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# Theory 1: Mathematical Foundations of Computer Science - COM00013C

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• Department: Computer Science
• Module co-ordinator: Prof. Nick Pears
• Credit value: 20 credits
• Credit level: C
• Academic year of delivery: 2023-24

## Module summary

Mathematical Foundations of Computer Science

## Module will run

Occurrence Teaching cycle
A Semester 1 2023-24

## 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.

## Assessment

Task Length % of module mark
Online Exam -less than 24hrs (Centrally scheduled)
Theory 1: Mathematical Foundations of Computer Science (THE1)
4 hours 100

None

### Reassessment

Task Length % of module mark
Online Exam -less than 24hrs (Centrally scheduled)
Theory 1: Mathematical Foundations of Computer Science (THE1)
4 hours 100

## Module feedback

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

** 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

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.