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## ECM1416 - Computational Mathematics (2023)

MODULE TITLE | Computational Mathematics | CREDIT VALUE | 15 |
---|---|---|---|

MODULE CODE | ECM1416 | MODULE CONVENER | Dr Tinkle Chugh (Coordinator) |

DURATION: TERM | 1 | 2 | 3 |
---|---|---|---|

DURATION: WEEKS | 0 | 11 | 0 |

Number of Students Taking Module (anticipated) | 70 |
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Computer science draws from a wide range of essential mathematical techniques. This module will provide a solid foundation on the required mathematical tools and how to use them in solving computer science problems. This module will introduce linear algebra and vector spaces, statistics and probabilities and numerical optimization. In the course of this module, you will learn to apply theoretical knowledge in concrete programming tasks. This module complements previous mathematics module and is essential for all engaged in a Computer Science program.

In this module we aim to provide you with a foundation in the essential mathematical tools used in advanced computer science topics. We will teach you how to use vector and matrices, statistics and probabilities and numerical optimization methods and implement them in computer programs.

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

**Module Specific Skills and Knowledge**

2. Display competence in using these mathematical tools

**Discipline Specific Skills and Knowledge**

6. Apply mathematical techniques to computer science problems

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

8. Adapt existing mathematical knowledge to learning new methods

Introduction to vector spaces and linear algebra:

Vectors and multidimensional spaces, matrices and operations (interpolation)

Matrices and operations, products transpose, inverse and determinants (with examples of rotation matrices). Eigen decomposition, solving systems of linear equations with linear algebra.

Derivatives in vector spaces, differential equations, partial derivatives, grad and Hessian. Taylor expansion

Optimization and numerical search: Linear optimization.

Gradient descent, Newton method Numerical methods

Statistics and probabilities:

Random variables & Distributions (Normal vs uniform distribution) Conditional probabilities, independence, marginalization Expectation, variance and covariance, significance.

Bayesian inference & Markov Chains.

Scheduled Learning & Teaching Activities | 33.00 | Guided Independent Study | 117.00 | Placement / Study Abroad | 0.00 |
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Category | Hours of study time | Description |

Scheduled Learning & Teaching | 22 | Lectures |

Scheduled Learning & Teaching | 11 | Workshops |

Guided independent study | 30 | Independent work on the two assignments |

Guided independent study | 87 | Independent study |

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

Linear Algebra programming coursework | 15 hours | 3,4,6,7,8 | Individual Marksheet |

Coursework | 0 | Written Exams | 100 | Practical Exams | 0 |
---|

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

Written Exam | 80 | 1 hour - Summer Exam Period | 1,2,5,7,8 | Orally, on request |

Assignment | 20 | One assignment, 30 hours total |

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

Written exam | Written Exam (1 hour) | All | August Ref Def Period |

Assignment | Assignment |

Reassessment will be by coursework and/or written exam in the failed or deferred element only. For referred candidates, the module mark will be capped at 40%. For deferred candidates, the module mark will be uncapped.

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

###
**Basic reading:**

Reading list for this module:

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

Set | Klein, Philip N. | Coding the Matrix: Linear Algebra through Applications to Computer Science | 1st | [Library] | |||

Set | Mitrani, I. | Probabilistic Modelling | [Library] | ||||

Set | Norris, J. R. | Markov Chains | Cambridge University Press | 1998 | 978-0521633963 | [Library] | |

Set | Tenenbaum, Morris; Pollard, Harry | Ordinary differential equation : an elementary textbook for students of mathematics, engineering, and the sciences | [Library] | ||||

Set | Blyth, T. S. | Basic Linear Algebra | Springer | 2002 | [Library] |

CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
---|---|---|---|

PRE-REQUISITE MODULES | None |
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CO-REQUISITE MODULES | None |

NQF LEVEL (FHEQ) | 5 | AVAILABLE AS DISTANCE LEARNING | No |
---|---|---|---|

ORIGIN DATE | Tuesday 10 July 2018 | LAST REVISION DATE | Wednesday 08 February 2023 |

KEY WORDS SEARCH | Mathematics, statistics, probabilities, linear algebra, matrix, vectors, optimisation. |
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