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Commutative Algebra (lecture notes, Master in Mathematics, Master in Secondary Education) Wiese, Gabor 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. Detailed reference viewed: 225 (16 UL)Strategies of non-formal education in the life course - from early childhood through adolescence and into adulthood! Schumacher, Anette ; Biewers, Sandra Learning material (2021) Detailed reference viewed: 37 (4 UL)Algèbre linéaire 2 (BMATH 2021) Wiese, Gabor Learning material (2021) Detailed reference viewed: 168 (17 UL)Lecture notes on Algebraic Geometry Kalugin, Alexey Learning material (2020) Lecture notes for the course given by the author at the University of Luxembourg during the winter term 2020. Detailed reference viewed: 58 (3 UL)Algorithmic Decision Theory: Lecture notes and presentation slides Bisdorff, Raymond 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 ▲] Detailed reference viewed: 248 (18 UL)Number Theory for Cryptography (Lecture Notes) Wiese, Gabor Learning material (2020) In these lectures (8 hours taught in November 2020), we mention some topics from (algebraic) number theory as well as some related concepts from (algebraic) geometry that can be useful in cryptography. We ... [more ▼] In these lectures (8 hours taught in November 2020), we mention some topics from (algebraic) number theory as well as some related concepts from (algebraic) geometry that can be useful in cryptography. We cannot go deeply into any of the topics and most results will be presented without any proofs. One of the things that one encounters are `ideal lattices'. In the examples I saw, this was nothing but (an ideal in) an order in a number field, which is one of the concepts that we present here in its mathematical context (i.e. embedded in a conceptual setting). It has been noted long ago (already in the 19th century) that number fields and function fields of curves have many properties in common. Accordingly, we shall also present some basic topics on affine plane curves and their function fields. This leads us to mention elliptic curves, however, only in an affine version (instead of the better projective one); we cannot go deeply into that topic at all. The material presented here is classical and very well known. [less ▲] Detailed reference viewed: 72 (9 UL)Algèbre (notes du cours, 3ème semestre BMATH) Wiese, Gabor 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. Detailed reference viewed: 146 (9 UL)Modelling Complex Systems: a primer - agent-based models, equation-based models, statistical models and Bayesian inference, digital twins Bordas, Stéphane Learning material (2019) Modelling Complex Systems: a primer - agent-based models, equation-based models, statistical models and Bayesian inference, digital twins Detailed reference viewed: 591 (24 UL)Особенности русской и английской речи детей-билингвов Ganschow, Inna ; Learning material (2019) В центре магистерской работы находился феномен детского билингвизма как динамичного явления в речевом развитии ребенка. Информанты с рождения взаимодействуют со взрослыми, родными для которых являются ... [more ▼] В центре магистерской работы находился феномен детского билингвизма как динамичного явления в речевом развитии ребенка. Информанты с рождения взаимодействуют со взрослыми, родными для которых являются разные (неродственные) языки – русский и английский.At the center of the master's work was the phenomenon of children's bilingualism as a dynamic phenomenon in the speech development of a child. From birth, informants interact with adults whose native languages are different (unrelated) languages - Russian and English. [less ▲] Detailed reference viewed: 77 (2 UL)Russia and Luxembourg in XX century. Crossroads of history Ganschow, Inna ; 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 ▲] Detailed reference viewed: 47 (1 UL)Computational Statistics: Lecture notes and presentation slides Bisdorff, Raymond 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 ▲] Detailed reference viewed: 743 (12 UL)skill training digital source criticism Doctoral Training Unit digital hermeneutics Scagliola, Stefania Learning material (2017) The skills training is organized by the DHH doctoral training unit and will be led by Prof. Andreas Fickers, Dr. Stefania Scagliola and Andy O’Dwyer. It consists of a two-day program, in which lectures ... [more ▼] The skills training is organized by the DHH doctoral training unit and will be led by Prof. Andreas Fickers, Dr. Stefania Scagliola and Andy O’Dwyer. It consists of a two-day program, in which lectures and theoretical discussions are combined with hands-on demonstrations and group experiments. The first day is dedicated to literature and to making sketches and drawings of how the digital affects the nature of a historical source. The second day the participants are going to digitize various datatypes and reflect on their observations of this process and the differences between data types. The last part of the training consists of a crowdsourcing experiment in which the genealogy of the term Digital Source Criticism is going to be traced and documented. [less ▲] Detailed reference viewed: 64 (2 UL)Towards a seamless Integration of CAD and Simulation: CISM Course 2017 Bordas, Stéphane 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 ▲] Detailed reference viewed: 857 (21 UL)Rahmenplan zur nonformalen Bildung im Kindes- und Jugendalter Biewers, Sandra Learning material (2017) Detailed reference viewed: 118 (7 UL)Basic Algebraic Structures - Lecture notes for the MICS Schlichenmaier, Martin Learning material (2017) Detailed reference viewed: 268 (12 UL)Séance 5. Une approche originale des marchés régulés Rassafi-Guibal, Hicham Learning material (2017) Detailed reference viewed: 59 (1 UL)Séance 2. Règles de fonctionnement et d'organisation du marché intérieur Rassafi-Guibal, Hicham Learning material (2017) Detailed reference viewed: 36 (0 UL)Séance 3. L'espace réservé aux aides d'État Rassafi-Guibal, Hicham Learning material (2017) Detailed reference viewed: 40 (1 UL)Comité économique et financier Rassafi-Guibal, Hicham Learning material (2017) Detailed reference viewed: 37 (0 UL)La procédure concernant les déficits excessifs Rassafi-Guibal, Hicham Learning material (2017) Detailed reference viewed: 36 (0 UL)Politique de la concurrence Rassafi-Guibal, Hicham Learning material (2017) Detailed reference viewed: 93 (0 UL)Linear Algebra 2 Wiese, Gabor ; Notarnicola, Luca ; Notarnicola, Massimo Learning material (2017) Detailed reference viewed: 209 (31 UL)Algebraic Curves Schlichenmaier, Martin Learning material (2017) Detailed reference viewed: 119 (4 UL)Tutorial Reproducible Research at the Cloud Era: Overview, Hands-on and Open challenges Varrette, Sébastien 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 ▲] Detailed reference viewed: 51 (1 UL)Rahmenplan zur nonformalen Bildung im Kindes und Jugendalter Biewers, Sandra Learning material (2016) Detailed reference viewed: 72 (1 UL)Expressions & relations mathématiques élémentaires Korvers, Stéphane 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 ▲] Detailed reference viewed: 78 (4 UL)Value Stream Management Training Plapper, Peter ; Oberhausen, Christof Learning material (2016) The VSM workshop deals with concepts in the area of Value Stream Management, comprising the analysis, design and optimization of internal material and information flows. The VSM workshop was held by Prof ... [more ▼] The VSM workshop deals with concepts in the area of Value Stream Management, comprising the analysis, design and optimization of internal material and information flows. The VSM workshop was held by Prof. Dr.-Ing. Peter Plapper and M.Sc. Christof Oberhausen, who contribute a profound knowledge in Value Stream Management based on their ongoing research in this field. The one-day VSM workshop is targeted at an audience of 8-12 participants with a background in Lean Engineering or Operational Excellence. [less ▲] Detailed reference viewed: 139 (8 UL)Algebraic Number Theory (Lecture Notes) ; Wiese, Gabor 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. Detailed reference viewed: 48 (5 UL)Riemann Surfaces. Lecture notes. Winter semester 2015/2016. Iena, Oleksandr Learning material (2015) These are the lecture notes for the course 'Riemann surfaces' (14 Lectures, 90 minutes each). The lectures are provided with exercises. Detailed reference viewed: 128 (9 UL)Mobilité transfrontalière des salariés luxembourgeois - Retour sur le cadre fiscal et social en vigueur Chaouche, Fatima Learning material (2015) Detailed reference viewed: 131 (35 UL)Introduction to Git and Vagrant Varrette, Sébastien Learning material (2015) Detailed reference viewed: 39 (2 UL)Commutative Algebra (Master in Mathematics, 2015) Wiese, Gabor Learning material (2015) Lecture notes with exercise sheets from the lecture Commutative Algebra held in winter term 2015 in the Master in Mathematics at the University of Luxembourg. Detailed reference viewed: 104 (6 UL)Algèbre 1 (BASI filière mathématiques, 2015) Wiese, Gabor 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. Detailed reference viewed: 95 (2 UL)Local Fields Arias De Reyna Dominguez, Sara 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 ▲] Detailed reference viewed: 176 (0 UL)Géométrie (lieux géométriques et courbes paramétrées) Poncin, Norbert Learning material (2015) Detailed reference viewed: 109 (2 UL)Introduction to the eXtended Discrete Element Method Estupinan Donoso, Alvaro Antonio Learning material (2014) Detailed reference viewed: 120 (3 UL)Géométrie différentielle des surfaces Korvers, Stéphane Learning material (2014) Detailed reference viewed: 99 (4 UL)The complex torus and elliptic curves: Lecture notes Riviere, Salim Learning material (2014) Lecture notes on Weierstrass uniformization of complex elliptic curves. Detailed reference viewed: 102 (3 UL)Riemann Surfaces. Lecture notes. Winter semester 2014/2015. Iena, Oleksandr 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. Detailed reference viewed: 113 (35 UL)Mécanique quantique : notes de cours Jubin, Benoît Michel Learning material (2014) These notes are a summary of the course "Physical Mathematics 3: Quantum Mechanics" of the Bachelor of Mathematics of the University of Luxembourg given in the second semesters of the academic years 2012 ... [more ▼] These notes are a summary of the course "Physical Mathematics 3: Quantum Mechanics" of the Bachelor of Mathematics of the University of Luxembourg given in the second semesters of the academic years 2012--2013 and 2013--2014. [less ▲] Detailed reference viewed: 198 (7 UL)Riemann Surfaces. Lecture notes. Winter semester 2013/2014. Iena, Oleksandr Learning material (2013) This is a preliminary version of lecture notes for the course 'Riemann surfaces' (14 Lectures, 90 minutes each). Detailed reference viewed: 92 (18 UL)Éléments de théorie de Lie Korvers, Stéphane Learning material (2013) Detailed reference viewed: 94 (3 UL)Algèbre 1 (BASI filière mathématiques, 2013) Wiese, Gabor ; David, Agnès Learning material (2013) Lecture notes written in French from the Algebra 1 lecture in the 1st term of the Bachelor programme BASI branch Mathematics at the University of Luxembourg. The lecture starts with preliminaries on logic ... [more ▼] Lecture notes written in French from the Algebra 1 lecture in the 1st term of the Bachelor programme BASI branch Mathematics at the University of Luxembourg. The lecture starts with preliminaries on logic, sets and functions, it builds the natural numbers (almost) from the Peano axioms, then constructs the integers and the rationals. Groups and rings are introduced in that context. The most basic definitions and results from abstract linear algebra are also given. The course finishes with some basic group theory. [less ▲] Detailed reference viewed: 91 (3 UL)Commutative Algebra (Master in Mathematics, 2013) Wiese, Gabor 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 ▲] Detailed reference viewed: 94 (2 UL)Algebra 3 Arias De Reyna Dominguez, Sara Learning material (2013) These lecture notes correspond to the course Algebra 3 from the Bachelor en Sciences et Ingénierie, Filière mathématiques, of the University of Luxembourg. This course was taught in the Winter Term 2013 ... [more ▼] These lecture notes correspond to the course Algebra 3 from the Bachelor en Sciences et Ingénierie, Filière mathématiques, of the University of Luxembourg. This course was taught in the Winter Term 2013 and it consists of 14 lectures of 90 minutes each. This lecture belongs to the third semester of the Bachelor, and it builds on the lectures Algebra 1 and Algebra 2, belonging to the first and second semester respectively. The aim of this course is to introduce the students to the theory of algebraic extensions of fields, and culminates with the application of the theory to the solution (negative solution, in fact) of the three classical Greek problems concerning constructions with ruler and compass. This lecture is also a preliminary step towards Galois theory, which is taught in the fourth semester of the Bachelor. [less ▲] Detailed reference viewed: 211 (2 UL)Algèbre 3 (théorie des corps et théorie de Galois) Wiese, Gabor 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 ▲] Detailed reference viewed: 160 (8 UL)Mathématique physique 1 et 2 Poncin, Norbert Learning material (2008) Detailed reference viewed: 111 (5 UL)Mathématique physique 3 Poncin, Norbert Learning material (2008) Detailed reference viewed: 117 (9 UL)Mécanique des solides déformables Poncin, Norbert Learning material (2000) Detailed reference viewed: 70 (1 UL)Vertexalgebren eine Einführung Schlichenmaier, Martin Learning material (1997) Detailed reference viewed: 51 (0 UL)Operaden und Vertexalgebren Schlichenmaier, Martin Learning material (1997) Detailed reference viewed: 59 (1 UL)Das Leben in der mittelalterlichen Stadt : Materalien für den projektorientierten Geschichtsunterricht Margue, Michel ; Pauly, Michel Learning material (1992) Detailed reference viewed: 71 (0 UL) |
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