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

Simon Julier (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.

Linear Algebra via Geometry

Vectors; matrices; eigenvalues; kernel spaces; singular value decomposition; co-ordinate systems; orthogonalisation; lines; planes; rotation and translation

Probability and Estimation

Forward probability; common probability distributions; Monte Carlo sampling; moments; inverse probability; Bayes Theorem; random variables; maximum likelihood estimation

Calculus

Ordinary differential equations (complementary functions and particular integrals); partial differential equations (separation of variables)

Fourier Transforms

Calculating Fourier series and transforms; interpreting Fourier series; Fast Fourier Transforms

Basic Algorithms

Dynamic programming; sorting; tree searches

Practicals

1. Linear algebra/ probability and estimation
2. Calculus
3. Fourier transforms
4. Basic algorithms

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

The course has the following assessment components:

• Written Examination (2.5 hours, 75%)
• Coursework Section (4 pieces, 25%)

To pass this course, students must:

• Obtain an overall pass mark of 50% for all sections combined

The examination rubric is:
Choice of 3 questions from 5. All questions carry equal marks.

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

Lecture notes (S.Julier)