# COMPM072 - Mathematical Methods Algorithms and Implementations

This database contains 2017-18 versions of the syllabuses. For current versions please see here.

Code COMPM072 (Also taught as COMPGV01) 4 (Masters) 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. 1 Bangti Jin (100%) 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. 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
• Obtain a minimum mark of 40% in each component worth ≥ 30% of the module as a whole.

# Resources

Reading list available via the UCL Library catalogue.