Methods in Computational Science

Computational methods are an integral part of most scientific disciplines, and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms with the aim of familiarizing the reader with the field’s theoretical foundations and providing the practical skills to use and develop computational methods. Methods in Computational Science extends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing, • is centered around a set of fundamental algorithms presented in the form of pseudocode, • presents theoretical material alongside several examples and exercises, and • provides Python implementations of many key algorithms. Methods in Computational Science is a textbook for computer science and data science students at the advanced undergraduate and graduate level. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. Because the text is self-contained, it can also be used to support continuous learning for practicing mathematicians, data scientists, computer scientists, and engineers in the field of computational science.

Johan Hoffman is professor of numerical analysis and deputy head of the division of Computational Science and Technology at KTH Royal Institute of Technology. He has been a visiting researcher at the University of Oxford, the University of Chicago, Stanford University, Heidelberg University, Universitat Polytècnica de Catalunya (UPC), the Auckland Bioengineering Institute at the University of Auckland, and the Basque Center for Applied Mathematics (BCAM). His research interests include computational science, specifically, computational mechanics and turbulence, with applications to aerodynamics, urban planning, renewable energy, and cardiovascular bioengineering. He is a founder of the FEniCS open source software project and of the spin-off company Ingrid Cloud.