LEARNING OUTCOMES

The course aims to consolidate and expand the skills of calculation, statistical analysis and programming, aimed at analyzing and acquiring data in laboratory experiences.

AIMS AND LEARNING OUTCOMES

The course deals with computational physics, addressing the numerical solution of ordinary differential equations and partial derivatives, and advanced methods of data analysis, dealing with Monte Carlo simulation rudiments, deepening the best-fit techniques and giving an overview of multivariate signal/background separation techniques.

The course also aims to extend the C++ programming skill (acquired during the first year) by more in-depth study of Object-Oriented programming in C ++ and providing rudiments of Python and shell scripting. Higher level packages will be also used (ROOT, Octave / Matlab).

At the end of the course the student will be able, exploiting C ++, python or Matlab programming, to:

• solve numerically ordinary and partial differential equations
• build simple simulations or integrations with the Monte Carlo method
• perform chi-square and maximum likelihood fits of various levels of complexity
• evaluate confidence intervals and perform hypothesis tests

PREREQUISITES

The course assume that computation skills contained in the first year coures are acquired.

TEACHING METHODS

Lectures and laboratory exercises.

SYLLABUS/CONTENT

Lectures schedule:

•  OO programming (inheritance, polymorphism), shell scripting and Python, use of specific packages / libraries (ROOT, Octave / Matlab)
•  Numerical solution of ordinary differential equations. Applications to classical physics and quantum mechanics problems (Numerov method for the Schrodinger equation).
•  Numerical solution of partial differential equations. Applications to eletromagnetism and heat propagation.
•  Introduction to the generation of random variables and Monte Carlo simulation
•  Extraction of quantities of interest from a data sample: binned and unbinned likelihood. Point estimate, confidence intervals. Hypothesis testing. Limits.
•  Overview of multivariate classification techniques (Likelihood ratio, neural networks).

RECOMMENDED READING/BIBLIOGRAPHY

Notes / slides are provided during the course. A list of possible texts for further information is available on the course page on Aulaweb.