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## ECM1707 - Probability and Discrete Mathematics (2015)

MODULE TITLE | Probability and Discrete Mathematics | CREDIT VALUE | 15 |
---|---|---|---|

MODULE CODE | ECM1707 | MODULE CONVENER | Dr Robin Chapman (Coordinator) |

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

Number of Students Taking Module (anticipated) | 260 |
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Discrete mathematics is concerned with quantities, which vary discretely, as opposed to the continuous variables you have encountered in calculus. Therefore, on this module, you will be concerned with counting rather than measuring. For example, you will learn how to enumerate permutations and combinations of objects satisfying specified conditions. This example provides a link 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. But probability also uses continuous mathematics for cases where the possible outcomes of an experiment form a continuous range. This module will provide you with the basic concepts and tools needed for the study of discrete mathematics and probability. As such, it forms an essential part of a rounded mathematical education, and in particular it is a prerequisite for the modules in the statistics stream within the mathematics syllabus.

Prerequisite module: ECM1702 and ECM1705 or equivalent

The aim of this module is to introduce you to some basic topics in discrete mathematics and to the elementary concepts of probability, including random variables and common probability distributions. In general, the module aims to provide you with some basic, essential knowledge relevant to all mathematical studies. In particular, it aims to provide a foundation for further study in statistics or stochastic processes.

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 of basic probability theory, including the ability to apply those concepts in tackling an appropriate range of problems.

**Discipline Specific Skills and Knowledge:**

2 show sufficient knowledge of fundamental mathematical concepts, manipulations and results, including relevant finite and infinite summations.

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

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

4 use learning resources appropriately;

5 exhibit self management and time management skills.

- review of set theory and standard notation;

- review of sums of standard finite and infinite series;

- counting principles;

- methods of proof;

- probability;

- random variables;

- discrete probability distributions;

- discrete bivariate and multivariate distributions;

- continuous random variables: the exponential, gamma, uniform and normal distributions, expectations and moments;

- continuous bivariate and multivariate distributions: joint, marginal and conditional distributions, conditional expectation and variance, covariance and independence;

- distributions of functions of random variables, linear combinations of random variables, the central limit theorem, approximations to the binomial and Poisson distributions; distributions derived from the normal distribution.

Scheduled Learning & Teaching Activities | 49.00 | Guided Independent Study | 101.00 | Placement / Study Abroad | 0.00 |
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Category | Hours of study time | Description |

Scheduled learning and teaching activities | 33 | Lectures |

Scheduled learning and teaching activities | 5 | Problem class |

Scheduled learning and teaching activities | 11 | Tutorials |

Guided independent study | 10 | Coursework |

Guided independent study | 91 | Guided independent study |

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

Fortnightly exercise | 10 hours | 1-4 | Tutorial |

Coursework | 20 | Written Exams | 80 | Practical Exams |
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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 | 1-4 | In accordance with CEMPS policy |

Coursework – based on questions submitted for formative assessment | 20 | 10 hours | 1-5 | Tutorial/seminar/written |

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

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

ELE – http://vle.exeter.ac.uk

Reading list for this module:

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

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

CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
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PRE-REQUISITE MODULES | ECM1702, ECM1705 |
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CO-REQUISITE MODULES |

NQF LEVEL (FHEQ) | 4 | AVAILABLE AS DISTANCE LEARNING | No |
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ORIGIN DATE | Friday 09 January 2015 | LAST REVISION DATE | Monday 12 January 2015 |

KEY WORDS SEARCH | Probability; discrete mathematics; probability distributions; continuous and discrete random variables; moment generating function. |
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