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Mathematics for Real-World Systems Centre for Doctoral Training

MA934: Numerical Algorithms and Optimisation (15 CATS)

Lecturer: Radu CimpeanuLink opens in a new window (from October 2022)

Students who are not in the MathSys CDT who wish to take this module should contact the module leader before registering. Registering on eVision/online does not guarantee you a place on the module.

Module Resources

Module Aims

This is one of four core taught modules for the MSc in Mathematics of Real-World Systems. This module provides students with knowledge (and practice) of important numerical optimisation concepts at the intersection between mathematics and scientific computing. Algorithmic structures, data structures, numerical method construction and performance assessment will form key parts of the module, with applications and use cases concentrated on topics in linear algebra, signal processing and optimisation.

Syllabus

The syllabus will be drawn from the following list of topics: algorithmic structures (iteration, recursion, memorization) and computational complexity, data structures (linked lists, stacks and queues, binary indexed trees), sorting and search algorithms, Fast Fourier Transform, automatic differentiation, linear systems and the Conjugate Gradient algorithm, Singular Value Decomposition, convex and nonconvex optimisation, constrained optimisation, linear programming, Dijkstra's algorithm and dynamic programming, discrete-event simulation.

Teaching

  • Per week: 2 x 2 hours of lectures, 2 x 2 hours of classwork
  • Duration: From the 2023/2024 academic year, this module will be taught in the second half of term 1 (weeks 6 to 10)

Classes are usually held on Mondays 10:00-12:00 (lectures) and 13:00-15:00 (classwork), and Tuesdays 10:00-12:00 (lectures) and 13:00-15:00 (classwork) in room D1.07, unless you are told otherwise.

Assessment

For deadlines see Module Resources page.

From the 2023/2024 academic year, the module will be assessed as follows:

  • Written homework assignments (worth 60%)
  • Oral viva examination (worth 40%)

Illustrative Bibliography

  • Lloyd N. Trefethen and David Bau, Numerical Linear Algebra, 3rd Edition, SIAM, 1997.
  • William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical recipes: The art of scientific computing, 3rd Edition, Cambridge University Press, New York, NY, USA, 2007.
  • David Kincaid and Ward Cheney. Numerical analysis : mathematics of scientific computing, 3rd Edition, American Mathematical Society, 2009.

    Research articles in the field will complement the textbooks above.