The Mathematics Of Meaning

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Meaning in Mathematics

Author : John Polkinghorne
Publisher : OUP Oxford
ISBN 13 : 0191621897
Total Pages : 176 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Meaning in Mathematics by : John Polkinghorne

Download or read book Meaning in Mathematics written by John Polkinghorne and published by OUP Oxford. This book was released on 2011-05-19 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics. The chapters are written by some of the world's finest mathematicians, mathematical physicists and philosophers of mathematics, each giving their perspective on this fascinating debate. Every chapter is followed by a short response from another member of the author team, reinforcing the main theme and raising further questions. Accessible to anyone interested in what mathematics really means, and useful for mathematicians and philosophers of science at all levels, Meaning in Mathematics offers deep new insights into a subject many people take for granted.

Numbers

Author : Graham Flegg
Publisher : Courier Corporation
ISBN 13 : 0486166511
Total Pages : 307 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Numbers by : Graham Flegg

Download or read book Numbers written by Graham Flegg and published by Courier Corporation. This book was released on 2013-05-13 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." — Choice.

Meaning in Mathematics Education

Author : Jeremy Kilpatrick
Publisher : Springer Science & Business Media
ISBN 13 : 0387240403
Total Pages : 267 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Meaning in Mathematics Education by : Jeremy Kilpatrick

Download or read book Meaning in Mathematics Education written by Jeremy Kilpatrick and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding the complexity of meaning in mathematics education is a matter of huge importance. There are twin directions in which discussions have developed—theoretical and practical—and this book seeks to move the debate forward along both dimensions while seeking to relate them where appropriate. A discussion of meaning can start from a theoretical examination of mathematics and how mathematicians over time have made sense of their work. However, from a more practical perspective, anybody involved in teaching mathematics is faced with the need to orchestrate the myriad of meanings derived from multiple sources that students develop of mathematical knowledge. This book presents a wide variety of theoretical reflections and research results about meaning in mathematics and mathematics education based on long-term and collective reflection by the group of authors as a whole. It is the outcome of the work of the BACOMET (BAsic COmponents of Mathematics Education for Teachers) group who spent several years deliberating on this topic. The ten chapters in this book, both separately and together, provide a substantial contribution to clarifying the complex issue of meaning in mathematics education. This book is of interest to researchers in mathematics education, graduate students of mathematics education, under graduate students in mathematics, secondary mathematics teachers and primary teachers with an interest in mathematics.

The Emergence of Mathematical Meaning

Author : Paul Cobb
Publisher : Routledge
ISBN 13 : 1136486100
Total Pages : 313 pages
Book Rating : 4.1/5 (364 download)

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Book Synopsis The Emergence of Mathematical Meaning by : Paul Cobb

Download or read book The Emergence of Mathematical Meaning written by Paul Cobb and published by Routledge. This book was released on 2012-12-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of a five-year collaboration between groups of American and German mathematics educators. The central issue addressed accounting for the messiness and complexity of mathematics learning and teaching as it occurs in classroom situations. The individual chapters are based on the view that psychological and sociological perspectives each tell half of a good story. To unify these concepts requires a combined approach that takes individual students' mathematical activity seriously while simultaneously seeing their activity as necessarily socially situated. Throughout their collaboration, the chapter authors shared a single set of video recordings and transcripts made in an American elementary classroom where instruction was generally compatible with recent reform recommendations. As a consequence, the book is much more than a compendium of loosely related papers. The combined approach taken by the authors draws on interactionism and ethnomethodology. Thus, it constitutes an alternative to Vygotskian and Soviet activity theory approaches. The specific topics discussed in individual chapters include small group collaboration and learning, the teacher's practice and growth, and language, discourse, and argumentation in the mathematics classroom. This collaborative effort is valuable to educators and psychologists interested in situated cognition and the relation between sociocultural processes and individual psychological processes.

What is Mathematics?

Author : Richard Courant
Publisher : Oxford University Press, USA
ISBN 13 : 9780195105193
Total Pages : 596 pages
Book Rating : 4.1/5 (51 download)

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Book Synopsis What is Mathematics? by : Richard Courant

Download or read book What is Mathematics? written by Richard Courant and published by Oxford University Press, USA. This book was released on 1996 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but not real understanding or greater intellectual independence. The new edition of this classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. "Lucid . . . easily understandable".--Albert Einstein. 301 linecuts.

Mathematics, Its Content, Methods, and Meaning

Author : Matematicheskiĭ institut im. V.A. Steklova
Publisher :
ISBN 13 :
Total Pages : 406 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Mathematics, Its Content, Methods, and Meaning by : Matematicheskiĭ institut im. V.A. Steklova

Download or read book Mathematics, Its Content, Methods, and Meaning written by Matematicheskiĭ institut im. V.A. Steklova and published by . This book was released on 1969 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Wonders of Numbers

Author : Clifford A. Pickover
Publisher : Oxford University Press
ISBN 13 : 9780195348002
Total Pages : 420 pages
Book Rating : 4.3/5 (48 download)

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Book Synopsis Wonders of Numbers by : Clifford A. Pickover

Download or read book Wonders of Numbers written by Clifford A. Pickover and published by Oxford University Press. This book was released on 2003-01-16 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Who were the five strangest mathematicians in history? What are the ten most interesting numbers? Jam-packed with thought-provoking mathematical mysteries, puzzles, and games, Wonders of Numbers will enchant even the most left-brained of readers. Hosted by the quirky Dr. Googol--who resides on a remote island and occasionally collaborates with Clifford Pickover--Wonders of Numbers focuses on creativity and the delight of discovery. Here is a potpourri of common and unusual number theory problems of varying difficulty--each presented in brief chapters that convey to readers the essence of the problem rather than its extraneous history. Peppered throughout with illustrations that clarify the problems, Wonders of Numbers also includes fascinating "math gossip." How would we use numbers to communicate with aliens? Check out Chapter 30. Did you know that there is a Numerical Obsessive-Compulsive Disorder? You'll find it in Chapter 45. From the beautiful formula of India's most famous mathematician to the Leviathan number so big it makes a trillion look small, Dr. Googol's witty and straightforward approach to numbers will entice students, educators, and scientists alike to pick up a pencil and work a problem.

Windows on Mathematical Meanings

Author : Richard Noss
Publisher : Springer Science & Business Media
ISBN 13 : 9400916965
Total Pages : 288 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Windows on Mathematical Meanings by : Richard Noss

Download or read book Windows on Mathematical Meanings written by Richard Noss and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book challenges some of the conventional wisdoms on the learning of mathematics. The authors use the computer as a window onto mathematical meaning-making. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.

The Mathematics of Meaning

Author : Svend Østergaard
Publisher :
ISBN 13 :
Total Pages : 228 pages
Book Rating : 4.X/5 (4 download)

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Book Synopsis The Mathematics of Meaning by : Svend Østergaard

Download or read book The Mathematics of Meaning written by Svend Østergaard and published by . This book was released on 1997 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Mathematics of Meaning" examines the foundation of mathematics, the fictions of Jose Luis Borges, and the aesthetics of Marcel Proust as it is unfolded in Remembrance of Things Past. In mathematics the logical foundation of reasoning is examined. In Borges it is the linguistic foundation of narration, and in Proust the perceptual foundation of aesthetics. The three types of studies converge towards the same point, because it turns out that in all cases where the foundation becomes indeterminable, the concept of infinity plays a decisive role. The dynamics of mathematics is decisively dependent on the assumption of the existence of infinite sets. In Borges the breakdown of narration is metaphorically staged through an impossible object representing an actual infinity. In Proust it is the concept of infinity implied in Leibniz' monadism. "The Mathematics of Meaning" also contains a semiotic theory of form, because the breakdown of the foundation is in all three cases uniquely connected to the existence of a form, the meaning of which is indeterminable in the situation.

Mathematics, Substance and Surmise

Author : Ernest Davis
Publisher : Springer
ISBN 13 : 331921473X
Total Pages : 374 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Mathematics, Substance and Surmise by : Ernest Davis

Download or read book Mathematics, Substance and Surmise written by Ernest Davis and published by Springer. This book was released on 2015-11-17 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Teaching Math with Meaning

Author : Cathy Marks Krpan
Publisher :
ISBN 13 : 9780134153483
Total Pages : 248 pages
Book Rating : 4.1/5 (534 download)

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Book Synopsis Teaching Math with Meaning by : Cathy Marks Krpan

Download or read book Teaching Math with Meaning written by Cathy Marks Krpan and published by . This book was released on 2018 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Meaning in Mathematics

Author : John Polkinghorne
Publisher : OUP Oxford
ISBN 13 : 0191621293
Total Pages : 176 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Meaning in Mathematics by : John Polkinghorne

Mathematics for Human Flourishing

Author : Francis Su
Publisher : Yale University Press
ISBN 13 : 0300237138
Total Pages : 287 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Mathematics for Human Flourishing by : Francis Su

Download or read book Mathematics for Human Flourishing written by Francis Su and published by Yale University Press. This book was released on 2020-01-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

Metaphysics, Mathematics, and Meaning

Author : Nathan U. Salmon
Publisher : Oxford University Press
ISBN 13 : 9780199281763
Total Pages : 458 pages
Book Rating : 4.2/5 (817 download)

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Book Synopsis Metaphysics, Mathematics, and Meaning by : Nathan U. Salmon

Download or read book Metaphysics, Mathematics, and Meaning written by Nathan U. Salmon and published by Oxford University Press. This book was released on 2005 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Metaphysics, Mathematics and Meaning' brings together Nathan Salmon's influential papers on topics in the metaphysics of existence, non-existence and fiction. He includes a previously unpublished essay and helpful new introduction to orient the reader.

The Mathematics of Life

Author : Ian Stewart
Publisher : Basic Books
ISBN 13 : 0465024408
Total Pages : 370 pages
Book Rating : 4.4/5 (65 download)

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Book Synopsis The Mathematics of Life by : Ian Stewart

Download or read book The Mathematics of Life written by Ian Stewart and published by Basic Books. This book was released on 2011-06-07 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biologists have long dismissed mathematics as being unable to meaningfully contribute to our understanding of living beings. Within the past ten years, however, mathematicians have proven that they hold the key to unlocking the mysteries of our world -- and ourselves. In The Mathematics of Life, Ian Stewart provides a fascinating overview of the vital but little-recognized role mathematics has played in pulling back the curtain on the hidden complexities of the natural world -- and how its contribution will be even more vital in the years ahead. In his characteristically clear and entertaining fashion, Stewart explains how mathematicians and biologists have come to work together on some of the most difficult scientific problems that the human race has ever tackled, including the nature and origin of life itself.

Information: A Very Short Introduction

Author : Luciano Floridi
Publisher : Oxford University Press
ISBN 13 : 0199551375
Total Pages : 153 pages
Book Rating : 4.1/5 (995 download)

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Book Synopsis Information: A Very Short Introduction by : Luciano Floridi

Download or read book Information: A Very Short Introduction written by Luciano Floridi and published by Oxford University Press. This book was released on 2010-02-25 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction; 1 The information revolution; 2 The language of information; 3 Mathematical information; 4 Semantic information; 5 Physical information; 6 Biological information; 7 Economic information; 8 The ethics of information; Conclusion; References.

Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being

Author : George Lakoff
Publisher :
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being by : George Lakoff

Download or read book Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being written by George Lakoff and published by . This book was released on 2000-11-02 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the cognitive science of mathematical ideas.