This course will introduce students to current research trends in an area of computational mathematics. Possible topics: data mining algorithms, multiscale and multilevel techniques, the numerical solution of PDEs, optimisation, approximation in particular of high-dimensional functions, algorithms for the solution of linear systems of equations including iterative methods.

Note: This is an HPC. It emphasises mathematical rigour and proof for a range of advanced computational mathematics topics.

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the fundamental concepts of a special topic in computational mathematics and its role in modern mathematics and applied contexts.
2. Demonstrate accurate and efficient use of specific computational mathematics techniques.
3. Demonstrate capacity for mathematical reasoning through analysing, proving and explaining concepts from computational mathematics.

4. Ability to conduct some (limited) independent research under expert supervision.

Assessment will be based on:

• Three assignments (45% in total; LO 1-4)
• Final examination (55%; LO 1-3)

36 lectures and regular tutorials.

A solid background in mathematics is expected. Typically requires MATH3320 and MATH3511 and/or MATH3512, but consultation with course coordinators is essential.