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MA934: Numerical Algorithms and Optimisation (15 CATS)

Lecturer: Radu Cimpeanu (from October 2022)

Module Aims

This is one of four core taught modules for the MSc in Mathematics of Real-World Systems. It teaches students the theory and implementation of a set of computational algorithms that provide the fundamental toolkit for advanced data analysis, simulation and optimisation. After completing this module, students will understand the theoretical underpinnings of the computational algorithms and optimisation methods that appear most frequently in advanced data analysis and mathematical modelling. They will gain experience of discrete and continuous problems. Students will also acquire practical coding experience from implementing, testing and benchmarking these algorithms on specific problems drawn from a range of applications.

Syllabus

  • 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

Teaching

  • Per week: 2 x 2 hours of lectures, 2 x 2 hours of classwork
  • Duration: 5 weeks (first half of term 1)

Classes are usually held on Mondays 10:00-12:00 and 13:00-15:00, and Tuesdays 10:00-12:00 and 13:00-15:00, although this is subject to change.

Assessment

For deadlines see Module Resources page

  • Written homework assignments (20%)
  • Written class test (40%) - to be held on Monday 31 October 2022, 10:00 - 12:30
  • Oral examination (40%) - to be held on Tuesday 01 November 2022, your timeslot will be confirmed nearer the time

Illustrative Bibliography

W. H. Press et al., “Numerical recipes in C”, Cambridge University Press, 2017

Research articles to be provided to students