Theory 1: Mathematical Foundations of Computer Science - COM00013C
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) | 100.0 |
Special assessment rules
None
Indicative reassessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 100.0 |
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