OVERVIEW

Computational and Statistical Methods Laboratory (LMCS, code 90741) is worth 6 credits and takes place in the first semester of the 3rd year of the three-year degree (L-30)
 

AIMS AND CONTENT

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.

TEACHERS AND EXAM BOARD

Exam Board

FABRIZIO PARODI (President)

STEFANO PASSAGGIO

ROBERTA CARDINALE (President Substitute)

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The final exam consists of two parts:

• computer exam
• oral exam

The exercises carried out and the tasks assigned during the year will contribute to the final evaluation.

ASSESSMENT METHODS

METHOD OF ASSESSMENT
The final grade is formed by the evaluation during the year, the score of the computer test and the score of the oral exam (with weights 0.3 / 0.35 / 0.35).

EVALUATION DURING THE YEAR.
The attendance to 7 exercises and 4 hands-on is mandatory. Every exercise is worth 2 points,  every hands-on 1 point. Students need at least 15 points to be admitted to the computer exam. Up to 3 experiences can be recovered offline.
After each experience, a homework is assigned; the evaluation of all the homeworks  is normalized to 15. The attendance score is added to the homework score thus forming the evaluation during the year.

CALCULATOR EXAM
The computer exam consists in developing programs to solve 2 problems out of the 3 proposed in 2 hours. The test is passed if a score higher than or equal to 15/33 is reported.

ORAL EXAM
The oral exam consists of two questions on different aspects of the program carried out. During the oral exam, the teachers verify the understanding of the fundamental teaching contents and the expository ability of the candidate.

Exam schedule