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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

Students who are not in the MathSys CDT or the Predictive Modelling and Scientific Computing programme 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, while also acting as core module for the MSc in Predictive Modelling and Scientific Computing. 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 non-convex 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 Thursdays 10:00-12:00 (lectures) and 13:00-15:00 (classwork) in room D1.07, unless announced 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

  • 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.
  • Gilbert Strang. Differential equations and linear algebra, Wellesley-Cambridge Press, 2014.
  • Lloyd N. Trefethen, David Bau, James G. Nagy and Yuji Nakatsukasa, Numerical Linear Algebra, 25th Edition, Society for Industrial and Applied Mathematics, 2022.

    Research articles in the field will complement the textbooks above.