| STUDENTS
> Mathematical Methods Algorithms and Implementations
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Mathematical Methods Algorithms and Implementations
Note:
Whilst every effort is made to keep the syllabus and assessment records correct
for this course, the precise details must be checked with the lecturer(s).
| Code: | M072
(Also taught as: GV01)
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| 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%)
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| 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.
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| Learning Outcomes: | To understand analytical and numerical methods for image processing, graphics and image reconstruction.
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Content:
| 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 |
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, 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. N.B. This course is examined in the pre-Easter exam session.Resources:
Numerical Recipes in C, W.H.Press et.al., Cambridge University Press
Lecture notes (S.Julier)
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