# COMPM072 - Mathematical Methods Algorithms and Implementations

**This database contains 2017-18 versions of the syllabuses.** For current versions please see here.

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

Year | 4 (Masters) |

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 | Bangti Jin (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%)
- Examination rubric:
Answer THREE questions out of FIVE

All questions carry equal marks

- Coursework Section (4 pieces of individual submission, 25%)
- Coursework 1 is due in Week 3
- Coursework 2 is due in Week 6
- Coursework 3 is due in Week 9
- Coursework 4 is due start of Term 2

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.

# Resources

Reading list available via the UCL Library catalogue.