Data sciences

Data Analysis for Physics introduces mathematical, statistical and computational tools for extracting information from data in physics and the sciences. The course starts with numerical linear algebra and basic data-analysis methods: eigenvalues and eigenvectors, the power method, singular value decomposition, principal component analysis, linear regression, least squares, regularization, overfitting, validation, gradient descent, logistic regression and simple neural networks.

The second part develops probability and statistics as the language of uncertainty in experiments. Topics include random-number generation, sampling from probability distributions, propagation of errors, correlated and independent uncertainties, the law of large numbers, the central limit theorem, statistical estimators and maximum likelihood estimation. Regression is then revisited from a probabilistic point of view, including error bars, weighted least squares and Bayesian regularization.

The final part turns to stochasticity as a modelling principle in physics. The course covers Brownian motion, diffusion, random walks, maximum entropy, rejection sampling and the curse of dimensionality, Markov chain Monte Carlo, the Metropolis rule, detailed balance and examples from interacting particle systems. It concludes with phase transitions, including percolation, or giant components in random graphs.