Introductory description

N/A.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

• algorithmic structures (iteration, recursion, memoization) and computational complexity
• data structures (linked lists, stacks and queues, binary indexed trees)
• sorting and search algorithms
• Fast Fourier Transform and its applications
• Topics in numerical linear algebra: solving linear systems, conjugate gradient algorithm, singular value decomposition
• unconstrained continuous optimisation: multivariate minimisation, Nelder-Mead algorithm, automatic differentiation, gradient descent
• constrained continuous optimisation: method of Lagrange multipliers, linear programming
• discrete optimisation: Dijkstra's algorithm, dynamic programming, combinatorial optimisation

Learning outcomes

By the end of the module, students should be able to:

• Students should be able to demonstrate a deep fundamental understanding of the most important computational algorithms used for advanced data analysis, mathematical modelling and optimisation of complex systems. They should be able to apply both discrete and continuous approaches depending on the requirements of a particular problem. They should understand algorithmic structures like iteration, recursion and memorization and be able to apply them.
• Mathematical manipulation and computational problem-solving techniques.
• Identify the most appropriate approach for computational solution of a mathematical problem and understand problems that can arise such as numerical error, poor conditioning or instability. Appreciate the computational complexity of an algorithm and the practical constraints it imposes on problem solving. Read and understand relevant research papers.
• Write efficient Julia code for computational solution of analysis and optimisation problems, select appropriate data structures and algorithms, present and visualise algorithm outputs and results of analyses in a clear and informative way.

Indicative reading list

W. H. Press et al., “Numerical recipes in C”, Cambridge University Press
Research articles to be provided to the students

Subject specific skills

See learning outcomes.

Transferable skills

Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.