# COMP0112 Mathematical Methods, Implementations and Algorithmics

This database contains the 2018-19 versions of syllabuses.

Note: Whilst every effort is made to keep the syllabus and assessment records correct, the precise details must be checked with the lecturer(s).

 Academic session 2018-19 Module Mathematical Methods, Algorithmics and Implementations Code COMP0112 Module delivery 1819/A7P/T1/COMP0112 Postgraduate Related deliveries 1819/A7U/T1/COMP0112 Masters (MEng) Prior deliveries COMPGV01 Level Postgraduate FHEQ Level L7 FHEQ credits 15 Term/s Term 1 Module leader Jin, Bangti Contributors Jin, Bangti Module administrator Horslen, Caroline

## 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

On successful completion of the module, a student will be able to:

1. understand analytical and numerical methods for image processing, graphics and image reconstruction.

## Availability and prerequisites

This module delivery is available for selection on the below-listed programmes. The relevant programme structure will specify whether the module is core, optional, or elective.

In order to be eligible to select this module as optional or elective, where available, students must meet all prerequisite conditions to the satisfaction of the module leader. Places for students taking the module as optional or elective are limited and will be allocated according to the department’s module selection policy.

 Programmes on which available: MRes Robotics MRes Virtual Reality MSc Computer Graphics, Vision and Imaging MSc Robotics and Computation MRes Medical Physics and Biomedical Engineering Prerequisites: There are no formal prerequisites.

## 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
• Gauss-Newton
• Dynamic programming