Commutative Algebra (lecture notes, Master in Mathematics, Master in Secondary Education)

Learning material (2022)

These are the lecture notes for the course Commutative Algebra in the Master in Mathematics and the Master in Secondary Education at the University of Luxembourg. Last update: winter term 2022.

Algèbre linéaire 2 (BMATH 2021)

Learning material (2021)

Algorithmic Decision Theory: Lecture notes and presentation slides

Learning material (2020)

The objective of this course is to introduce students to ADT, a new interdisciplinary field at the intersection of decision theory, discrete mathematics, theoretical computer science and artificial ... [more ▼]

The objective of this course is to introduce students to ADT, a new interdisciplinary field at the intersection of decision theory, discrete mathematics, theoretical computer science and artificial intelligence. ADT proposes new ideas, approaches and tools for supporting decision making processes in presence of massive databases, combinatorial structures, partial and/or uncertain information, and distributed, possibly inter-operating, decision makers. Such problems arise in several real-world decision making problems such as humanitarian logistics, epidemiology, risk assessment and management, e-government, electronic commerce, and the implementation of recommender systems [less ▲]

Algèbre (notes du cours, 3ème semestre BMATH)

Learning material (2020)

These are the lecture notes for the lecture `Algèbre' in the 3rd semester of the Bachelor in Mathematics at the University of Luxembourg. Last update: winter term 2020.

Russia and Luxembourg in XX century. Crossroads of history

Learning material (2019)

The course presentation contains the concept of the bilateral seminar for the students of the University of Luxembourg and the University of Tambov which was conducted 2018-2019 in Luxemburg and Tambov on ... [more ▼]

The course presentation contains the concept of the bilateral seminar for the students of the University of Luxembourg and the University of Tambov which was conducted 2018-2019 in Luxemburg and Tambov on site and 2020 online. The historical connection between two cities through the prisoners of war and the civil forced labourers from 1942 until 1944 and their exchange in 1945 created a base for the deeper research in this intersection and the search for the other ones. [less ▲]

Computational Statistics: Lecture notes and presentation slides

Learning material (2018)

The objective of this course is to introduce the students to the R language and environment for statistical computing and graphics (a GNU project). In particular, the course proposes effective data ... [more ▼]

The objective of this course is to introduce the students to the R language and environment for statistical computing and graphics (a GNU project). In particular, the course proposes effective data handling and storage solutions as well as useful operators for calculations on arrays, in particular matrices. A selected collection of intermediate tools for data analysis, graphical facilities for data analysis and display either on-screen or on hard copy will be illustrated from examples of statistical analyses. Finally, the course will by the way acquaint the students with a well-developed, simple and effective programming language which includes conditionals, loops, user-defined recursive functions and input and output facilities. [less ▲]

Towards a seamless Integration of CAD and Simulation: CISM Course 2017

Learning material (2017)

Isogeometric analysis relies on the use of the same basis functions as employed in Computer Aided Design (CAD). This offers the possibility to facilitate design and optimisation. The previous course ... [more ▼]

Isogeometric analysis relies on the use of the same basis functions as employed in Computer Aided Design (CAD). This offers the possibility to facilitate design and optimisation. The previous course “Isogeometric methods for numerical simulation” held in 2013 had the aim to give an introduction to isogeometric analysis, its advantages, drawbacks and to the range of its applications. The aim of the proposed new course will be different. The focus will be more on the connection of simulation to CAD systems and how CAD data can be used directly for simulation, leading to a seamless integration. An overview of recent advances and applications will be also presented. The course will start with an introduction to NURBS and their use in describing geometry and in simulation. This will be followed by lectures from a CAD vendor describing the current state of development. Currently available connections to simulation software will also be discussed. Next the use of NURBS for 3D structural analysis, structural optimisation and damage tolerance assessment will be presented, including such advanced topics as the treatment of discontinuities and real-time solvers. It will also be discussed when it might be advantageous to decouple the boundary discretisation from the field variable discretisation, in particular in shape optimisation. Isogeometric methods for the analysis of beam and shell structures, including shape optimisation and fluid structure interaction, will be presented. Lectures on the mathematical and algorithmic foundations of analysis-suitable geometry will follow. This includes an introduction to T-splines and multilevel spline schemes such as hierarchical B- splines. Common analysis-suitable spline algorithms will be presented in the context of Bézier extraction and projection as well as its application as a foundation for integrated engineering design and analysis. An important aspect of analysis-suitable geometry is the ability to locally adapt the smooth spline basis. Several common refinement algorithms will be reviewed as well as their application in several demanding areas of application. The emerging area of weak geometry will be introduced as well as its application to the rapid construction of complex structural assemblies. With the rapid development of isogeometric analysis in recent years, there is an urgent need for volumetric parameterization such as volumetric T-spline model construction. Several volumetric T- spline modeling techniques, that were developed in recent years will be presented. They include converting any quad/ hex meshes to standard and rational T-splines, polycube-based parametric mapping, feature preservation using eigenfunctions, Boolean operations and skeletons, truncated hierarchical Catmull-Clark subdivision, weighted T-splines, conformal T-spline modeling, as well as incorporating T-splines into commercial CAD and FEA software, will be presented. The target audience will be engineers, interested in simulation, software developers and researchers. [less ▲]

Comité économique et financier

Learning material (2017)

Algebraic Curves

Learning material (2017)

Séance 5. Une approche originale des marchés régulés

Learning material (2017)

La procédure concernant les déficits excessifs

Learning material (2017)

Séance 2. Règles de fonctionnement et d'organisation du marché intérieur

Learning material (2017)

Tutorial Reproducible Research at the Cloud Era: Overview, Hands-on and Open challenges

Learning material (2016)

The term Reproducible Research (RR) refers to “the idea that the ultimate product of academic research is the paper along with the full computational environment used to produce the results in the paper ... [more ▼]

The term Reproducible Research (RR) refers to “the idea that the ultimate product of academic research is the paper along with the full computational environment used to produce the results in the paper such as the code, data, etc. that can be used to reproduce the results and create new work based on the research.” Source: Wikipedia. The need for reproducibility is increasing dramatically as data analyses become more complex, involving larger datasets and more sophisticated computations. Obviously, the advent of the Cloud Computing paradigm is expected to provide the appropriate means for RR. This tutorial is meant to provide an overview of sensible tools every researcher (in computer science but not only) should be aware of to enable RR in its own work. In particular, and after a general talk presenting RR and the existing associated tools and workflow, this tutorial will propose several practical exercises and hands-on meant to be performed on each attendee’s laptop, to cover the management of sharable Development environment using Vagrant. Resources of this tutorial will be available on Github. [less ▲]

Expressions & relations mathématiques élémentaires

Learning material (2016)

Ce texte introduit les outils de base des mathématiques que sont les expressions algébriques et numériques. Les nombres réels, les opérations sur les nombres, les moyennes, les sommes partielles de ... [more ▼]

Ce texte introduit les outils de base des mathématiques que sont les expressions algébriques et numériques. Les nombres réels, les opérations sur les nombres, les moyennes, les sommes partielles de termes de suites particulières, les polynômes ou la factorisation des expressions algébriques sont à compter parmi les thèmes abordés. La structure des notes vise à accompagner le lecteur au travers de ces éléments théoriques et à lui permettre de développer ses compétences mathématiques par la réalisation des nombreux exercices proposés. [less ▲]

Algebraic Number Theory (Lecture Notes)

Learning material (2016)

These are lecture notes for the course Algebraic Number Theory taught in the Master in Mathematics and Master in Secondary Education at the University of Luxembourg.

Mobilité transfrontalière des salariés luxembourgeois - Retour sur le cadre fiscal et social en vigueur

Learning material (2015)

Algèbre 1 (BASI filière mathématiques, 2015)

Learning material (2015)

Course notes with exercises from the lecture Algèbre 1, taught in the BASI track mathematics at the University of Luxembourg in 2015.

Local Fields

Learning material (2015)

These lecture notes correspond to the course Local Fields from the Master in Mathematics of the University of Luxembourg, taught in the Winter Term 2015. It consists of 14 lectures of 90 minutes each ... [more ▼]

These lecture notes correspond to the course Local Fields from the Master in Mathematics of the University of Luxembourg, taught in the Winter Term 2015. It consists of 14 lectures of 90 minutes each. This lecture belongs to the fourth semester of the Master, and it builds on the lectures Commutative Algebra and Algebraic Number Theory, belonging to the first and second semester respectively. The aim of the lecture is to explain the basic theory of local fields, and apply this theory to obtain information about number fields. [less ▲]

Introduction to the eXtended Discrete Element Method

Learning material (2014)

Riemann Surfaces. Lecture notes. Winter semester 2014/2015.

Learning material (2014)

This is a preliminary version of lecture notes for the course 'Riemann surfaces' (14 Lectures, 90 minutes each). The lectures are provided with exercises.

The complex torus and elliptic curves: Lecture notes

Learning material (2014)

Lecture notes on Weierstrass uniformization of complex elliptic curves.

Éléments de théorie de Lie

Learning material (2013)

Commutative Algebra (Master in Mathematics, 2013)

Learning material (2013)

Lecture notes from the 1st year of Master in Mathematics at the University of Luxembourg. Rings of integers of number fields and coordinate rings of plane curves are the central examples around which the ... [more ▼]

Lecture notes from the 1st year of Master in Mathematics at the University of Luxembourg. Rings of integers of number fields and coordinate rings of plane curves are the central examples around which the theory is developed: integrality, noetherian rings, localisation, Noether normalisation, Hilbert's Nullstellensatz, etc. [less ▲]

Algèbre 3 (théorie des corps et théorie de Galois)

Learning material (2012)

Lecture notes written in French from the Algebra 3 lecture in the 3rd term of the Bachelor programme BASI branch Mathematics (old version) at the University of Luxembourg. The lecture covers field theory ... [more ▼]

Lecture notes written in French from the Algebra 3 lecture in the 3rd term of the Bachelor programme BASI branch Mathematics (old version) at the University of Luxembourg. The lecture covers field theory and Galois theory and includes a treatment of the solvability of equations by radicals and a treatment of classical construction problems with ruler and compass. [less ▲]

Mathématique physique 3

Learning material (2008)

Mécanique des solides déformables

Learning material (2000)

Vertexalgebren eine Einführung

Learning material (1997)

Das Leben in der mittelalterlichen Stadt : Materalien für den projektorientierten Geschichtsunterricht

Learning material (1992)