20410429 - FS510 - MONTECARLO METHODS

Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.

Curriculum

teacher profile | teaching materials

Programme

Presentation of the problems that can be treated through integrals on large number of dimensions

Basics

Probability and Random variables

Measurement, uncertainty and its propagation

Curve-fitting, least-squares, optimization

Classical numerical integration, speed of convergence

Integration MC (Mean, variance)

Sampling Strategies

Applications

Propagation of uncertainties

Generation according to a distribution

Real World Applications

Cosmic Rays Shower

System Availabilty

Further applications

Core Documentation

Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269

Taylor, J. - Introduzione all'analisi degli errori : lo studio delle incertezze nelle misure fisiche - Zanichelli Disponibile nella biblioteca Scientifica di Roma Tre

Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre

Type of delivery of the course

Lectures (about 24 hours) and Activities in Laboratory (about 36 hours). During the Laboratory Activities, each student can access a Personal Computer. The topics discussed during the Lectures will be worked out during the Laboratory Activities, using Mathematica, Python or C++.

Type of evaluation

Written and oral exams. Written test: design and coding of a computer program. The written exam consists of two parts. The first part is devoted to verify the specific knowledge of the techniques presented during the lectures. In the second part it will be required to apply these techniques in a broader context. Oral: discussion and presentation of a topic to be agreed upon. The preparation of this seminar will require personal study of some chapters of a book.

teacher profile | teaching materials

Programme

Presentation of the problems that can be treated through integrals on large number of dimensions

Basics

Probability and Random variables

Measurement, uncertainty and its propagation

Curve-fitting, least-squares, optimization

Classical numerical integration, speed of convergence

Integration MC (Mean, variance)

Sampling Strategies

Applications

Propagation of uncertainties

Generation according to a distribution

Real World Applications

Cosmic Rays Shower

System Availability

Further applications



Core Documentation

Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California
Dubi, A. - Monte Carlo applications in systems engineering - Wiley

Type of delivery of the course

Lectures (about 24 hours) and Activities in Laboratory (about 36 hours). During the Laboratory Activities, each student can access a Personal Computer. The topics discussed during the Lectures will be worked out during the Laboratory Activities, using Mathematica, Python or C++.

Type of evaluation

Written and oral exam. Written test: design and coding of a computer program. The written exam consists of two parts. The first part is devoted to verify the specific knowledge of the techniques presented during the lectures. In the second part it will be required to apply these techniques in a broader context. Oral: discussion and presentation of a topic to be agreed upon. The preparing of this seminar will require a personal study of some chapters of a book.

teacher profile | teaching materials

Programme

Presentation of the problems that can be treated through integrals on large number of dimensions

Basics

Probability and Random variables

Measurement, uncertainty and its propagation

Curve-fitting, least-squares, optimization

Classical numerical integration, speed of convergence

Integration MC (Mean, variance)

Sampling Strategies

Applications

Propagation of uncertainties

Generation according to a distribution

Real World Applications

Cosmic Rays Shower

System Availabilty

Further applications

Core Documentation

Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269

Taylor, J. - Introduzione all'analisi degli errori : lo studio delle incertezze nelle misure fisiche - Zanichelli Disponibile nella biblioteca Scientifica di Roma Tre

Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre

Type of delivery of the course

Lectures (about 24 hours) and Activities in Laboratory (about 36 hours). During the Laboratory Activities, each student can access a Personal Computer. The topics discussed during the Lectures will be worked out during the Laboratory Activities, using Mathematica, Python or C++.

Type of evaluation

Written and oral exams. Written test: design and coding of a computer program. The written exam consists of two parts. The first part is devoted to verify the specific knowledge of the techniques presented during the lectures. In the second part it will be required to apply these techniques in a broader context. Oral: discussion and presentation of a topic to be agreed upon. The preparation of this seminar will require personal study of some chapters of a book.

teacher profile | teaching materials

Programme

Presentation of the problems that can be treated through integrals on large number of dimensions

Basics

Probability and Random variables

Measurement, uncertainty and its propagation

Curve-fitting, least-squares, optimization

Classical numerical integration, speed of convergence

Integration MC (Mean, variance)

Sampling Strategies

Applications

Propagation of uncertainties

Generation according to a distribution

Real World Applications

Cosmic Rays Shower

System Availability

Further applications



Core Documentation

Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California
Dubi, A. - Monte Carlo applications in systems engineering - Wiley

Type of delivery of the course

Lectures (about 24 hours) and Activities in Laboratory (about 36 hours). During the Laboratory Activities, each student can access a Personal Computer. The topics discussed during the Lectures will be worked out during the Laboratory Activities, using Mathematica, Python or C++.

Type of evaluation

Written and oral exam. Written test: design and coding of a computer program. The written exam consists of two parts. The first part is devoted to verify the specific knowledge of the techniques presented during the lectures. In the second part it will be required to apply these techniques in a broader context. Oral: discussion and presentation of a topic to be agreed upon. The preparing of this seminar will require a personal study of some chapters of a book.

teacher profile | teaching materials

Programme

Presentation of the problems that can be treated through integrals on large number of dimensions

Basics

Probability and Random variables

Measurement, uncertainty and its propagation

Curve-fitting, least-squares, optimization

Classical numerical integration, speed of convergence

Integration MC (Mean, variance)

Sampling Strategies

Applications

Propagation of uncertainties

Generation according to a distribution

Real World Applications

Cosmic Rays Shower

System Availabilty

Further applications

Core Documentation

Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269

Taylor, J. - Introduzione all'analisi degli errori : lo studio delle incertezze nelle misure fisiche - Zanichelli Disponibile nella biblioteca Scientifica di Roma Tre

Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre

Type of delivery of the course

Lectures (about 24 hours) and Activities in Laboratory (about 36 hours). During the Laboratory Activities, each student can access a Personal Computer. The topics discussed during the Lectures will be worked out during the Laboratory Activities, using Mathematica, Python or C++.

Type of evaluation

Written and oral exams. Written test: design and coding of a computer program. The written exam consists of two parts. The first part is devoted to verify the specific knowledge of the techniques presented during the lectures. In the second part it will be required to apply these techniques in a broader context. Oral: discussion and presentation of a topic to be agreed upon. The preparation of this seminar will require personal study of some chapters of a book.

teacher profile | teaching materials

Programme

Presentation of the problems that can be treated through integrals on large number of dimensions

Basics

Probability and Random variables

Measurement, uncertainty and its propagation

Curve-fitting, least-squares, optimization

Classical numerical integration, speed of convergence

Integration MC (Mean, variance)

Sampling Strategies

Applications

Propagation of uncertainties

Generation according to a distribution

Real World Applications

Cosmic Rays Shower

System Availability

Further applications



Core Documentation

Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California
Dubi, A. - Monte Carlo applications in systems engineering - Wiley

Type of delivery of the course

Lectures (about 24 hours) and Activities in Laboratory (about 36 hours). During the Laboratory Activities, each student can access a Personal Computer. The topics discussed during the Lectures will be worked out during the Laboratory Activities, using Mathematica, Python or C++.

Type of evaluation

Written and oral exam. Written test: design and coding of a computer program. The written exam consists of two parts. The first part is devoted to verify the specific knowledge of the techniques presented during the lectures. In the second part it will be required to apply these techniques in a broader context. Oral: discussion and presentation of a topic to be agreed upon. The preparing of this seminar will require a personal study of some chapters of a book.