Download or read book Model and Mathematics From the 19th to the 21st Century written by Michael Friedman and published by Birkhäuser. This book was released on 2022-07-05 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models. This book is open access under a CC BY 4.0 license.
Download or read book Mathematical Modelling written by Murray S. Klamkin and published by SIAM. This book was released on 1987-01-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for classroom use, this book contains short, self-contained mathematical models of problems in the physical, mathematical, and biological sciences first published in the Classroom Notes section of the SIAM Review from 1975-1985. The problems provide an ideal way to make complex subject matter more accessible to the student through the use of concrete applications. Each section has extensive supplementary references provided by the editor from his years of experience with mathematical modelling.
Download or read book Modeling with Mathematics written by Nancy Butler Wolf and published by Heinemann Educational Books. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Nancy's in-depth look at mathematical modeling offers middle school teachers the kind of practical help they need for incorporating modeling into their classrooms." -Cathy Seeley, Past President of NCTM, author of Faster Isn't Smarter and Smarter Than We Think "This is the book that math teachers and parents have been waiting for. Nancy provides a comprehensive step-by-step guide to modeling in mathematics at the middle school level." -David E. Drew, author of STEM the Tide: Reforming Science, Technology, Engineering, and Math Education in America We all use math to analyze everyday situations we encounter. Whether we realize it or not, we're modeling with mathematics: taking a complex situation and figuring out what we need to make sense of it. In Modeling with Mathematics, Nancy Butler Wolf shows that math is most powerful when it means something to students. She provides clear, friendly guidance for teachers to use authentic modeling projects in their classrooms and help their students develop key problem-solving skills, including: collecting data and formulating a mathematical model interpreting results and comparing them to reality learning to communicate their solutions in meaningful ways. This kind of teaching can be challenging because it is open-ended: it asks students to make decisions about their approach to a scenario, the information they will need, and the tools they will use. But Nancy proves there is ample middle ground between doing all of the work for your students and leaving them to flail in the dark. Through detailed examples and hands-on activities, Nancy shows how to guide your students to become active participants in mathematical explorations who are able to answer the question, "What did I just figure out?" Her approach values all students as important contributors and shows how instruction focused on mathematical modeling engages every learner regardless of their prior history of success or failure in math.
Download or read book Concepts of Mathematical Modeling written by Walter J. Meyer and published by Courier Corporation. This book was released on 2012-10-23 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each section is preceded by an abstract and statement of prerequisites, and answers or hints are provided for selected exercises. 1984 edition.
Download or read book Mathematical Modelling Education and Sense making written by Gloria Ann Stillman and published by Springer Nature. This book was released on 2020-05-14 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume documents on-going research and theorising in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in people’s everyday lives as well as sophisticated new problems for society at large. Mathematical modelling and real world applications are considered as having potential for cultivating sense making in classroom settings. This book focuses on the educational perspective, researching the complexities encountered in effective teaching and learning of real world modelling and applications for sense making is only beginning. All authors of this volume are members of the International Community of Teachers of Mathematical Modelling (ICTMA), the peak research body into researching the teaching and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace.
Download or read book Methods of Mathematical Modelling written by Thomas Witelski and published by Springer. This book was released on 2015-09-18 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Download or read book Mathematical Modelling in Education Research and Practice written by Gloria Ann Stillman and published by Springer. This book was released on 2015-07-20 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume cultural, social and cognitive influences on the research and teaching of mathematical modelling are explored from a variety of theoretical and practical perspectives. The authors of the current volume are all members of the International Community of Teachers of Mathematical Modelling and Applications, the peak research body in this field. A distinctive feature of this volume is the high number of authors from South American countries. These authors bring quite a different perspective to modelling than has been showcased in previous books in this series, in particular from a cultural point of view. As well as recent international research, there is a strong emphasis on pedagogical issues including those associated with technology and assessment, in the teaching and learning of modelling. Applications at various levels of education are exemplified. The contributions reflect common issues shared globally and represent emergent or on-going challenges.
Download or read book A Primer on Mathematical Modelling written by Alfio Quarteroni and published by Springer Nature. This book was released on 2020-10-09 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers. A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites. This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio This book is addressed to any student interested in learning how to construct and apply mathematical models.
Download or read book Trends in Teaching and Learning of Mathematical Modelling written by Gabriele Kaiser and published by Springer Science & Business Media. This book was released on 2011-06-23 with total page 711 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains suggestions for and reflections on the teaching, learning and assessing of mathematical modelling and applications in a rapidly changing world, including teaching and learning environments. It addresses all levels of education from universities and technical colleges to secondary and primary schools. Sponsored by the International Community of Teachers of Mathematical Modelling and Applications (ICTMA), it reflects recent ideas and methods contributed by specialists from 30 countries in Africa, the Americas, Asia, Australia and Europe. Inspired by contributions to the Fourteenth Conference on the Teaching of Mathematical Modelling and Applications (ICTMA14) in Hamburg, 2009, the book describes the latest trends in the teaching and learning of mathematical modelling at school and university including teacher education. The broad and versatile range of topics will stress the international state-of-the-art on the following issues: Theoretical reflections on the teaching and learning of modelling Modelling competencies Cognitive perspectives on modelling Modelling examples for all educational levels Practice of modelling in school and at university level Practices in Engineering and Applications
Download or read book Learning How to Teach Mathematical Modeling in School and Teacher Education written by Rita Borromeo Ferri and published by Springer. This book was released on 2017-11-26 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This timely resource fills a gap in existing literature on mathematical modeling by presenting both theory- and evidence-based ideas for its teaching and learning. The book outlines four key professional competencies that must be developed in order to effectively and appropriately teach mathematical modeling, and in so doing it seeks to reduce the discrepancies between educational policy and educational research versus everyday teaching practice. Among the key competencies covered are: Theoretical competency for practical work. Task competency for instructional flexibility. Instructional competency for effective and quality lessons. Diagnostic competency for assessment and grading. Learning How to Teach Mathematical Modeling in School and Teacher Education is relevant to practicing and future mathematics teachers at all levels, as well as teacher educators, mathematics education researchers, and undergraduate and graduate mathematics students interested in research based methods for teaching mathematical modeling.
Download or read book Modelling Nature written by Edward Gillman and published by CABI. This book was released on 2019-05-30 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This short textbook introduces students to the concept of describing natural systems using mathematical models. We highlight the variety of ways in which natural systems lend themselves to mathematical description and the importance of models in revealing fundamental processes. The process of science via the building, testing and use of models (theories) is described and forms the structure of the book. The book covers a broad range from the molecular to ecosystems and whole-Earth phenomena. Themes running through the chapters include scale (temporal and spatial), change (linear and nonlinear), emergent phenomena and uncertainty. Mathematical descriptions are kept to a minimum and we illustrate mechanisms and results in graphical form wherever possible. Essential mathematical details are described fully, with the use of boxes. The mathematics supports but does not lead the text.
Download or read book On the Mathematics of Modelling Metamodelling Ontologies and Modelling Languages written by Brian Henderson-Sellers and published by Springer Science & Business Media. This book was released on 2012-06-13 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computing as a discipline is maturing rapidly. However, with maturity often comes a plethora of subdisciplines, which, as time progresses, can become isolationist. The subdisciplines of modelling, metamodelling, ontologies and modelling languages within software engineering e.g. have, to some degree, evolved separately and without any underpinning formalisms. Introducing set theory as a consistent underlying formalism, Brian Henderson-Sellers shows how a coherent framework can be developed that clearly links these four, previously separate, areas of software engineering. In particular, he shows how the incorporation of a foundational ontology can be beneficial in resolving a number of controversial issues in conceptual modelling, especially with regard to the perceived differences between linguistic metamodelling and ontological metamodelling. An explicit consideration of domain-specific modelling languages is also included in his mathematical analysis of models, metamodels, ontologies and modelling languages. This encompassing and detailed presentation of the state-of-the-art in modelling approaches mainly aims at researchers in academia and industry. They will find the principled discussion of the various subdisciplines extremely useful, and they may exploit the unifying approach as a starting point for future research.
Download or read book Mathematics for Dynamic Modeling written by Edward Beltrami and published by Academic Press. This book was released on 2014-05-10 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics for Dynamic Modeling provides an introduction to the mathematics of dynamical systems. This book presents the mathematical formulations in terms of linear and nonlinear differential equations. Organized into two parts encompassing nine chapters, this book begins with an overview of the notions of equilibrium and stability in differential equation modeling that occur in the guise of simple models in the plane. This text then focuses on nonlinear models in which the limiting behavior of orbits can be more complicated. Other chapters consider the problems that illustrate the concepts of equilibrium and stability, limit cycles, chaos, and bifurcation. This book discusses as well a variety of topics, including cusp catastrophes, strange attractors, and reaction–diffusion and shock phenomena. The final chapter deals with models that are based on the notion of optimization. This book is intended to be suitable for students in upper undergraduate and first-year graduate course in mathematical modeling.
Download or read book Mathematical Modelling and Applications written by Gloria Ann Stillman and published by Springer. This book was released on 2017-11-05 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume documents on-going research and theorising in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in the life world of people whether these range from the everyday individual numeracy level to sophisticated new problems for society at large. Mathematical modelling and real world applications are considered as having potential for multi-disciplinary work that involves knowledge from a variety of communities of practice such as those in different workplaces (e.g., those of educators, designers, construction engineers, museum curators) and in different fields of academic endeavour (e.g., history, archaeology, mathematics, economics). From an educational perspective, researching the development of competency in real world modelling involves research situated in crossing the boundaries between being a student engaged in modelling or mathematical application to real word tasks in the classroom, being a teacher of mathematical modelling (in or outside the classroom or bridging both), and being a modeller of the world outside the classroom. This is the focus of many of the authors of the chapters in this book. All authors of this volume are members of the International Community of Teachers of Mathematical Modelling (ICTMA), the peak research body into researching the teaching and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace.
Download or read book Mathematical Modeling written by Christof Eck and published by Springer. This book was released on 2017-04-11 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.
Download or read book Teaching Mathematical Modelling Connecting to Research and Practice written by Gloria Ann Stillman and published by Springer Science & Business Media. This book was released on 2013-10-27 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with an overview of recent international research and developments in the teaching and learning of modelling and applications from a variety of theoretical and practical perspectives. There is a strong focus on pedagogical issues for teaching and learning of modelling as well as research into teaching and practice. The teaching of applications of mathematics and mathematical modelling from the early years through primary and secondary school and at tertiary level is rising in prominence in many parts of the world commensurate with an ever-increasing usage of mathematics in business, the environment, industry and everyday life. The authors are all members of the International Community of Teachers of Mathematical Modelling and Applications and important researchers in mathematics education and mathematics. The book will be of interest to teachers, practitioners and researchers in universities, polytechnics, teacher education, curriculum and policy.
Download or read book Multidisciplinary Mathematical Modelling written by Francesc Font and published by Springer Nature. This book was released on 2021-04-13 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a selection of the talks resulting from research carried out by different groups at the Centre de Recerca Matemàtica and presented at the International Congress on Industrial and Applied Mathematics, held in Valencia in 2019. The various chapters describe a wide variety of topics: cancer modelling, carbon capture by adsorption, nanoscale diffusion and complex systems to predict earthquakes. These mathematical studies were specifically aided via collaborations with biomedical engineers, physicists and chemists. The book is addressed to researchers in all of these areas as well as in general mathematical modelling.
