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| MATH0054-1 | Compléments de mathématique
- Analysis II, 1st part
- Statistics of experimental data in physics
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| Duration : | Analysis II, 1st part : 30h Th, 30h Pr
Statistics of experimental data in physics : 22,5h Th, 15h Pr
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| Credits/ECTS : |
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| Holder(s) : | Analysis II, 1st part : Françoise Bastin
Statistics of experimental data in physics : Paul Gérard
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| Language : | Langue française |
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| Course contents : |
 | | Analysis II, 1st part |
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| Short table of contents.
-Uniform convergence.
-Integrales 'Euleriennes'
-Integrable and square integrable functions.
-Convolution of functions.
-Fourier transforms.
-Trigonometric Fourier series.
-Orthogonal bases in infinite dimensional spaces.
-Applications. |
| | Statistics of experimental data in physics |
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| The course is devoted to the fundamentals of probability theory and gives an introduction to statistical data analysis.
Probability theory: discussion about the meaning of the word "probability", random events, Kolmogorov's axiomatic definition of probability, independence of events, conditional probability, sensitivity and specificity of a binary test, positive and negative predictive values, random variables and usual distributions, multivariate distributions, conditional distributions, independence, expectation and variance, conditional expectation and variance, linear regression, laws of great numbers, central limit theorems, characteristic function.
Introduction to statistics: populations and samples, descriptive statistics (graphical techniques, estimates of position and of dispersion, correlation and regression), sampling theory and estimation (confidence intervals), introduction to statistical tests. |
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| Course objective : |
| | Analysis II, 1st part |
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| The purpose of the course is to present standard techniques of analysis with theoritical mathematical support, with the aim of being carefully used in applications. |
| | Statistics of experimental data in physics |
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| The main goal of the course is to have a first but rigourous look to probability theory in order to prepare the comprehension of some main applications in physics (quantum mechanics, statistical physics). Some elements of descriptive statistics will help to be reactive with experimental data. Elements of sampling theory will prepare to inferential statistics. |
| | Statistics of experimental data in physics |
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| The main goal of the course is to have a first but rigourous look to probability theory in order to prepare the comprehension of some main applications in physics (quantum mechanics, statistical physics). Some elements of descriptive statistics will help to be reactive with experimental data. Elements of sampling theory will prepare to inferential statistics. |
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| Prerequisites : |
| | Analysis II, 1st part |
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| Knowledge of basic analysis (series, functions of one and more than one variables, integration, differentiation, ... ) |
| | Statistics of experimental data in physics |
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| Elements of set theory, differential and integral calculus. |
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| Workshops : |
| | Analysis II, 1st part |
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| Many exercices will be presented and suggested to students following a precise schedule (available at the beginning of the academic year). |
| | Statistics of experimental data in physics |
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| Exercices on probability theory: discussion questions, class exercices and problems. Treament of experimental data: applications of the classic tools of descriptive statistics , introduction to the Statistica software. |
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| Organization : |
| | Analysis II, 1st part |
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| The precise schedule will be available no later than at the middle of next September. |
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| Written notes : |
| | Analysis II, 1st part |
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| Notes de cours:
-Analyse mathématique, Introduction aux espaces fonctionnels, J. Schmets.
Ces notes sont disponibles dès le début du cours.
-Cahier d'exercices: Exercices d'analyse mathématique, Notes du cours de la seconde candidature en sciences mathématiques et en sciences physiques, F. Bastin - J.P. Schneiders.
Ce fascicule d'exercices est disponible dès le début des séances de répétition.
-De nombreuses références sont indiquées au cours et dans les notes de cours. |
| | Statistics of experimental data in physics |
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| Synthetic notes on the course are available for photocopy
Reference book:
Initiation aux probabilités
by Sheldon Ross
Presses polytechniques romandes |
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| Assessment : |
| | Analysis II, 1st part |
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| Everything is organized following the official academic division between periods of sessions and examinations. Written and oral exams will be organized.
''Local '' precisions could be added after a meeting of the Departement. |
| | Statistics of experimental data in physics |
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| Written (exercices) examination and oral (theory) examination |
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| Contacts : |
| | Analysis II, 1st part |
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| Françoise BASTIN,
Institute of Mathematics, B37
Tel 04 366 94 74
email F.Bastin@ulg.ac.be
(Secretary Department:
04 366 94 10)
Samuel NICOLAY
Institute of Mathematics, B37
Tel 04 366 94 33
email S.Nicolay@ulg.ac.be |
| | Statistics of experimental data in physics |
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| Paul GERARD: Institut de mathématique, B37 , Sart Tilman, B-4000 Liège
paul.gerard@ulg.ac.be
Tél: 00-32-(0)43-366.93.84
Laetitia COMTE: Institut de mathématique, B37 , Sart Tilman, B-4000 Liège
l.comte@ulg.ac.be(l.comte@ulg.ac.be)
Tél: 00-32-(0)43-366.94.60 |
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