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Modeling with Mathematics

Author: Nancy Butler Wolf

Publisher: Heinemann Educational Books

Published: 2015

Total Pages: 0

ISBN-13: 9780325062594

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"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.

Book Synopsis Modeling with Mathematics by : Nancy Butler Wolf

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.

Concepts of Mathematical Modeling

Author: Walter J. Meyer

Publisher: Courier Corporation

Published: 2012-10-23

Total Pages: 450

ISBN-13: 0486137244

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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.

Book Synopsis Concepts of Mathematical Modeling by : Walter J. Meyer

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.

Model and Mathematics: From the 19th to the 21st Century

Author: Michael Friedman

Publisher: Birkhäuser

Published: 2022-07-05

Total Pages: 443

ISBN-13: 9783030978327

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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.

Book Synopsis Model and Mathematics: From the 19th to the 21st Century by : Michael Friedman

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.

Mathematics for Dynamic Modeling

Author: Edward Beltrami

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 294

ISBN-13: 1483267865

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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.

Book Synopsis Mathematics for Dynamic Modeling by : Edward Beltrami

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.

Modeling Life

Author: Alan Garfinkel

Publisher: Springer

Published: 2017-09-06

Total Pages: 445

ISBN-13: 3319597310

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This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?

Book Synopsis Modeling Life by : Alan Garfinkel

Download or read book Modeling Life written by Alan Garfinkel and published by Springer. This book was released on 2017-09-06 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?

Principles of Mathematical Modeling

Author: Clive Dym

Publisher: Elsevier

Published: 2004-08-10

Total Pages: 323

ISBN-13: 0080470289

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Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making. Prospective students should have already completed courses in elementary algebra, trigonometry, and first-year calculus and have some familiarity with differential equations and basic physics. Serves as an introductory text on the development and application of mathematical models Focuses on techniques of particular interest to engineers, scientists, and others who model continuous systems Offers more than 360 problems, providing ample opportunities for practice Covers a wide range of interdisciplinary topics--from engineering to economics to the sciences Uses straightforward language and explanations that make modeling easy to understand and apply New to this Edition: A more systematic approach to mathematical modeling, outlining ten specific principles Expanded and reorganized chapters that flow in an increasing level of complexity Several new problems and updated applications Expanded figure captions that provide more information Improved accessibility and flexibility for teaching

Book Synopsis Principles of Mathematical Modeling by : Clive Dym

Download or read book Principles of Mathematical Modeling written by Clive Dym and published by Elsevier. This book was released on 2004-08-10 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making. Prospective students should have already completed courses in elementary algebra, trigonometry, and first-year calculus and have some familiarity with differential equations and basic physics. Serves as an introductory text on the development and application of mathematical models Focuses on techniques of particular interest to engineers, scientists, and others who model continuous systems Offers more than 360 problems, providing ample opportunities for practice Covers a wide range of interdisciplinary topics--from engineering to economics to the sciences Uses straightforward language and explanations that make modeling easy to understand and apply New to this Edition: A more systematic approach to mathematical modeling, outlining ten specific principles Expanded and reorganized chapters that flow in an increasing level of complexity Several new problems and updated applications Expanded figure captions that provide more information Improved accessibility and flexibility for teaching

Modeling With Mathematics

Author: COMAP

Publisher: Macmillan

Published: 2006-02-28

Total Pages: 632

ISBN-13: 9780716707806

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"Designed for juniors and seniors in high school who have not succeeded using traditional approaches to teaching mathematics, but want to prepare for Algebra II or a College Algebra course" -- Publisher.

Book Synopsis Modeling With Mathematics by : COMAP

Download or read book Modeling With Mathematics written by COMAP and published by Macmillan. This book was released on 2006-02-28 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Designed for juniors and seniors in high school who have not succeeded using traditional approaches to teaching mathematics, but want to prepare for Algebra II or a College Algebra course" -- Publisher.

Mathematical Modelling

Author: John Berry

Publisher: Gulf Professional Publishing

Published: 1995-06-17

Total Pages: 157

ISBN-13: 0340614048

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Assuming virtually no prior knowledge, Modular Mathematics encourages the reader to develop and solve real models, as well as looking at traditional examples. Accessible and concise, it contains tutorial problems, case studies and exercises.

Book Synopsis Mathematical Modelling by : John Berry

Download or read book Mathematical Modelling written by John Berry and published by Gulf Professional Publishing. This book was released on 1995-06-17 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming virtually no prior knowledge, Modular Mathematics encourages the reader to develop and solve real models, as well as looking at traditional examples. Accessible and concise, it contains tutorial problems, case studies and exercises.

Mathematical Modeling and Modeling Mathematics

Author: Christian R. Hirsch

Publisher:

Published: 2016

Total Pages: 0

ISBN-13: 9780873539739

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Mathematical modeling plays an increasingly important role both in real-life applications and within mathematics education itself. This 2016 volume of Annual Perspectives in Mathematics Education (APME) focuses on this key topic from a wide variety of perspectives and distinguishes it from modeling mathematics.

Book Synopsis Mathematical Modeling and Modeling Mathematics by : Christian R. Hirsch

Download or read book Mathematical Modeling and Modeling Mathematics written by Christian R. Hirsch and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling plays an increasingly important role both in real-life applications and within mathematics education itself. This 2016 volume of Annual Perspectives in Mathematics Education (APME) focuses on this key topic from a wide variety of perspectives and distinguishes it from modeling mathematics.

Modeling and Simulation in Science and Mathematics Education

Author: Wallace Feurzeig

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 352

ISBN-13: 1461214149

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This book/software package brings the tools and excitement of modeling to pre-college teachers, to researchers involved in curriculum development, and to software developers interested in the pre-college market.

Book Synopsis Modeling and Simulation in Science and Mathematics Education by : Wallace Feurzeig

Download or read book Modeling and Simulation in Science and Mathematics Education written by Wallace Feurzeig and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book/software package brings the tools and excitement of modeling to pre-college teachers, to researchers involved in curriculum development, and to software developers interested in the pre-college market.