# CS137 Discrete Mathematics and its Applications 2

# CS137-12 Discrete Mathematics & its Applications 2

##### Introductory description

This module is designed to introduce students to language and methods of the area of Discrete Mathematics.

##### Module aims

The focus of the module is on basic mathematical concepts in discrete maths and on applications of discrete mathematics in algorithms and data structures. One of the aims will be to show students how discrete mathematics can be used in modem computer science (with the focus on algorithmic applications).

##### 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.

Introduction to combinatorics: counting techniques, pigeonhole principle, inclusion-exclusion.

Recurrence relations, solving recurrences using generating functions.

Master Theorem for solving recurrences.

Graphs. Basic graph algorithms. Trees. Applications of graphs.

Applications of linear algebra and matrix algebra in algorithms (e.g., in web searching).

Algorithmic applications of random processes and Markov chains, for example, cover time in graphs and card shuffling.

Partitions, enumerations with symmetries.

##### Learning outcomes

By the end of the module, students should be able to:

- - Understand the notion of mathematical thinking, mathematical proofs, and algorithmic thinking, and be able to apply them in problem solving.
- - Understand the basics of discrete probability and number theory, and be able to apply the methods from these subjects in problem solving.
- - Use effectively algebraic techniques to analyse basic discrete structures and algorithms.
- - Understand asymptotic notation, its significance, and be able to use it to analyse asymptotic performance for some basic algorithmic examples.
- - Understand some basic properties of graphs and related discrete structures, and be able to relate these to practical examples.

##### Indicative reading list

Please see Talis Aspire link for most up to date list.

View reading list on Talis Aspire

##### Subject specific skills

Basic knowledge of graph theory and its applications in algorithms

Basic knowledge of discrete probability and its applications in algorithms

Understanding and using asymptotic notations in design and analysis of algorithms

##### Transferable skills

Communication - Reading and writing mathematical proofs

Critical thinking - problem solving

Technical - Technological competence and staying current with knowledge

## Study time

Type | Required |
---|---|

Lectures | 30 sessions of 1 hour (25%) |

Seminars | 9 sessions of 1 hour (8%) |

Private study | 81 hours (68%) |

Total | 120 hours |

##### Private study description

Revision of lectures

Going through the problems solved during seminar sessions

Solving past exam papers

## Costs

No further costs have been identified for this module.

You do not need to pass all assessment components to pass the module.

Students can register for this module without taking any assessment.

##### Assessment group D1

Weighting | Study time | |
---|---|---|

Coursework | 20% | |

CS137 exam | 80% | |

~Platforms - AEP |

##### Assessment group R

Weighting | Study time | |
---|---|---|

CS137 resit exam | 100% | |

CS137 resit exam ~Platforms - AEP |

##### Feedback on assessment

Marked scripts available on students' request

## Courses

This module is Core for:

- Year 1 of UCSA-G4G1 Undergraduate Discrete Mathematics
- Year 1 of UCSA-G4G3 Undergraduate Discrete Mathematics

This module is Option list B for:

- Year 1 of UMAA-G100 Undergraduate Mathematics (BSc)
- Year 1 of UMAA-G103 Undergraduate Mathematics (MMath)
- Year 1 of UMAA-G106 Undergraduate Mathematics (MMath) with Study in Europe
- Year 1 of UMAA-G1NC Undergraduate Mathematics and Business Studies
- Year 1 of UMAA-G1N2 Undergraduate Mathematics and Business Studies (with Intercalated Year)
- Year 1 of UMAA-GL11 Undergraduate Mathematics and Economics
- Year 1 of UECA-GL12 Undergraduate Mathematics and Economics (with Intercalated Year)
- Year 1 of UMAA-GV18 Undergraduate Mathematics and Philosophy with Intercalated Year
- Year 1 of UMAA-G101 Undergraduate Mathematics with Intercalated Year