The aim of the course is to learn the basic tools to deal with Lie algebras and their representations and to acquire computer calculation techniques,both for symbolic and for numerical calculations. Topics of the course
will be dealt with using either Wolfram Language and Python or alternative computer languages preferred by the student.
will be dealt with using either Wolfram Language and Python or alternative computer languages preferred by the student.
Curriculum
teacher profile teaching materials
SU(2) and SU(3)
The Killing Form
Simple Lie Algebras
Representations
Simple Roots and the Cartan Matrix
The Classical Lie Algebras
The Exceptional Lie Algebras
Casimir Operators and Freudenthal’s Formula
The Weyl Group
Weyl’s Dimension Formula
Reducing Product Representations
Subalgebras
Branching Rules
Numerical Methods
Refresh on Probability and Random variables
Refresh on Measurement, uncertainty and its propagation
Refresh on 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
Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html
Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre
Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre
readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html
Programme
Group Theory (CA)SU(2) and SU(3)
The Killing Form
Simple Lie Algebras
Representations
Simple Roots and the Cartan Matrix
The Classical Lie Algebras
The Exceptional Lie Algebras
Casimir Operators and Freudenthal’s Formula
The Weyl Group
Weyl’s Dimension Formula
Reducing Product Representations
Subalgebras
Branching Rules
Numerical Methods
Refresh on Probability and Random variables
Refresh on Measurement, uncertainty and its propagation
Refresh on 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
Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html
Core Documentation
Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre
Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre
readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html
Type of delivery of the course
Lectures in the classroom and in the computer lab. Exercises sessions in the classroom, computer lab, and at home.Type of evaluation
Oral and written examination. The written exam requires to write a short computer program to solve a problem in group theory or in numerical methods. The oral exam is a discussion on the topics of the syllabus and a presentation given by the student on a topic to be agreed upon. During the oral examination the student will be asked to state and prove properties of Lie Algebras and their representations, as illustrated during class, or to describe a numerical method in the syllabus giving details on its aim and properties. Possible topics for the presentations will be presented each year on the group theory and numerical methods material presented during the class. Topics for the presentations are listed each year on http://webusers.fis.uniroma3.it/franceschini/cmm.html teacher profile teaching materials
SU(2) and SU(3)
The Killing Form
Simple Lie Algebras
Representations
Simple Roots and the Cartan Matrix
The Classical Lie Algebras
The Exceptional Lie Algebras
Casimir Operators and Freudenthal’s Formula
The Weyl Group
Weyl’s Dimension Formula
Reducing Product Representations
Subalgebras
Branching Rules
Numerical Methods
Refresh on Probability and Random variables
Refresh on Measurement, uncertainty and its propagation
Refresh on 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
Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html
Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre
Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre
readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html
Programme
Group Theory (CA)SU(2) and SU(3)
The Killing Form
Simple Lie Algebras
Representations
Simple Roots and the Cartan Matrix
The Classical Lie Algebras
The Exceptional Lie Algebras
Casimir Operators and Freudenthal’s Formula
The Weyl Group
Weyl’s Dimension Formula
Reducing Product Representations
Subalgebras
Branching Rules
Numerical Methods
Refresh on Probability and Random variables
Refresh on Measurement, uncertainty and its propagation
Refresh on 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
Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html
Core Documentation
Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre
Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre
readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html
Type of delivery of the course
Lectures in the classroom and in the computer lab. Exercises sessions in the classroom, computer lab, and at home.Type of evaluation
Oral and written examination. The written exam requires to write a short computer program to solve a problem in group theory or in numerical methods. The oral exam is a discussion on the topics of the syllabus and a presentation given by the student on a topic to be agreed upon. During the oral examination the student will be asked to state and prove properties of Lie Algebras and their representations, as illustrated during class, or to describe a numerical method in the syllabus giving details on its aim and properties. Possible topics for the presentations will be presented each year on the group theory and numerical methods material presented during the class. Topics for the presentations are listed each year on http://webusers.fis.uniroma3.it/franceschini/cmm.html teacher profile teaching materials
SU(2) and SU(3)
The Killing Form
Simple Lie Algebras
Representations
Simple Roots and the Cartan Matrix
The Classical Lie Algebras
The Exceptional Lie Algebras
Casimir Operators and Freudenthal’s Formula
The Weyl Group
Weyl’s Dimension Formula
Reducing Product Representations
Subalgebras
Branching Rules
Numerical Methods
Refresh on Probability and Random variables
Refresh on Measurement, uncertainty and its propagation
Refresh on 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
Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html
Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre
Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre
readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html
Programme
Group Theory (CA)SU(2) and SU(3)
The Killing Form
Simple Lie Algebras
Representations
Simple Roots and the Cartan Matrix
The Classical Lie Algebras
The Exceptional Lie Algebras
Casimir Operators and Freudenthal’s Formula
The Weyl Group
Weyl’s Dimension Formula
Reducing Product Representations
Subalgebras
Branching Rules
Numerical Methods
Refresh on Probability and Random variables
Refresh on Measurement, uncertainty and its propagation
Refresh on 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
Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html
Core Documentation
Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre
Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre
readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html
Type of delivery of the course
Lectures in the classroom and in the computer lab. Exercises sessions in the classroom, computer lab, and at home.Type of evaluation
Oral and written examination. The written exam requires to write a short computer program to solve a problem in group theory or in numerical methods. The oral exam is a discussion on the topics of the syllabus and a presentation given by the student on a topic to be agreed upon. During the oral examination the student will be asked to state and prove properties of Lie Algebras and their representations, as illustrated during class, or to describe a numerical method in the syllabus giving details on its aim and properties. Possible topics for the presentations will be presented each year on the group theory and numerical methods material presented during the class. Topics for the presentations are listed each year on http://webusers.fis.uniroma3.it/franceschini/cmm.html teacher profile teaching materials
SU(2) and SU(3)
The Killing Form
Simple Lie Algebras
Representations
Simple Roots and the Cartan Matrix
The Classical Lie Algebras
The Exceptional Lie Algebras
Casimir Operators and Freudenthal’s Formula
The Weyl Group
Weyl’s Dimension Formula
Reducing Product Representations
Subalgebras
Branching Rules
Numerical Methods
Refresh on Probability and Random variables
Refresh on Measurement, uncertainty and its propagation
Refresh on 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
Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html
Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre
Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre
readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html
Programme
Group Theory (CA)SU(2) and SU(3)
The Killing Form
Simple Lie Algebras
Representations
Simple Roots and the Cartan Matrix
The Classical Lie Algebras
The Exceptional Lie Algebras
Casimir Operators and Freudenthal’s Formula
The Weyl Group
Weyl’s Dimension Formula
Reducing Product Representations
Subalgebras
Branching Rules
Numerical Methods
Refresh on Probability and Random variables
Refresh on Measurement, uncertainty and its propagation
Refresh on 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
Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html
Core Documentation
Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre
Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre
readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html
Type of delivery of the course
Lectures in the classroom and in the computer lab. Exercises sessions in the classroom, computer lab, and at home.Type of evaluation
Oral and written examination. The written exam requires to write a short computer program to solve a problem in group theory or in numerical methods. The oral exam is a discussion on the topics of the syllabus and a presentation given by the student on a topic to be agreed upon. During the oral examination the student will be asked to state and prove properties of Lie Algebras and their representations, as illustrated during class, or to describe a numerical method in the syllabus giving details on its aim and properties. Possible topics for the presentations will be presented each year on the group theory and numerical methods material presented during the class. Topics for the presentations are listed each year on http://webusers.fis.uniroma3.it/franceschini/cmm.html teacher profile teaching materials
SU(2) and SU(3)
The Killing Form
Simple Lie Algebras
Representations
Simple Roots and the Cartan Matrix
The Classical Lie Algebras
The Exceptional Lie Algebras
Casimir Operators and Freudenthal’s Formula
The Weyl Group
Weyl’s Dimension Formula
Reducing Product Representations
Subalgebras
Branching Rules
Numerical Methods
Refresh on Probability and Random variables
Refresh on Measurement, uncertainty and its propagation
Refresh on 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
Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html
Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre
Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre
readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html
Programme
Group Theory (CA)SU(2) and SU(3)
The Killing Form
Simple Lie Algebras
Representations
Simple Roots and the Cartan Matrix
The Classical Lie Algebras
The Exceptional Lie Algebras
Casimir Operators and Freudenthal’s Formula
The Weyl Group
Weyl’s Dimension Formula
Reducing Product Representations
Subalgebras
Branching Rules
Numerical Methods
Refresh on Probability and Random variables
Refresh on Measurement, uncertainty and its propagation
Refresh on 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
Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html
Core Documentation
Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre
Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre
readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html
Type of delivery of the course
Lectures in the classroom and in the computer lab. Exercises sessions in the classroom, computer lab, and at home.Type of evaluation
Oral and written examination. The written exam requires to write a short computer program to solve a problem in group theory or in numerical methods. The oral exam is a discussion on the topics of the syllabus and a presentation given by the student on a topic to be agreed upon. During the oral examination the student will be asked to state and prove properties of Lie Algebras and their representations, as illustrated during class, or to describe a numerical method in the syllabus giving details on its aim and properties. Possible topics for the presentations will be presented each year on the group theory and numerical methods material presented during the class. Topics for the presentations are listed each year on http://webusers.fis.uniroma3.it/franceschini/cmm.html teacher profile teaching materials
SU(2) and SU(3)
The Killing Form
Simple Lie Algebras
Representations
Simple Roots and the Cartan Matrix
The Classical Lie Algebras
The Exceptional Lie Algebras
Casimir Operators and Freudenthal’s Formula
The Weyl Group
Weyl’s Dimension Formula
Reducing Product Representations
Subalgebras
Branching Rules
Numerical Methods
Refresh on Probability and Random variables
Refresh on Measurement, uncertainty and its propagation
Refresh on 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
Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html
Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre
Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre
readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html
Programme
Group Theory (CA)SU(2) and SU(3)
The Killing Form
Simple Lie Algebras
Representations
Simple Roots and the Cartan Matrix
The Classical Lie Algebras
The Exceptional Lie Algebras
Casimir Operators and Freudenthal’s Formula
The Weyl Group
Weyl’s Dimension Formula
Reducing Product Representations
Subalgebras
Branching Rules
Numerical Methods
Refresh on Probability and Random variables
Refresh on Measurement, uncertainty and its propagation
Refresh on 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
Sections of the textbooks for each topic are listed on http://webusers.fis.uniroma3.it/franceschini/cmm.html
Core Documentation
Robert Cahn - Semi-Simple Lie Algebras and Their Representations - Dover Publications 2014 (available at Roma TRE BAST Sede Centrale and from the author's web page )
Weinzierl, S. - Introduction to Monte Carlo methods arXiv:hep-ph/0006269
Taylor, J. - An introduction to error analysis - University Science Books Sausalito, California Disponibile nella biblioteca Scientifica di Roma Tre
Dubi, A. - Monte Carlo applications in systems engineering - Wiley Disponibile nella biblioteca Scientifica di Roma Tre
readings supplied during class and listed on the web http://webusers.fis.uniroma3.it/franceschini/cmm.html
Type of delivery of the course
Lectures in the classroom and in the computer lab. Exercises sessions in the classroom, computer lab, and at home.Type of evaluation
Oral and written examination. The written exam requires to write a short computer program to solve a problem in group theory or in numerical methods. The oral exam is a discussion on the topics of the syllabus and a presentation given by the student on a topic to be agreed upon. During the oral examination the student will be asked to state and prove properties of Lie Algebras and their representations, as illustrated during class, or to describe a numerical method in the syllabus giving details on its aim and properties. Possible topics for the presentations will be presented each year on the group theory and numerical methods material presented during the class. Topics for the presentations are listed each year on http://webusers.fis.uniroma3.it/franceschini/cmm.html