Mathematics Substance And Surmise

Author : Ernest Davis,Philip J. Davis
Publisher : Springer
Page : 379 pages
File Size : 42,6 Mb
Release : 2015-11-17
Category : Mathematics
ISBN : 9783319214733

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Mathematics, Substance and Surmise by Ernest Davis,Philip J. Davis Pdf

The seventeen thought-provoking and engaging essays in this collection present readers with a wide range of diverse perspectives on the ontology of mathematics. The essays address such questions as: What kind of things are mathematical objects? What kinds of assertions do mathematical statements make? How do people think and speak about mathematics? How does society use mathematics? How have our answers to these questions changed over the last two millennia, and how might they change again in the future? The authors include mathematicians, philosophers, computer scientists, cognitive psychologists, sociologists, educators and mathematical historians; each brings their own expertise and insights to the discussion. Contributors to this volume: Jeremy Avigad Jody Azzouni David H. Bailey David Berlinski Jonathan M. Borwein Ernest Davis Philip J. Davis Donald Gillies Jeremy Gray Jesper Lützen Ursula Martin Kay O’Halloran Alison Pease Steven Piantadosi Lance Rips Micah T. Ross Nathalie Sinclair John Stillwell Hellen Verran

Author : Mircea Pitici
Publisher : Princeton University Press
Page : 408 pages
File Size : 40,8 Mb
Release : 2017-02-14
Category : Mathematics
ISBN : 9781400885602

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The Best Writing on Mathematics 2016 by Mircea Pitici Pdf

The year's finest mathematics writing from around the world This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2016 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Burkard Polster shows how to invent your own variants of the Spot It! card game, Steven Strogatz presents young Albert Einstein's proof of the Pythagorean Theorem, Joseph Dauben and Marjorie Senechal find a treasure trove of math in New York's Metropolitan Museum of Art, and Andrew Gelman explains why much scientific research based on statistical testing is spurious. In other essays, Brian Greene discusses the evolving assumptions of the physicists who developed the mathematical underpinnings of string theory, Jorge Almeida examines the misperceptions of people who attempt to predict lottery results, and Ian Stewart offers advice to authors who aspire to write successful math books for general readers. And there's much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

Author : Iliada Elia,Joanne Mulligan,Ann Anderson,Anna Baccaglini-Frank,Christiane Benz
Publisher : Springer
Page : 326 pages
File Size : 47,5 Mb
Release : 2018-02-21
Category : Education
ISBN : 9783319734323

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Contemporary Research and Perspectives on Early Childhood Mathematics Education by Iliada Elia,Joanne Mulligan,Ann Anderson,Anna Baccaglini-Frank,Christiane Benz Pdf

This book brings together a collection of research-based papers on current issues in early childhood mathematics education that were presented in the Topic Study Group 1 (TSG 1) at the 13th International Congress on Mathematical Education (ICME-13), held at the University of Hamburg in 2016. It will help readers understand a range of key issues that early childhood mathematics educators encounter today. Research on early childhood mathematics education has grown in recent years, due in part to the well-documented, positive relation between children’s early mathematical knowledge and their later mathematics learning, and to the considerable emphasis many countries are now placing on preschool education. The book addresses a number of central questions, including: What is mathematical structural development and how can we promote it in early childhood? How can multimodality and embodiment contribute to early mathematics learning and to acquiring a better understanding of young children’s mathematical development? How can children’s informal mathematics-related experiences affect instruction and children’s learning in different mathematics content areas? What is the role of tools, including technology and picture books, in supporting early mathematics learning? What are the challenges in early childhood mathematics education for teachers’ education and professional development?

Author : Mircea Pitici
Publisher : Princeton University Press
Page : 242 pages
File Size : 46,5 Mb
Release : 2017-11-14
Category : Mathematics
ISBN : 9780691178639

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The Best Writing on Mathematics 2017 by Mircea Pitici Pdf

The year's finest mathematics writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2017 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here Evelyn Lamb describes the excitement of searching for incomprehensibly large prime numbers, Jeremy Gray speculates about who would have won math’s highest prize—the Fields Medal—in the nineteenth century, and Philip Davis looks at mathematical results and artifacts from a business and marketing viewpoint. In other essays, Noson Yanofsky explores the inherent limits of knowledge in mathematical thinking, Jo Boaler and Lang Chen reveal why finger-counting enhances children’s receptivity to mathematical ideas, and Carlo Séquin and Raymond Shiau attempt to discover how the Renaissance painter Fra Luca Pacioli managed to convincingly depict his famous rhombicuboctahedron, a twenty-six-sided Archimedean solid. And there’s much, much more. In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

Author : Eleonora Faggiano,Francesca Ferrara,Antonella Montone
Publisher : Springer
Page : 257 pages
File Size : 44,6 Mb
Release : 2017-10-14
Category : Education
ISBN : 9783319614885

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Innovation and Technology Enhancing Mathematics Education by Eleonora Faggiano,Francesca Ferrara,Antonella Montone Pdf

This book addresses key issues of Technology and Innovation(s) in Mathematics Education, drawing on heterogeneous ways of positioning about innovation in mathematical practice with technology. The book offers ideas and meanings of innovation as they emerge from the entanglement of the various researchers with the mathematical practice, the teacher training program, the student learning and engagement, or the research method that they are telling stories about. The multiple theoretical or empirical perspectives capture a rich landscape, in which the presence of digital technology entails the emergence of new practices, techniques, environments and devices, or new ways of making sense of technology in research, teaching and learning.

Author : Mark Burgin,Marek Czachor
Publisher : World Scientific
Page : 960 pages
File Size : 52,9 Mb
Release : 2020-11-04
Category : Mathematics
ISBN : 9789811214325

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Non-diophantine Arithmetics In Mathematics, Physics And Psychology by Mark Burgin,Marek Czachor Pdf

For a long time, all thought there was only one geometry — Euclidean geometry. Nevertheless, in the 19th century, many non-Euclidean geometries were discovered. It took almost two millennia to do this. This was the major mathematical discovery and advancement of the 19th century, which changed understanding of mathematics and the work of mathematicians providing innovative insights and tools for mathematical research and applications of mathematics.A similar event happened in arithmetic in the 20th century. Even longer than with geometry, all thought there was only one conventional arithmetic of natural numbers — the Diophantine arithmetic, in which 2+2=4 and 1+1=2. It is natural to call the conventional arithmetic by the name Diophantine arithmetic due to the important contributions to arithmetic by Diophantus. Nevertheless, in the 20th century, many non-Diophantine arithmetics were discovered, in some of which 2+2=5 or 1+1=3. It took more than two millennia to do this. This discovery has even more implications than the discovery of new geometries because all people use arithmetic.This book provides a detailed exposition of the theory of non-Diophantine arithmetics and its various applications. Reading this book, the reader will see that on the one hand, non-Diophantine arithmetics continue the ancient tradition of operating with numbers while on the other hand, they introduce extremely original and innovative ideas.

Author : Toke Knudsen,Jessica Carter
Publisher : Walter de Gruyter GmbH & Co KG
Page : 358 pages
File Size : 50,5 Mb
Release : 2024-06-04
Category : History
ISBN : 9783110770070

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Mastering the History of Pure and Applied Mathematics by Toke Knudsen,Jessica Carter Pdf

The present collection of essays are published in honor of the distinguished historian of mathematics Professor Emeritus Jesper Lützen. In a career that spans more than four decades, Professor Lützen's scholarly contributions have enhanced our understanding of the history, development, and organization of mathematics. The essays cover a broad range of areas connected to Professor Lützen's work. In addition to this noteworthy scholarship, Professor Lützen has always been an exemplary colleague, providing support to peers as well as new faculty and graduate students. We dedicate this Festschrift to Professor Lützen—as a scholarly role model, mentor, colleague, and friend.

Author : Nicolas Fillion,Robert M. Corless,Ilias S. Kotsireas
Publisher : Springer
Page : 294 pages
File Size : 41,7 Mb
Release : 2019-02-07
Category : Mathematics
ISBN : 9781493990511

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Algorithms and Complexity in Mathematics, Epistemology, and Science by Nicolas Fillion,Robert M. Corless,Ilias S. Kotsireas Pdf

ACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including numerical analysis and its underlying philosophy, computer algebra, reliability and uncertainty quantification, computation and complexity theory, combinatorics, error analysis, perturbation theory, experimental mathematics, scientific epistemology, and foundations of mathematics. By bringing together contributions from researchers who approach the mathematical sciences from different perspectives, the volume will further readers' understanding of the multifaceted role of mathematics in modern science, informed by the state of the art in mathematics, scientific computing, and current modeling techniques.

Author : Bharath Sriraman
Publisher : Springer Nature
Page : 3221 pages
File Size : 53,8 Mb
Release : 2024-06-02
Category : Electronic
ISBN : 9783031408465

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Handbook of the History and Philosophy of Mathematical Practice by Bharath Sriraman Pdf

Author : Wenceslao J. Gonzalez
Publisher : Springer Nature
Page : 286 pages
File Size : 47,8 Mb
Release : 2021-04-27
Category : Science
ISBN : 9783030605377

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Language and Scientific Research by Wenceslao J. Gonzalez Pdf

This book analyzes the role of language in scientific research and develops the semantics of science from different angles. The philosophical investigation of the volume is divided into four parts, which covers both basic science and applied science: I) The Problem of Reference and Potentialities of the Language in Science; II) Language and Change in Scientific Research: Evolution and Historicity; III) Scientific Language in the Context of Truth and Fiction; and IV) Language in Mathematics and in Empirical Sciences. Language plays a key role in science: our access to the theoretical, practical or evaluative dimensions of scientific activity begins with the mastery of language, continues with a deepening in the use of language and reaches the level of contribution when it creates new terms or changes them in sense and reference. This reveals the compatibility between objectivity in semantic contents and historicity in the progress of science. This volume is a valuable enrichment to students, academics and other professionals interested in science in all its forms, who seek to deepen the role that language plays in its structure and dynamics.

Author : Emily Rolfe Grosholz
Publisher : Springer
Page : 274 pages
File Size : 49,6 Mb
Release : 2018-11-13
Category : Mathematics
ISBN : 9783319982311

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Great Circles by Emily Rolfe Grosholz Pdf

This volume explores the interaction of poetry and mathematics by looking at analogies that link them. The form that distinguishes poetry from prose has mathematical structure (lifting language above the flow of time), as do the thoughtful ways in which poets bring the infinite into relation with the finite. The history of mathematics exhibits a dramatic narrative inspired by a kind of troping, as metaphor opens, metonymy and synecdoche elaborate, and irony closes off or shifts the growth of mathematical knowledge. The first part of the book is autobiographical, following the author through her discovery of these analogies, revealed by music, architecture, science fiction, philosophy, and the study of mathematics and poetry. The second part focuses on geometry, the circle and square, launching us from Shakespeare to Housman, from Euclid to Leibniz. The third part explores the study of dynamics, inertial motion and transcendental functions, from Descartes to Newton, and in 20th c. poetry. The final part contemplates infinity, as it emerges in modern set theory and topology, and in contemporary poems, including narrative poems about modern cosmology.

Author : Carey Jewitt,Jeff Bezemer,Kay O'Halloran
Publisher : Routledge
Page : 220 pages
File Size : 40,6 Mb
Release : 2016-03-22
Category : Language Arts & Disciplines
ISBN : 9781317269793

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Introducing Multimodality by Carey Jewitt,Jeff Bezemer,Kay O'Halloran Pdf

This accessible introduction to multimodality illuminates the potential of multimodal research for understanding the ways in which people communicate. Readers will become familiar with the key concepts and methods in various domains while learning how to engage critically with the notion of multimodality. The book challenges widely held assumptions about language and presents the practical steps involved in setting up a multimodal study, including: formulating research questions collecting research materials assessing and developing methods of transcription considering the ethical dimensions of multimodal research. A self-study guide is also included, designed as an optional stand-alone resource or as the basis for a short course. With a wide range of examples, clear practical support and a glossary of terms, Introducing Multimodality is an ideal reference for undergraduate and postgraduate students in multimodality, semiotics, applied linguistics and media and communication studies. Online materials, including colour images and more links to relevant resources, are available on the companion website at www.routledge.com/cw/jewitt and the Routledge Language and Communication Portal.

Author : Vicky Neale
Publisher : Oxford University Press
Page : 171 pages
File Size : 47,9 Mb
Release : 2017
Category : Mathematics
ISBN : 9780198788287

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Closing the Gap by Vicky Neale Pdf

Mathematicians have recently made dramatic progress on the Twin Primes Conjecture, which asserts that there are infinitely many pairs of prime numbers that differ by 2. This book will describe two stories: that of the recent work on the Twin Primes Conjecture, and in parallel the related ideas from the previous two thousand years of mathematics.--

Author : Elizabeth de Freitas,Nathalie Sinclair,Alf Coles
Publisher : Cambridge University Press
Page : 301 pages
File Size : 51,5 Mb
Release : 2017-06-22
Category : Education
ISBN : 9781107134638

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What is a Mathematical Concept? by Elizabeth de Freitas,Nathalie Sinclair,Alf Coles Pdf

Leading thinkers in mathematics, philosophy and education offer new insights into the fundamental question: what is a mathematical concept?

Author : Evans, Jeff,Ruane, Sally
Publisher : Policy Press
Page : 414 pages
File Size : 55,5 Mb
Release : 2019-08-21
Category : Social Science
ISBN : 9781447348221

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Data in Society by Evans, Jeff,Ruane, Sally Pdf

Statistical data and evidence-based claims are increasingly central to our everyday lives. Critically examining ‘Big Data’, this book charts the recent explosion in sources of data, including those precipitated by global developments and technological change. It sets out changes and controversies related to data harvesting and construction, dissemination and data analytics by a range of private, governmental and social organisations in multiple settings. Analysing the power of data to shape political debate, the presentation of ideas to us by the media, and issues surrounding data ownership and access, the authors suggest how data can be used to uncover injustices and to advance social progress.