COMPM072 - Mathematical Methods Algorithms and Implementations
This database contains 2016-17 versions of the syllabuses. For current versions please see here.
|Code||COMPM072 (Also taught as: COMPGV01)|
|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.|
|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.|
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.
Ordinary differential equations (complementary functions and particular integrals); Partial differential equations (separation of variables);Vector and matrix calculus.
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.
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
- Obtain a minimum mark of 40% in each component worth ≥ 30% of the module as a whole.
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.
Numerical Recipes in C, W.H.Press et.al., Cambridge University Press.