Astrophysics and Cosmology

Programming Languages: - Fortran & Python from C language - Fortran: from basics to dynamic memory management - Python: numpy, matplotlib, astropy, scipy - Introduction to parallel computing - Distributed memory systems and MPI - openMP and shared memory - Optional: Introduction to GPU computing - Fortran, advanced features, and new standards - Fortran: Types and Modules: writing modular, typed, and easily parallelizable software. Principles of software analysis. - Fortran: Pointers and pointer to functions Algorithms: - Linear systems – Stability and efficiency, Sparse linear system solvers, Iterative methods - LU – Cholesky – SVD – EVD – PCG - Ordinary Differential Equations – Explicit methods and stability - Euler - EP -RK3-4 - PC - Stiff differential equations - Implicit methods - Monte Carlo methods for integration and parameter estimation: - Metropolis-Hastings – GW10 Signal Processing in Astrophysics: - Signal Processing: - Signal Sampling - Sampling Theorem, Convolution, Correlation, and Fourier Transform - Discrete Fourier Transform and Fast Fourier Transform - Introduction to signal analysis on a sphere - Sphere discretization - Numerical decomposition into spherical harmonics - Processing of astronomical images - Spectral estimations – stationary noise and noise color. Introduction to Numerical simulations ◦ N-Body and gravity for large scale dark matter distribution. ◦ Computational Fluiddyamics: Galactic and extragalactic Baryonic distribution ( AMR/Voronoi e SPH schemes). ◦ Radiative Transfer and Feedback: Cosmic Reionization ( Ray tracing and Monte Carlo Methods).

Basic knowledge of a structured programming language (e.g. modern Fortran, C, C++, and/or Python). Proficiency in using shells and basic UNIX commands.

- Modern Fortran Explained: Incorporating Fortran 2018 (M. Metcalf), Springer - Fortran for Scientists & Engineers (S.J. Chapman) McGraw-Hill - A Student’s Guide to Python for Physical Modeling (J. M. Kinder and P. Nelson), Princeton University Press - A Primer on Scientific Programming with Python (H.P. Langtangen) Springer - An Introduction to Python and Computer Programming (Y. Zhang) Springer - The OpenMP Common Core (Mattson et al.), MIT Press - Using MPI ( W. Gropp et al.), MIT Press Free online resources and materials provided by teachers. - Free online book on Computational Physics: https://courses.physics.ucsd.edu/2017/Spring/physics142/Lectures/Lecture18/Hjorth-JensenLectures2010.pdf - The old Numerical Recipes book has very good discussions on coding and algorithms: https://numerical.recipes/

Attendance is optional although strongly recommended.

3/4 projects (mandatory: 1 in Fortran, 1 in Python, 1/2 free) for individual or group work Alternatively: two mandatory projects, individual or group work, to be completed during the course and a project suggested by research groups in the Astrophysics area Exam: personal presentation of a project and oral exam on the course program.

Theoretical lectures and exercises (possibly including seminars or monographic lessons on specific topics).