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COMPGV01 - Mathematical Methods Algorithms and Implementations

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

Code COMPGV01 (Also taught as: COMPM072)
Year MSc
Prerequisites N/A
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.


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