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## ECM1415 - Discrete Mathematics for Computer Science (2015)

MODULE TITLE | Discrete Mathematics for Computer Science | CREDIT VALUE | 15 |
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MODULE CODE | ECM1415 | MODULE CONVENER | Prof Mitchell Berger (Coordinator) |

DURATION: TERM | 1 | 2 | 3 |
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DURATION: WEEKS | 11 | 0 | 0 |

Number of Students Taking Module (anticipated) | 73 |
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Discrete mathematics is concerned with quantities which vary discretely, and because of that has an important role in computer science, in which discrete structures such as sets, graphs, lists, and trees play a fundamental role, and the underlying forms of reasoning are based on propositional and predicate logic rather than on calculus and mathematical analysis. The emphasis Is on counting rather than measuring, e.g. enumerating permutations and combinations of objects satisfying specified conditions, and this links directly to probability theory, where we determine the probability of each outcome of a combinatorial experiment by expressing the number of different ways that outcome can be realised as a fraction of all the possibilities. This module will provide a thorough grounding in the fundamental structures and methods of discrete mathematics that are required for computer science.

The aim of this module is to provide you with the basic concepts and tools developed in discrete mathematics disciplines but needed for the study of computer science. As such, it forms an essential part of a rounded education of a computer scientist or computer expert whose work includes computer-based data manipulations.

On successful completion of this module, **you should be able to**:

**Module Specific Skills and Knowledge**:

1 demonstrate a sound understanding of selected essential topics in discrete mathematics and their importance in computer science disciplines.

**Discipline Specific Skills and Knowledge**:

2 reveal sufficient knowledge of fundamental discrete mathematics concepts.

**Personal and Key Transferable / Employment Skills and Knowledge**:

3 show independent learning skills;

4 reason using abstract ideas, formulate and solve problems and communicate reasoning and solutions effectively in writing;

5 use learning resources appropriately.

- number systems and representations;

- set theory and standard notation: Intersection, union, complement, power set, Cartesian product;

- functions and relations;

- methods of proof;

- propositional and first-order logic;

- sums of standard finite and infinite series;

- counting principles: the addition principle, the multiplication principle, permutations, combinations; some counting problems;

- probability: definitions of probability, the axiomatic approach, conditional probability, independence;

- random variables: discrete and continuous probability distributions, marginal and conditional distributions, conditional expectation and variance, covariance and independence;

- graph theory: basic concepts, definitions and results. Trees, balanced trees.

Scheduled Learning & Teaching Activities | 32.00 | Guided Independent Study | 118.00 | Placement / Study Abroad | 0.00 |
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Category | Hours of study time | Description |

Scheduled learning and teaching | 22 | Lectures |

Scheduled learning and teaching | 10 | Problem classes |

Guided independent study | 20 | Coursework |

Guided independent study | 98 | Independent study |

Form of Assessment | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|

Problem sets | All | Verbal and written | |

Coursework | 20 | Written Exams | 80 | Practical Exams | 0 |
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Form of Assessment | % of Credit | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|---|

Written exam – Closed book | 80% | 2 hours | All | Model answers supplied on request |

Coursework | 20% | 20 hours | All | Written feedback |

Original Form of Assessment | Form of Re-assessment | ILOs Re-assessed | Time Scale for Re-assessment |
---|---|---|---|

All above | Written exam (100%) | All | August Ref/Def period |

Referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

information that you are expected to consult. Further guidance will be provided by the Module Convener

Reading list for this module:

Type | Author | Title | Edition | Publisher | Year | ISBN | Search |
---|---|---|---|---|---|---|---|

Set | McColl, J | Probability | Arnold | 1995 | 0000340614269 | [Library] | |

Set | McGregor C., Nimmo J. & Stothers W. | Fundamentals of University Mathematics | 2nd | Horwood, Chichester | 2000 | 000-1-898-56310-1 | [Library] |

Set | Biggs N.L. | Discrete Mathematics | Oxford University Press | 1989 | 000-0-198-53427-2 | [Library] | |

Extended | James, G | Modern Engineering Mathematics | 4th with MyMathLab | Addison Wesley | 2010 | 027373413x | [Library] |

CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
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PRE-REQUISITE MODULES | None |
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CO-REQUISITE MODULES | None |

NQF LEVEL (FHEQ) | L4 | AVAILABLE AS DISTANCE LEARNING | No |
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ORIGIN DATE | Friday 09 January 2015 | LAST REVISION DATE | Friday 09 January 2015 |

KEY WORDS SEARCH | Discrete mathematics; computer science; set theory; functions and relations; graph theory. |
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