe real-world logical problems.