The material here aims at giving you an introduction to several of the most used algorithms in Computational Science. These algorithms cover topics such as advanced numerical integration using Gaussian quadrature, Monte Carlo methods with applications to random processes, Markov chains, integration of multidimensional integrals and applications to problems in statistical physics and quantum mechanics. Other methods which are presented are eigenvalue problems, from the simple Jacobi method to iterative Krylov methods. Popular methods from linear algebra such as the LU-decomposition method and spline interpolation are also discussed as well as regression methods and simple neural networks. A good fraction of the course is also devoted to solving ordinary differential equations with or without boundary conditions and finally methods for solving partial differential equations. You will also find material on popular Machine Learning algorithms, starting with various linear regression methods and ending with neural networks. The focus for the Machine Learning algorithms is on supervised learning.
The course is project based and through various projects, normally four to five, you will be exposed to fundamental research problems from various fields (Physics, Geophysics, Chemistry, Mathematics, Statistics etc), where, if possible, we aim at reproducing state of the art scientific results. You will learn to develop and structure codes when solving the projects, develop a critical understanding of the strengths and limits of the various numerical methods, become familiar with supercomputing facilities and parallel computing and learn to write scientific projects.