Mathematics And Materials

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A New Direction in Mathematics for Materials Science

Susumu Ikeda,Motoko Kotani
A New Direction in Mathematics for Materials Science Book PDF

Author : Susumu Ikeda,Motoko Kotani
Publisher : Springer
Page : 86 pages
File Size : 52,8 Mb
Release : 2015-12-08
Category : Mathematics
ISBN : 9784431558644

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A New Direction in Mathematics for Materials Science by Susumu Ikeda,Motoko Kotani Pdf

This book is the first volume of the SpringerBriefs in the Mathematics of Materials and provides a comprehensive guide to the interaction of mathematics with materials science. The anterior part of the book describes a selected history of materials science as well as the interaction between mathematics and materials in history. The emergence of materials science was itself a result of an interdisciplinary movement in the 1950s and 1960s. Materials science was formed by the integration of metallurgy, polymer science, ceramics, solid state physics, and related disciplines. We believe that such historical background helps readers to understand the importance of interdisciplinary interaction such as mathematics–materials science collaboration. The middle part of the book describes mathematical ideas and methods that can be applied to materials problems and introduces some examples of specific studies—for example, computational homology applied to structural analysis of glassy materials, stochastic models for the formation process of materials, new geometric measures for finite carbon nanotube molecules, mathematical technique predicting a molecular magnet, and network analysis of nanoporous materials. The details of these works will be shown in the subsequent volumes of this SpringerBriefs in the Mathematics of Materials series by the individual authors. The posterior section of the book presents how breakthroughs based on mathematics–materials science collaborations can emerge. The authors' argument is supported by the experiences at the Advanced Institute for Materials Research (AIMR), where many researchers from various fields gathered and tackled interdisciplinary research.

Elementary Mathematics Curriculum Materials

Janine T. Remillard,Ok-Kyeong Kim
Elementary Mathematics Curriculum Materials Book PDF

Author : Janine T. Remillard,Ok-Kyeong Kim
Publisher : Springer Nature
Page : 329 pages
File Size : 45,7 Mb
Release : 2020-03-16
Category : Education
ISBN : 9783030385880

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Elementary Mathematics Curriculum Materials by Janine T. Remillard,Ok-Kyeong Kim Pdf

The book presents comparative analyses of five elementary mathematics curriculum programs used in the U.S. from three different perspectives: the mathematical emphasis, the pedagogical approaches, and how authors communicate with teachers. These perspectives comprise a framework for examining what curriculum materials are comprised of, what is involved in reading and interpreting them, and how curriculum authors can and do support teachers in this process. Although the focus of the analysis is 5 programs used at a particular point in time, this framework extends beyond these specific programs and illuminates the complexity of curriculum materials and their role in teaching in general. Our analysis of the mathematical emphasis considers how the mathematics content is presented in each program, in terms of sequencing, the nature of mathematical tasks (cognitive demand and ongoing practice), and the way representations are used. Our analysis of the pedagogical approach examines explicit and implicit messages about how students should interact with mathematics, one another, the teacher, and the textbook around these mathematical ideas, as well as the role of the teacher. In order to examine how curriculum authors support teachers, we analyze how they communicate with teachers and what they communicate about, including the underlying mathematics, noticing student thinking, and rationale for design elements. The volume includes a chapter on curriculum design decisions based on interviews with curriculum authors.

Mathematics Teachers at Work

Janine T. Remillard,Beth A. Herbel-Eisenmann,Gwendolyn M. Lloyd
Mathematics Teachers at Work Book PDF

Author : Janine T. Remillard,Beth A. Herbel-Eisenmann,Gwendolyn M. Lloyd
Publisher : Routledge
Page : 499 pages
File Size : 54,7 Mb
Release : 2011-09-20
Category : Education
ISBN : 9781135855628

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Mathematics Teachers at Work by Janine T. Remillard,Beth A. Herbel-Eisenmann,Gwendolyn M. Lloyd Pdf

This book compiles and synthesizes existing research on teachers’ use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on – but not restricted to – those materials developed in the 1990s in response to the NCTM’s Principles and Standards for School Mathematics. Despite the substantial amount of curriculum development activity over the last 15 years and growing scholarly interest in their use, the book represents the first compilation of research on teachers and mathematics curriculum materials and the first volume with this focus in any content area in several decades.

Mathematical Research in Materials Science

National Research Council,Division on Engineering and Physical Sciences,Commission on Physical Sciences, Mathematics, and Applications,Committee on Mathematical Sciences Applied to Materials Science
Mathematical Research in Materials Science Book PDF

Author : National Research Council,Division on Engineering and Physical Sciences,Commission on Physical Sciences, Mathematics, and Applications,Committee on Mathematical Sciences Applied to Materials Science
Publisher : National Academies Press
Page : 142 pages
File Size : 53,7 Mb
Release : 1993-02-01
Category : Technology & Engineering
ISBN : 9780309049306

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Mathematical Research in Materials Science by National Research Council,Division on Engineering and Physical Sciences,Commission on Physical Sciences, Mathematics, and Applications,Committee on Mathematical Sciences Applied to Materials Science Pdf

This book describes fruitful past collaborations between the mathematical and materials sciences and indicates future challenges. It seeks both to encourage mathematical sciences research that will complement vital research in materials science and to raise awareness of the value of quantitative methods. The volume encourages both communities to increase cross-disciplinary collaborations, emphasizing that each has much to gain from such an increase, and it presents recommendations for facilitating such work. This book is written for both mathematical and materials science researchers interested in advancing research at this interface; for federal and state agency representatives interested in encouraging such collaborations; and for anyone wanting information on how such cross-disciplinary, collaborative efforts can be accomplished successfully.

Environmental Mathematics in the Classroom

B. A. Fusaro,Patricia Clark Kenschaft
Environmental Mathematics in the Classroom Book PDF

Author : B. A. Fusaro,Patricia Clark Kenschaft
Publisher : American Mathematical Soc.
Page : 268 pages
File Size : 45,5 Mb
Release : 2020-07-14
Category : Mathematics
ISBN : 9781470457105

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Environmental Mathematics in the Classroom by B. A. Fusaro,Patricia Clark Kenschaft Pdf

Environmental Mathematics seeks to marry the most pressing challenge of our time with the most powerful technology of our time - mathematics. This book does this at an elementary level and demonstrates a wide variety of significant environmental applications that can be explored without resorting to calculus. Environmental Mathematics in the Classroom includes several chapters accessible enough to be a text in a general education course or to enrich an elementary algebra course. Ground-level ozone, pollution and water use, preservation of whales, mathematical economics, the movement of clouds over a mountain range, at least one population model, and a smorgasbord of 'newspaper mathematics' can be studied at this level and would form a stimulating course. It would prepare future teachers not only to learn basic mathematics, but to understand how they can integrate it into other topics that will intrigue students.

Mathematics and Materials

Mark J. Bowick,David Kinderlehrer,Govind Menon,Charles Radin
Mathematics and Materials Book PDF

Author : Mark J. Bowick,David Kinderlehrer,Govind Menon,Charles Radin
Publisher : American Mathematical Soc.
Page : 327 pages
File Size : 41,9 Mb
Release : 2017-08-25
Category : Convex and discrete geometry -- Discrete geometry -- Quasicrystals, aperiodic tilings
ISBN : 9781470429195

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Mathematics and Materials by Mark J. Bowick,David Kinderlehrer,Govind Menon,Charles Radin Pdf

A co-publication of the AMS, IAS/Park City Mathematics Institute, and Society for Industrial and Applied Mathematics Articles in this volume are based on lectures presented at the Park City summer school on “Mathematics and Materials” in July 2014. The central theme is a description of material behavior that is rooted in statistical mechanics. While many presentations of mathematical problems in materials science begin with continuum mechanics, this volume takes an alternate approach. All the lectures present unique pedagogical introductions to the rich variety of material behavior that emerges from the interplay of geometry and statistical mechanics. The topics include the order-disorder transition in many geometric models of materials including nonlinear elasticity, sphere packings, granular materials, liquid crystals, and the emerging field of synthetic self-assembly. Several lectures touch on discrete geometry (especially packing) and statistical mechanics. The problems discussed in this book have an immediate mathematical appeal and are of increasing importance in applications, but are not as widely known as they should be to mathematicians interested in materials science. The volume will be of interest to graduate students and researchers in analysis and partial differential equations, continuum mechanics, condensed matter physics, discrete geometry, and mathematical physics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price. NOTE: This discount does not apply to volumes in this series co-published with the Society for Industrial and Applied Mathematics (SIAM).

Research in Mathematics of Materials Science

Malena I. Español,Marta Lewicka,Lucia Scardia,Anja Schlömerkemper
Research in Mathematics of Materials Science Book PDF

Author : Malena I. Español,Marta Lewicka,Lucia Scardia,Anja Schlömerkemper
Publisher : Springer Nature
Page : 514 pages
File Size : 50,8 Mb
Release : 2022-09-27
Category : Mathematics
ISBN : 9783031044960

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Research in Mathematics of Materials Science by Malena I. Español,Marta Lewicka,Lucia Scardia,Anja Schlömerkemper Pdf

This volume highlights contributions of women mathematicians in the study of complex materials and includes both original research papers and reviews. The featured topics and methods draw on the fields of Calculus of Variations, Partial Differential Equations, Functional Analysis, Differential Geometry and Topology, as well as Numerical Analysis and Mathematical Modelling. Areas of applications include foams, fluid-solid interactions, liquid crystals, shape-memory alloys, magnetic suspensions, failure in solids, plasticity, viscoelasticity, homogenization, crystallization, grain growth, and phase-field models.

Tactile Learning Activities in Mathematics

Julie Barnes,Jessica M. Libertini
Tactile Learning Activities in Mathematics Book PDF

Author : Julie Barnes,Jessica M. Libertini
Publisher : American Mathematical Soc.
Page : 303 pages
File Size : 41,6 Mb
Release : 2018-08-06
Category : Mathematics
ISBN : 9781470448011

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Tactile Learning Activities in Mathematics by Julie Barnes,Jessica M. Libertini Pdf

Q: What do feather boas, cookies, and paper shredders have in common? A: They are all ingredients that have the potential to help your undergraduate students understand a variety of mathematical concepts. In this book, 43 faculty from a wide range of institutional settings share a total of 64 hands-on activities that allow students to physically engage with mathematical ideas ranging from the basics of precalculus to special topics appropriate for upper-level courses. Each learning activity is presented in an easy-to-read recipe format that includes a list of supplies; a narrative briefly describing the reasons, logistics, and helpful hints for running the activity; and a page that can be used as a handout in class. Purchase of the book also includes access to electronic printable versions of the handouts. With so many activities, it might be hard to decide where to start. For that reason, there are four indices to help the reader navigate this book: a concept index, a course index, an [Author]; index, and a main ingredient index. In addition to providing activities for precalculus, calculus, commonly required mathematics courses for majors, and more specialized upper-level electives, there is also a section describing how to modify many of the activities to fit into a liberal arts mathematics class. Whether you are new to using hands-on activities in class or are more experienced, the [Author];s hope that this book will encourage and inspire you to explore the possibilities of using more hands-on activities in your classes. Bon appetit!

From Text to 'Lived' Resources

Ghislaine Gueudet,Birgit Pepin,Luc Trouche
From Text to Lived Resources Book PDF

Author : Ghislaine Gueudet,Birgit Pepin,Luc Trouche
Publisher : Springer Science & Business Media
Page : 365 pages
File Size : 52,9 Mb
Release : 2011-09-06
Category : Education
ISBN : 9789400719668

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From Text to 'Lived' Resources by Ghislaine Gueudet,Birgit Pepin,Luc Trouche Pdf

What kinds of curriculum materials do mathematics teachers select and use, and how? This question is complex, in a period of deep evolutions of teaching resources, with the proficiency of online resources in particular. How do teachers learn from these materials, and in which ways do they ‘tailor’ them for their use and pupil learning? Teachers collect resources, select, transform, share, implement, and revise them. Drawing from the French term « ingénierie documentaire »,we call these processes « documentation ». The literal English translation is « to work with documents », but the meaning it carries is richer. Documentation refers to the complex and interactive ways that teachers work with resources; in-class and out-of-class, individually, but also collectively.

A New Direction in Mathematics for Materials Science

Susumu Ikeda,Motoko Kotani
A New Direction in Mathematics for Materials Science Book PDF

Author : Susumu Ikeda,Motoko Kotani
Publisher : Springer
Page : 0 pages
File Size : 49,8 Mb
Release : 2015-12-18
Category : Mathematics
ISBN : 4431558624

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A New Direction in Mathematics for Materials Science by Susumu Ikeda,Motoko Kotani Pdf

This book is the first volume of the SpringerBriefs in the Mathematics of Materials and provides a comprehensive guide to the interaction of mathematics with materials science. The anterior part of the book describes a selected history of materials science as well as the interaction between mathematics and materials in history. The emergence of materials science was itself a result of an interdisciplinary movement in the 1950s and 1960s. Materials science was formed by the integration of metallurgy, polymer science, ceramics, solid state physics, and related disciplines. We believe that such historical background helps readers to understand the importance of interdisciplinary interaction such as mathematics–materials science collaboration. The middle part of the book describes mathematical ideas and methods that can be applied to materials problems and introduces some examples of specific studies—for example, computational homology applied to structural analysis of glassy materials, stochastic models for the formation process of materials, new geometric measures for finite carbon nanotube molecules, mathematical technique predicting a molecular magnet, and network analysis of nanoporous materials. The details of these works will be shown in the subsequent volumes of this SpringerBriefs in the Mathematics of Materials series by the individual authors. The posterior section of the book presents how breakthroughs based on mathematics–materials science collaborations can emerge. The authors' argument is supported by the experiences at the Advanced Institute for Materials Research (AIMR), where many researchers from various fields gathered and tackled interdisciplinary research.

Discrete Geometric Analysis

Motoko Kotani,Tomoyuki Shirai,Toshikazu Sunada
Discrete Geometric Analysis Book PDF

Author : Motoko Kotani,Tomoyuki Shirai,Toshikazu Sunada
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 40,5 Mb
Release : 2004
Category : Mathematics
ISBN : 0821856820

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Discrete Geometric Analysis by Motoko Kotani,Tomoyuki Shirai,Toshikazu Sunada Pdf

This book is a collection of papers from the proceedings of the first symposium of the Japan Association for Mathematical Sciences. Topics covered center around problems of geometric analysis in relation to heat kernels, random walks, and Poisson boundaries on discrete groups, graphs, and other combinatorial objects. The material is suitable for graduate students and research mathematicians interested in heat kernels and random works on groups and graphs.

50 Visions of Mathematics

Dara O' Briain
50 Visions of Mathematics Book PDF

Author : Dara O' Briain
Publisher : OUP Oxford
Page : 224 pages
File Size : 48,6 Mb
Release : 2014-05-01
Category : Mathematics
ISBN : 9780191005343

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50 Visions of Mathematics by Dara O' Briain Pdf

Relax: no one understands technical mathematics without lengthy training but we all have an intuitive grasp of the ideas behind the symbols. To celebrate the 50th anniversary of the founding of the Institute of Mathematics and its Applications (IMA), this book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain. The book is a collection of 50 original essays contributed by a wide variety of authors. It contains articles by some of the best expositors of the subject (du Sautoy, Singh and Stewart for example) together with entertaining biographical pieces and articles of relevance to our everyday lives (such as Spiegelhalter on risk and Elwes on medical imaging). The topics covered are deliberately diverse and involve concepts from simple numerology to the very cutting edge of mathematics research. Each article is designed to be read in one sitting and to be accessible to a general audience. There is also other content. There are 50 pictorial 'visions of mathematics' which were supplied in response to an open call for contributions from IMA members, Plus readers and the worldwide mathematics community. You'll also find a series of "proofs " of Phythagoras's Theorem - mathematical, literary and comedy - after this, you'll never think of Pythagoras the same way again.

Mathematics for Social Justice: Resources for the College Classroom

Gizem Karaali,Lily S. Khadjavi
Mathematics for Social Justice Resources for the College Classroom Book PDF

Author : Gizem Karaali,Lily S. Khadjavi
Publisher : American Mathematical Soc.
Page : 277 pages
File Size : 47,6 Mb
Release : 2019-07-09
Category : Mathematics
ISBN : 9781470449261

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Mathematics for Social Justice: Resources for the College Classroom by Gizem Karaali,Lily S. Khadjavi Pdf

Mathematics for Social Justice offers a collection of resources for mathematics faculty interested in incorporating questions of social justice into their classrooms. The book begins with a series of essays from instructors experienced in integrating social justice themes into their pedagogy; these essays contain political and pedagogical motivations as well as nuts-and-bolts teaching advice. The heart of the book is a collection of fourteen classroom-tested modules featuring ready-to-use activities and investigations for the college mathematics classroom. The mathematical tools and techniques used are relevant to a wide variety of courses including college algebra, math for the liberal arts, calculus, differential equations, discrete mathematics, geometry, financial mathematics, and combinatorics. The social justice themes include human trafficking, income inequality, environmental justice, gerrymandering, voting methods, and access to education. The volume editors are leaders of the national movement to include social justice material into mathematics teaching. Gizem Karaali is Associate Professor of Mathematics at Pomona College. She is one of the founding editors of The Journal of Humanistic Mathematics, and an associate editor for The Mathematical Intelligencer and Numeracy ; she also serves on the editorial board of the MAA's Carus Mathematical Monographs. Lily Khadjavi is Associate Professor of Mathematics at Loyola Marymount University and is a past co-chair of the Infinite Possibilities Conference. She has served on the boards of Building Diversity in Science, the Barbara Jordan-Bayard Rustin Coalition, and the Harvard Gender and Sexuality Caucus.

Math Made Visual

Claudi Alsina,Roger B. Nelsen
Math Made Visual Book PDF

Author : Claudi Alsina,Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 173 pages
File Size : 52,7 Mb
Release : 2006-12-31
Category : Mathematics
ISBN : 9781614441007

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Math Made Visual by Claudi Alsina,Roger B. Nelsen Pdf

Is it possible to make mathematical drawings that help to understand mathematical ideas, proofs, and arguments? The [Author];s of this book are convinced that the answer is yes and the objective of this book is to show how some visualization techniques may be employed to produce pictures that have both mathematical and pedagogical interest. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece, and India, but only in the last thirty years has there been a growing interest in so-called ``proofs without words''. Hundreds of these have been published in Mathematics Magazine and The College Mathematics Journal, as well as in other journals, books, and on the internet. Often a person encountering a ``proof without words'' may have the feeling that the pictures involved are the result of a serendipitous discovery or the consequence of an exceptional ingenuity on the part of the picture's creator. In this book, the [Author];s show that behind most of the pictures, ``proving'' mathematical relations are some well-understood methods. As the reader shall see, a given mathematical idea or relation may have many different images that justify it, so that depending on the teaching level or the objectives for producing the pictures, one can choose the best alternative.

Materials Physics and Chemistry

Satya Bir Singh,Alexander V. Vakhrushev,A. K. Haghi
Materials Physics and Chemistry Book PDF

Author : Satya Bir Singh,Alexander V. Vakhrushev,A. K. Haghi
Publisher : CRC Press
Page : 309 pages
File Size : 51,8 Mb
Release : 2020-11-02
Category : Mathematics
ISBN : 9781000727951

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Materials Physics and Chemistry by Satya Bir Singh,Alexander V. Vakhrushev,A. K. Haghi Pdf

This volume focuses on the development and application of fundamental concepts in mechanics and physics of solids as they pertain to the solution of challenging new problems in diverse areas, such as materials science and micro- and nanotechnology. In this volume, emphasis is placed on the development of fundamental concepts of mechanics and novel applications of these concepts based on theoretical, experimental, or computational approaches, drawing upon the various branches of engineering science and the allied areas within applied mathematics, materials science, and applied physics. Materials Physics and Chemistry: Applied Mathematics and Chemo-Mechanical Analysis emphasizes the basics, such as design, equilibrium, material behavior, and geometry of deformation in simple structures or machines. Readers will find a thorough treatment of stress, strain, and the stress-strain relationships. Meanwhile it provides a solid foundation upon which readers can begin work in composite materials science and engineering. Many chapters include theory components with the equations students need to calculate different properties.