Making And Breaking Mathematical Sense

Author : Roi Wagner
Publisher : Princeton University Press
ISBN 13 : 0691171718
Total Pages : 250 pages
Book Rating : 4.15/5 ( download)

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Download or read book Making and Breaking Mathematical Sense written by Roi Wagner and published by Princeton University Press. This book was released on 2017-01-10 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.

Author : Roi Wagner
Publisher : Princeton University Press
ISBN 13 : 1400883784
Total Pages : 256 pages
Book Rating : 4.83/5 ( download)

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Download or read book Making and Breaking Mathematical Sense written by Roi Wagner and published by Princeton University Press. This book was released on 2017-01-10 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.

Author : James Hiebert
Publisher : Heinemann Educational Books
ISBN 13 :
Total Pages : 214 pages
Book Rating : 4.69/5 ( download)

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Download or read book Making Sense written by James Hiebert and published by Heinemann Educational Books. This book was released on 1997 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents several key principles for teaching mathematics for understanding that you can use to reflect on your own teaching, make more informed decisions, and develop more effective systems of instruction.

Author : Mircea Pitici
Publisher : Princeton University Press
ISBN 13 : 0691178631
Total Pages : 242 pages
Book Rating : 4.39/5 ( download)

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Download or read book The Best Writing on Mathematics 2017 written by Mircea Pitici and published by Princeton University Press. This book was released on 2017-11-14 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Cary Wolfe
Publisher : Routledge
ISBN 13 : 1000533611
Total Pages : 196 pages
Book Rating : 4.13/5 ( download)

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Download or read book Ontogenesis Beyond Complexity written by Cary Wolfe and published by Routledge. This book was released on 2021-12-27 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based upon the collaborative efforts of the Ontogenetics Process Group (OPG) – an interdisciplinary, multi-institutional, multi-national research group that began meeting in 2017 to explore new and innovative ways of thinking the problem of complexity in living, physical, and social systems outside the algorithmic models that have dominated paradigms of complexity to date. For all the descriptive and predictive power that the complexity sciences offer (the ability to compute feedback systems, recursive networks, emergent dynamics, etc.), they also presume that the living world in all of its modalities (biological, semiotic, economic, affective, social) can be reduced to finite schema of description that delimits in advance all possible outcomes. What is proposed in this volume are conceptual architectures for the living that are not only irreducible to physico-mathematical frames of reference, but that are also as vital as the phenomena they wish to express. In short: life is more complex than complexity. What emerges from this engagement is not the ascendance of a new transcendental principle (or, what amounts to the same thing, a foundational bedrock) derived from the physico-mathematical sciences, but just the opposite: a domain in which the ontological and the epistemological domains enter a zone of strange (and unavoidable) entanglement. The chapters in this book were originally published as a special issue of Angelaki.

Author : Mircea Pitici
Publisher : Princeton University Press
ISBN 13 : 0691198357
Total Pages : 288 pages
Book Rating : 4.54/5 ( download)

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Download or read book The Best Writing on Mathematics 2019 written by Mircea Pitici and published by Princeton University Press. This book was released on 2019-11-05 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: An anthology of the year's finest writing on mathematics from around the world, featuring promising new voices as well as some of the foremost names in mathematics.

Author : Stefania Centrone
Publisher : Springer Nature
ISBN 13 : 3030156559
Total Pages : 511 pages
Book Rating : 4.58/5 ( download)

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Download or read book Reflections on the Foundations of Mathematics written by Stefania Centrone and published by Springer Nature. This book was released on 2019-11-11 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.

Author : Victor J. Katz
Publisher : Princeton University Press
ISBN 13 : 1400883202
Total Pages : 593 pages
Book Rating : 4.02/5 ( download)

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Download or read book Sourcebook in the Mathematics of Medieval Europe and North Africa written by Victor J. Katz and published by Princeton University Press. This book was released on 2016-10-18 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon’s use of mathematical induction in combinatorial proofs; Al-Mu’taman Ibn Hūd’s extensive survey of mathematics, which included proofs of Heron’s Theorem and Ceva’s Theorem; and Muhyī al-Dīn al-Maghribī’s interesting proof of Euclid’s parallel postulate. The book includes a general introduction, section introductions, footnotes, and references. The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics.

Author : Bharath Sriraman
Publisher : Springer Nature
ISBN 13 : 3031408462
Total Pages : 3221 pages
Book Rating : 4.65/5 ( download)

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Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Paul A. Wagner
Publisher : Rowman & Littlefield
ISBN 13 : 1475862997
Total Pages : 153 pages
Book Rating : 4.97/5 ( download)

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Download or read book The Personality of Math written by Paul A. Wagner and published by Rowman & Littlefield. This book was released on 2022-06-06 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: If our goal is to broaden and deepen students’ awareness and understanding of mathematics, we advance the idea that engaging students with what we metaphorically call the personality of math. That is, we think that students who engage with the math’s (1) human champions, (2) with its history and philosophy, and (3) with the nature of its problems and inferential challenges, are more likely to have a positive attitude toward math that will encourage greater learning.