## CORE COURSES

1) COMPUTATIONAL TOOLS

• Linux operating system: basic commands, the VI editor, scripts and Bash Shell
• Introduction to programming in high-level languages: Fortran 90. Libraries
• Precision and errors in computation
• Basic algorithmic structures
• Basic concepts in code optimization, parallelization and vectorization
• Use of software of general interest for scientific applications: Python, Maxima, Gnuplot/Origin/VMD.

2) INTRODUCTION TO SCIENTIFIC COMPUTATION

• Data: Variables. Tables and lists. Functions. Matrices and vectors
• Functions: discretization and precision. Zeros. Series, products and continued fractions.
• Methods for approximating functions by means of lineal, polynomial and multilinear regressions. Interpolation and series approximations.
• Elements of applied linear algebra: vector spaces and operators. Orthonormalization. Operations with matrices. Sets of linear equations. Matrix inversions. Eigenvectors and eigenvalues. Diagonalization. Linear transformations.
• Numerical intergration and differentiation. Differentiation and integration of single-variable functions. Multivariate functions. Partial derivatives. Line, surface and volume integrals.
• Ordinary differential equations. Formal aspects. Methods for their numerical solutions. Fourier methods. Nonlinear differential equations.
• Partial derivative equations. Formal aspects: definitions and boundary conditions. Methods for their numerical solutions.
• Optimization methods. Monte Carlo.

3) MULTISCALE MODELLING

• Introduction to the scientific method and to the length and time scales present in Nature
• Systems in equilibrium. The microscopic world: atomic-molecular structure. The macroscopic world: Equilibrium Thermodynamics. The mesoscopic world: Equilibrium Statistical Mechanics.
• Examples of structure and macroscopic properties
• Transport phenomena
• Chemical reactivity
• Complex systems

4) MOLECULAR MODELLING

• Description of atomic and molecular systems at different scales
• Mechanical and statistical basis of molecular modelling
• Quantum models
• Molecular Dynamics
• The Monte Carlo method
• Practical sessions of molecular modelling