OVERVIEW

The course covers introductory topics of physics laboratory, focusing on the concept of measurement and uncertainty, as well as the foundations of data analysis. The course also gives an introduction to computer programming for scientific applications.

AIMS AND CONTENT

LEARNING OUTCOMES

The course provides an introduction to experimental physics, with focus on the concepts of measurable quantities and uncertainty. The course includes simple experiments involving the measurement of mechanical and electrical quantities. Basic concepts of probability, statistics and data analysis will be introduced as well. A part of the course gives an introduction to computer science, with focus on procedural programming in C++ and the use of software libraries for the realization of plots and fits.

AIMS AND LEARNING OUTCOMES

The student will learn the basics of the experimental activity in a physics laboratory. He will learn to use instruments for the measurement of mechanical and electrical quantities. The student will develop team working skills and will be able to describe a measurement procedure and report its outcome in written form in a concise and comprehensive way. The student will master the concepts of dimensional analysis and measurement theory, and will be able to solve simple problems in probability, statistics and data analysis.

The student will know the basic syntax of C/C++ and will be able to write simple programs for the processing, analysis and display of scientific data. He will be able to understand and modify simple programs written by someone else. He will develop the skills required to learn autonomously other programming concepts and languages not treated explicitly during the course.

TEACHING METHODS

The course will consist of lectures (80 hours) devoted to the presentation of the theoretical topics whose understanding is required for the hand-on laboratory experiences. These include dimensional analysis, measurement and data analysis, probability, statistics, introduction to computer programming. During these lectures, practical exercises will be also presented as a support and integration to the theoretical arguments.

The course also consists of hands-on laboratory experiences (80 hours), performed either face to face in the University laboratories or from remote, over a video conferencing system. Laboratory experiences usually take place in the afternoon and are organized in groups of 2-3 students. Participation in laboratory experiences is mandatory.

SYLLABUS/CONTENT

Physics laboratory

1. Physical quantities: operative definition and methodology of measurements. Physical dimensions and dimensional analysis. Systems of measurement units,  International System of Units, conversions between systems of units. General features of measuring instruments: sensitivity, accuracy, range.

2. Non reproducible measurements. Absolute and relative frequency histograms. Average, mode, median, full width at half maximum, standard deviation, variance, standard error. Rectangular distribution, Gaussian distribution. Propagation of maximum and statistical uncertainty. Covariance.

3. Graphical representation of data and non-linear scales. Graphical estimate of the best fit line, least squares method and weighted average.

4. Introduction to the hands-on laboratory experiences.

5. Definition of probability and combinatory calculus.Axiomatic probability and Venn diagrams. Conditional probability, independent and disjoint events, Bayes’ theorem.

6. Random variables, distribution functions, probability density functions, cumulative function. Mode, median, average, variance. Sum and product of two random variables, covariance and correlation coefficient.

7. Probability distributions: Binomial distribution, Poisson distribution, Gaussian distribution.

8. Statistical inference: maximum likelihood method, hypothesis testing, Chi square test

Introduction to computer programming

1. Positional numeral systems: decimal, binary and hexadecimal systems. Two’s complement, floating point numbers.

2. Microprocessor systems, Von Neumann architecture, operating systems.

3. The GNU/linux operating system and the terminal. Introduction to some useful shell commands. Basic software for file system exploration and manipulation, text editors, spreadsheets.

4. Introduction to the C++ programming language. The main function, preprocessor directives, variables declaration and initialization.Variable types: char, int, double, bool. Arithmetic and logic operators. Structures and cycles: if/else, while, do/while. Arrays, vectors and strings. Input/output from/to terminal and file. Functions. Introduction to classes and object-oriented programming.

5. Introduction to the ROOT data analysis libraries for the production of plots and fits.

RECOMMENDED READING/BIBLIOGRAPHY

Slides will be available in the Aulaweb page of the course

Taylor John R. "Introduzione all'analisi degli errori. Lo studio delle incertezze nelle misure fisiche" Editore Zanichelli

Further suggestions on books and other material will be available in the Aulaweb page of the course.

TEACHERS AND EXAM BOARD

Exam Board

FRANCESCO BUATIER DE MONGEOT (President)

ANDREA BERSANI

CLAUDIO CANALE

ROBERTA CARDINALE

ENRICO ROBUTTI

SERGIO DI DOMIZIO (President Substitute)

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The final mark refers to the whole course of “Laboratorio 1”, it corresponds to a global evaluation of the preparation of the students and their level of achievement of the learning objectives.

The students’ preparation on computer programming, experimental laboratory activity, theory of measurement and uncertainty, data analysis, probability and statistics, are evaluated by means of separate exams (practical, oral or written). A positive evaluation on each of these exams is required in order to obtain a final mark for the course.

ASSESSMENT METHODS

The exam is divided in three parts. One exam will evaluate results achieved by the students on conceptual and methodological aspects such as dimensional analysis, theory of measurement and uncertainty, data analysis, probability and statistics.

Another exam will test the computer and programming skills acquired by the students, and their capability of solving simple problems (read a file, manipulate data, produce plots and fits) by means of a computer program.

A third exam will evaluate the students’ ability to perform a physics laboratory experiment: make physical measurements, estimate their uncertainty, analyze the data, interpret the results and report them in a concise and comprehensive written form.

Exam schedule