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industrial engineering --- operations research --- intelligent systems --- decision making --- mathematical modelling
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applied mathematics --- computational physics --- mathematical modelling --- computer science
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The main focus of this thesis is the discussion of stability of an objective (atomic) structure consisting of single atoms which interact via a potential. We define atomistic stability using a second derivative test. More precisely, atomistic stability is equivalent to a vanishing first derivative of the configurational energy (at the corresponding point) and the coerciveness of the second derivative of the configurational energy with respect to an appropriate semi-norm. Atomistic stability of a lattice is well understood, see, e.,g., [40]. The aim of this thesis is to generalize the theory to objective structures. In particular, we first investigate discrete subgroups of the Euclidean group, then define an appropriate seminorm and the atomistic stability for a given objective structure, and finally provide an efficient algorithm to check its atomistic stability. The algorithm particularly checks the validity of the Cauchy-Born rule for objective structures. To illustrate our results, we prove numerically the stability of a carbon nanotube by applying the algorithm.
Mathematical physics. --- Mathematics. --- Mathematical modelling --- theory and applications.
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applied mathematics --- numerical linear algebra --- stochastic systems --- differential equations --- mathematical modelling --- imaging and data analysis --- Mathematics --- Math --- Science
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This open access book presents a structural model and an associated test instrument designed to provide a detailed analysis of professional competences for teaching mathematical modelling. The conceptualisation is based on the COACTIV model, which describes aspects, areas and facets of professional competences of teachers. The manual provides an overview of the essential teaching skills in application-related contexts and offers the tools needed to capture these aspects. It discusses the objectives and application areas of the instrument, as well as the development of the test. In addition, it describes the implementation and evaluates the quality and results of the structural equation analysis of the model. Teaching mathematical modelling is a cognitively challenging activity for (prospective) teachers. Thus, teacher education requires a detailed analysis of professional competence for teaching mathematical modelling. Measuring this competence requires theoretical models that accurately describe requirements placed upon teachers, as well as appropriate evaluation tools that adequately capture skills and abilities in this field. This book presents an instrument that measures the professional competences in a sample of 349 prospective teachers.
Teaching of a specific subject --- Teacher training --- Education --- Teaching mathematical modelling --- Professional Competences for Teaching Mathematical Modelling --- COACTIV model --- professional competences of teachers --- BELIEFS ABOUT MATHEMATICAL MODELLING --- Test Instrument --- text vignette --- Formació del professorat --- Professors de matemàtica --- Professors --- Formació d'educadors --- Formació dels mestres --- Perfeccionament del professorat --- Formació --- Escoles normals --- Observació (Mètode d'ensenyament) --- Pràctiques pedagògiques
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This open access book is based on selected presentations from Topic Study Group 21: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics at the 13th International Congress on Mathematical Education (ICME 13), held in Hamburg, Germany on July 24–31, 2016. It contributes to the theory, research and teaching practice concerning this key topic by taking into account the importance of relations between mathematics and the real world. Further, the book addresses the “balancing act” between developing students’ modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. The contributions, prepared by authors from 9 countries, reflect the spectrum of international debates on the topic, and the examples presented span schooling from years 1 to 12, teacher education, and teaching modelling at the tertiary level. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught. Given its scope, the book will appeal to researchers and teacher educators in mathematics education, as well as pre-service teachers and school and university educators.
Mathematics. --- Mathematics Education. --- Learning & Instruction. --- Teaching and Teacher Education. --- Math --- Science --- Mathematics—Study and teaching . --- Learning. --- Instruction. --- Teaching. --- Didactics --- Instruction --- Pedagogy --- School teaching --- Schoolteaching --- Education --- Instructional systems --- Pedagogical content knowledge --- Training --- Learning process --- Comprehension --- Mathematics Education --- Learning & Instruction --- Teaching and Teacher Education --- Pedagogical issues of integration into classroom practice --- assessment of modelling competencies --- teachers as learners of mathematical modelling --- technological influences on modelling education --- managing group interactions in modelling --- mathematical model --- modelling problems --- heuristic strategies --- teaching mathematical modelling --- modelling competencies --- learning mathematics modelling --- interpretations modelling --- pedagogical practice and research --- modelling perspective --- teaching practices in mathematical modelling --- Open Access --- Teaching of a specific subject --- Mathematics --- Teaching skills & techniques --- Cognition & cognitive psychology --- Teacher training
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Business --- Manufacturing processes --- Data processing --- Automation --- Data processing. --- Automation. --- information technology --- automation --- mathematical modelling --- Electronic data processing --- Industrial processing --- Manufacture --- Process engineering (Manufactures) --- Processes, Manufacturing --- Processing, Industrial --- Production processes --- Industrial arts --- Production engineering --- Machine-tools --- Materials
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Modelling as Research Methodology is written for the scientist and student researching the (expected) functioning of systems under specified conditions. As such, it represents an introduction to the use of modelling in natural, human and economical sciences. The book is divided into two sections. The first section illustrates the universal nature of modelling as aid to the researcher. In the second section, several typical examples of modelling are described.
Research methods: general --- modelling --- mathematical modelling --- physical modelling --- science and knowledge --- types of models --- human and economic sciences --- humanities --- business and human sciences --- modelling of terrains and structures --- mechatronic design process --- data acquisition
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Statistical decision --- Decision making --- Decision making. --- Statistical decision. --- Mathematical Sciences --- Applied Mathematics --- Economic growth --- Business policy --- Zarządzanie --- Badania operacyjne --- Decision problems --- Game theory --- Operations research --- Statistics --- Management science --- Deciding --- Decision analysis --- Decision processes --- Decision (Psychology) --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- mathematical modelling --- forecasting --- econometrics and statistical methods --- optimization --- computer applications in optimization
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Engineering --- Computer simulation --- Computer simulation. --- Mathematical models --- Mathematical models. --- Mathematics --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Construction --- Electromechanical analogies --- Simulation methods --- Model-integrated computing --- Industrial arts --- Technology --- Information Technology --- Mathematical Sciences --- Civil Engineering --- General and Others --- mathematics --- mathematical modelling --- dynamical systems --- complex systems
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