# COMPM072 - Mathematical Methods Algorithms and Implementations

**This database contains 2016-17 versions of the syllabuses.** For current versions please see here.

Code | COMPM072 (Also taught as: COMPGV01) |
---|---|

Year | 4 |

Prerequisites | Successful completion of years 1 and 2 of the Computer Science programme, including the mathematics course/option, or core courses in computer science and mathematics. |

Term | 1 |

Taught By | Dan Stoyanov (100%) |

Aims | To provide a rigorous mathematical approach: in particular to define standard notations for consistent usage in other modules. To present relevant theories and results. To develop algorithmic approach from mathematical formulation through to hardware implications. |

Learning Outcomes | To understand analytical and numerical methods for image processing, graphics and image reconstruction. |

# Content:

**Linear Algebra via Geometry**

Vectors and matrices; Eigenvalues; Kernel spaces; Singular value decomposition; Coordinate systems, lines, planes, rotation and translation.**Probability and Estimation**

Forward probability; Common probability distributions; Monte Carlo sampling; Moments; Inverse probability; Bayes Theorem; Maximum likelihood estimation.**Calculus**

Ordinary differential equations (complementary functions and particular integrals); Partial differential equations (separation of variables);Vector and matrix calculus.**Fourier Transforms**

Calculating Fourier series and transforms; Discrete and Fast Fourier Transforms.**Basic Algorithms and Optimization**

Dynamic programming; Gradient Descent; Gauss-Newton.

# Method of Instruction:

Lecture presentations with associated class coursework and laboratory sessions. There are 4 pieces of coursework, all equally weighted.

# Assessment:

The course has the following assessment components:

- Written Examination (2.5 hours, 75%)
- Coursework Section (4 pieces of individual submission, 25%)

To pass this course, students must:

- Obtain an overall pass mark of 50% for all sections combined
- Obtain a minimum mark of 40% in each component worth ≥ 30% of the module as a whole.

Note that Coursework 1 is due in Week 3, Coursework 2 is due in Week 6, Coursework 3 is due in Week 9 and Coursework 4 is due start of Term 2.

The examination rubric is: answer THREE questions out of FIVE. All questions carry equal marks.

# Resources:

Numerical Recipes in C, W.H.Press et.al., Cambridge University Press.