Meaning In Mathematics

Author : John Polkinghorne
Publisher : OUP Oxford
ISBN 13 : 0191621897
Total Pages : 176 pages
Book Rating : 4.95/5 ( download)

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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.

Author : Jeremy Kilpatrick
Publisher : Springer Science & Business Media
ISBN 13 : 0387240403
Total Pages : 260 pages
Book Rating : 4.04/5 ( download)

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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 260 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.

Author : Gabriele Lolli
Publisher : MIT Press
ISBN 13 : 0262371049
Total Pages : 177 pages
Book Rating : 4.49/5 ( download)

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Download or read book The Meaning of Proofs written by Gabriele Lolli and published by MIT Press. This book was released on 2022-09-27 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story. In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.

Author : Graham Flegg
Publisher : Courier Corporation
ISBN 13 : 0486166511
Total Pages : 304 pages
Book Rating : 4.13/5 ( download)

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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 304 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.

Author : David Pimm
Publisher : Routledge
ISBN 13 : 1134823665
Total Pages : 235 pages
Book Rating : 4.66/5 ( download)

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Download or read book Symbols and Meanings in School Mathematics written by David Pimm and published by Routledge. This book was released on 2002-11 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This timely book explores the various uses and aspects of symbols in school mathematics and the notion of mathematical meaning. In addition, the author addresses a number of key issues for the 1990s eg.changes within mathematical functioning.

Author : John Polkinghorne
Publisher : Oxford University Press
ISBN 13 : 019960505X
Total Pages : 172 pages
Book Rating : 4.57/5 ( download)

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Download or read book Meaning in Mathematics written by John Polkinghorne and published by Oxford University Press. This book was released on 2011-05-19 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is mathematics invented or discovered? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? Famous mathematicians, mathematical physicists and philosophers of mathematics try to answer these questions in a series of accessible chapters that shed light on what mathematics really means.

Author : Matematicheskiĭ institut im. V.A. Steklova
Publisher :
ISBN 13 :
Total Pages : 384 pages
Book Rating : 4.59/5 ( download)

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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 1964 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Richard Courant
Publisher : Oxford University Press, USA
ISBN 13 : 9780195105193
Total Pages : 596 pages
Book Rating : 4.92/5 ( download)

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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.

Author : Clifford A. Pickover
Publisher : Oxford University Press
ISBN 13 : 9780195348002
Total Pages : 420 pages
Book Rating : 4.01/5 ( download)

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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.

Author : Ernest Davis
Publisher : Springer
ISBN 13 : 331921473X
Total Pages : 379 pages
Book Rating : 4.33/5 ( download)

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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 379 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