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Unit of study_

MATH4411: Applied Computational Mathematics

Computational mathematics fulfils two distinct purposes within Mathematics. On the one hand the computer is a mathematician's laboratory in which to model problems too hard for analytical treatment and to test existing theories; on the other hand, computational needs both require and inspire the development of new mathematics. Computational methods are an essential part of the tool box of any mathematician. This unit will introduce you to a suite of computational methods and highlight the fruitful interplay between analytical understanding and computational practice. In particular, you will learn both the theory and use of numerical methods to simulate partial differential equations, how numerical schemes determine the stability of your method and how to assure stability when simulating Hamiltonian systems, how to simulate stochastic differential equations, as well as modern approaches to distilling relevant information from data using machine learning. By doing this unit you will develop a broad knowledge of advanced methods and techniques in computational applied mathematics and know how to use these in practice. This will provide a strong foundation for research or further study.

Code MATH4411
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Assumed knowledge:
A thorough knowledge of vector calculus (e.g., MATH2X21) and of linear algebra (e.g., MATH2X22). Some familiarity with partial differential equations (e.g., MATH3X78) and mathematical computing (e.g., MATH3X76) would be useful

At the completion of this unit, you should be able to:

  • LO1. Demonstrate a broad understanding of key concepts in computational mathematics.
  • LO2. Use these concepts to create numerical schemes to solve qualitative and quantitative mathematical problems in scientific contexts, using appropriate mathematical and computing techniques.
  • LO3. Evaluate the behaviour of numerical schemes using mathematical analysis of numerical methods.
  • LO4. Communicate mathematical information deeply and coherently, both orally and through written work in the project reports.
  • LO5. Differentiate and distinguish problem situations for various different numerical strategies and methods.

Unit outlines

Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.