COMP0112 Mathematical Methods, Implementations and Algorithmics

This database contains the 2018-19 versions of syllabuses. These are still being finalised and changes may occur before the start of the session.

Syllabuses from the 2017-18 session are available here.

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

Tickle, Charlie

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
    • Gradient Descent
    • Gauss-Newton
    • Dynamic programming

 An indicative reading list is available via http://readinglists.ucl.ac.uk/departments/comps_eng.html.

Delivery

The module is delivered through a combination of lectures, tutorials, and courseworks.

Assessment

This module delivery is assessed as below:

#

Title

Weight (%)

Notes

1

Written examination (2hrs 30mins)

75

LSA exam

2

Coursework

8

Will be assessed in LSA in the same format.

3

Coursework

8

Will be assessed in LSA in the same format.

4

Coursework

9

Will be assessed in LSA in the same format.

In order to pass this module delivery, students must achieve an overall weighted module mark of 50%.