COMPGV01 - Mathematical Methods Algorithms and Implementations

This database contains the 2017-18 versions of syllabuses. Syllabuses from the 2016-17 session are available here.

Note: Whilst every effort is made to keep the syllabus and assessment records correct, the precise details must be checked with the lecturer(s).

Code COMPGV01 (Also taught as COMPM072)
Year MSc
Prerequisites N/A
Term 1
Taught By Bangti Jin (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%)
    • Examination rubric:

      Answer THREE questions out of FIVE
      All questions carry equal marks

  • Coursework Section (4 pieces of individual submission, 25%)
    • Coursework 1 is due in Week 3
    • Coursework 2 is due in Week 6
    • Coursework 3 is due in Week 9
    • Coursework 4 is due start of Term 2

To pass this course, students must:

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

Resources

Reading list available via the UCL Library catalogue.