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## Autor Hersh, Reuben |

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18 Unconventional Essays on the Nature of Mathematics / SpringerLink (Online service) ; Hersh, Reuben (2006)

Título : 18 Unconventional Essays on the Nature of Mathematics Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Hersh, Reuben Editorial: New York, NY : Springer New York Fecha de publicación: 2006 Número de páginas: XXII, 326 p. 10 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-29831-3 Idioma : Inglés ( eng)Palabras clave: Mathematics Mathematical logic Mathematics, general Logic and Foundations Clasificación: 51 Matemáticas Resumen: Advance praise for 18 Unconventional Essays on the Nature of Mathematics: "I was pleasantly surprised to find that this book does not treat mathematics as dessicated formal logic but as a living organism, immediately recognizable to any working mathematician." - Sir Michael Atiyah, University of Edinburgh "A wonderful collection of essays on the philosophy of mathematics, some by mathematicians, others by philosophers, and all having significant things to say. Most readers will be informed, some will be infuriated, but all will be stimulated." - John H. Conway, John von Neumann Distinguished Professor of Mathematics, Princeton University This startling new collection of essays edited by Reuben Hersh contains frank facts and opinions from leading mathematicians, philosophers, sociologists, cognitive scientists, and even an anthropologist. Each essay provides a challenging and thought-provoking look at recent advances in the philosophy of mathematics, demonstrating the possibilities of thinking fresh, sticking close to actual practice, and fearlessly letting go of standard shibboleths. The following essays are included: * Alfred Renyi: Socratic Dialogue * Carlo Cellucci: Filosofia e Matematica, introduction * William Thurston: On Proof and Progress in Mathematics * Andrew Aberdein: The Informal Logic of Mathematical Proof * Yehuda Rav: Philosophical Problems of Mathematics in Light of Evolutionary Epistemology * Brian Rotman: Towards a Semiotics of Mathematics * Donald Mackenzie: Computers and the Sociology of Mathematical Proof * Terry Stanway: From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management * Rafael Nunez: Do Numbers Really Move? * Timothy Gowers: Does Mathematics Need a Philosophy? * Jody Azzouni: How and Why Mathematics is a Social Practice * Gian-Carlo Rota: The Pernicious Influence of Mathematics Upon Philosophy * Jack Schwartz: The Pernicious Influence of Mathematics on Science * Alfonso Avila del Palacio: What is Philosophy of Mathematics Looking For? * Andrew Pickering: Concepts and the Mangle of Practice: Constructing Quaternions * Eduard Glas: Mathematics as Objective Knowledge and as Human Practice * Leslie White: The Locus of Mathematical Reality: An Anthropological Footnote * Reuben Hersh: Inner Vision, Outer Truth Nota de contenido: A Socratic Dialogue on Mathematics -- “Introduction” to Filosofia e matematica -- On Proof and Progress in Mathematics -- The Informal Logic of Mathematical Proof -- Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology -- Towards a Semiotics of Mathematics -- Computers and the Sociology of Mathematical Proof -- From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management -- Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics -- Does Mathematics Need a Philosophy? -- How and Why Mathematics Is Unique as a Social Practice -- The Pernicious Influence of Mathematics upon Philosophy -- The Pernicious Influence of Mathematics on Science -- What Is Philosophy of Mathematics Looking for? -- Concepts and the Mangle of Practice Constructing Quaternions -- Mathematics as Objective Knowledge and as Human Practice -- The Locus of Mathematical Reality: An Anthropological Footnote -- Inner Vision, Outer Truth En línea: http://dx.doi.org/10.1007/0-387-29831-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34764 18 Unconventional Essays on the Nature of Mathematics [documento electrónico] / SpringerLink (Online service) ; Hersh, Reuben . - New York, NY : Springer New York, 2006 . - XXII, 326 p. 10 illus : online resource.ISBN: 978-0-387-29831-3

Idioma : Inglés (eng)

Palabras clave: Mathematics Mathematical logic Mathematics, general Logic and Foundations Clasificación: 51 Matemáticas Resumen: Advance praise for 18 Unconventional Essays on the Nature of Mathematics: "I was pleasantly surprised to find that this book does not treat mathematics as dessicated formal logic but as a living organism, immediately recognizable to any working mathematician." - Sir Michael Atiyah, University of Edinburgh "A wonderful collection of essays on the philosophy of mathematics, some by mathematicians, others by philosophers, and all having significant things to say. Most readers will be informed, some will be infuriated, but all will be stimulated." - John H. Conway, John von Neumann Distinguished Professor of Mathematics, Princeton University This startling new collection of essays edited by Reuben Hersh contains frank facts and opinions from leading mathematicians, philosophers, sociologists, cognitive scientists, and even an anthropologist. Each essay provides a challenging and thought-provoking look at recent advances in the philosophy of mathematics, demonstrating the possibilities of thinking fresh, sticking close to actual practice, and fearlessly letting go of standard shibboleths. The following essays are included: * Alfred Renyi: Socratic Dialogue * Carlo Cellucci: Filosofia e Matematica, introduction * William Thurston: On Proof and Progress in Mathematics * Andrew Aberdein: The Informal Logic of Mathematical Proof * Yehuda Rav: Philosophical Problems of Mathematics in Light of Evolutionary Epistemology * Brian Rotman: Towards a Semiotics of Mathematics * Donald Mackenzie: Computers and the Sociology of Mathematical Proof * Terry Stanway: From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management * Rafael Nunez: Do Numbers Really Move? * Timothy Gowers: Does Mathematics Need a Philosophy? * Jody Azzouni: How and Why Mathematics is a Social Practice * Gian-Carlo Rota: The Pernicious Influence of Mathematics Upon Philosophy * Jack Schwartz: The Pernicious Influence of Mathematics on Science * Alfonso Avila del Palacio: What is Philosophy of Mathematics Looking For? * Andrew Pickering: Concepts and the Mangle of Practice: Constructing Quaternions * Eduard Glas: Mathematics as Objective Knowledge and as Human Practice * Leslie White: The Locus of Mathematical Reality: An Anthropological Footnote * Reuben Hersh: Inner Vision, Outer Truth Nota de contenido: A Socratic Dialogue on Mathematics -- “Introduction” to Filosofia e matematica -- On Proof and Progress in Mathematics -- The Informal Logic of Mathematical Proof -- Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology -- Towards a Semiotics of Mathematics -- Computers and the Sociology of Mathematical Proof -- From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management -- Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics -- Does Mathematics Need a Philosophy? -- How and Why Mathematics Is Unique as a Social Practice -- The Pernicious Influence of Mathematics upon Philosophy -- The Pernicious Influence of Mathematics on Science -- What Is Philosophy of Mathematics Looking for? -- Concepts and the Mangle of Practice Constructing Quaternions -- Mathematics as Objective Knowledge and as Human Practice -- The Locus of Mathematical Reality: An Anthropological Footnote -- Inner Vision, Outer Truth En línea: http://dx.doi.org/10.1007/0-387-29831-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34764 ## Ejemplares

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Título : The Mathematical Experience, Study Edition Tipo de documento: documento electrónico Autores: Davis, Philip J ; SpringerLink (Online service) ; Hersh, Reuben ; Marchisotto, Elena Anne Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2012 Colección: Modern Birkhäuser Classics Número de páginas: XXV, 500 p. 139 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-8295-8 Idioma : Inglés ( eng)Palabras clave: Mathematics Philosophy and social sciences science History Mathematical logic Study teaching Mathematics, general Education of Sciences Logic Foundations Science Clasificación: 51 Matemáticas Resumen: Winner of the 1983 National Book Award, The Mathematical Experience presented a highly insightful overview of mathematics that effectively conveyed its power and beauty to a large audience of mathematicians and non-mathematicians alike. The study edition of the work followed about a decade later, supplementing the original material of the book with exercises to provide a self-contained treatment usable for the classroom. This softcover version reproduces the study edition and includes epilogues by the three original authors to reflect on the book's content 15 years after its publication, and to demonstrate its continued applicability to the classroom. Moreover, The Companion Guide to the Mathematical Experience—originally published and sold separately—is freely available online to instructors who use the work, further enhancing its pedagogical value and making it an exceptionally useful and accessible resource for a wide range of lower-level courses in mathematics and mathematics education. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto (elena.marchisotto@csun.edu) upon request. Reviews [The authors] have tried to provide a book usable in a course for liberal arts students and for future secondary teachers. They have done much more! This course should be required of every undergraduate major employing the mathematical sciences. It differs from the “mathematics appreciation” courses—courses that are merely a collection of amusing puzzles and toy problems giving an illusion of a mathematical encounter—presently found in many institutions. Students of this course are introduced to the context in which mathematics exists and the incredible magnitude of words devoted to communicating mathematics (hundreds of thousands of theorems each year). How much mathematics can there be? they are asked. Instructors in a “Mathematical Experience” course must be prepared to respond to questions from students concerning the fundamental nature of the whole mathematical enterprise. Stimulated by their reading of the text, students will ask about the underlying logical and philosophical issues, the role of mathematical methods and their origins, the substance of contemporary mathematical advances, the meaning of rigor and proof in mathematics, the role of computational mathematics, and issues of teaching and learning. How real is the conflict between “pure” mathematics, as represented by G.H. Hardy’s statements, and “applied” mathematics? they may ask. Are there other kinds of mathematics, neither pure nor applied? This edition of the book provides a source of problems, collateral readings, references, essay and project assignments, and discussion guides for the course. I believe that it is likely that this course would be a challenge to many teachers and students alike, especially those teachers and students who are willing to follow their curiosity beyond the confines of this book and follow up on the many references that are provided. —Notices of the AMS (Kenneth C. Millett) This beautifully written book can be recommended to any cultivated person with a certain sophistication of thought, and also to the practicing mathematician who will find here a vantage point from which to make a tour d'horizon of his science. —Publ. Math. Debrecen This is an unusual book, being more a book about mathematics than a mathematics book. It includes mathematical issues, but also questions from the philosophy of mathematics, the psychology of mathematical discovery, the history of mathematics, and biographies of mathematicians, in short, a book about the mathematical experience broadly considered… The book found its way into "Much for liberal arts students" courses and into education courses directed at future teachers. Term paper topics, essay assignments, problems, computer applications, and suggested readings are included. This new material should greatly enhance the usefulness of this very creative book. The range of topics covered is immense and the contents cannot easily be summarized. The book makes excellent casual reading, would make a good textbook, or could easily be used as a supplement to nearly any course concerned with mathematics. —Zentralblatt MATH Nota de contenido: Preface -- Preface to the Study Edition -- Acknowledgements -- Introduction -- Overture -- 1. The Mathematical Landscape -- 2. Varieties of Mathematical Experience -- 3. Outer Issues -- 4. Inner Issues -- 5. Selected Topics in Mathematics -- 6. Teaching and Learning -- 7. From Certainty to Fallibility -- 8. Mathematical Reality -- Glossary -- Bibliography -- Index -- Epilogue En línea: http://dx.doi.org/10.1007/978-0-8176-8295-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32687 The Mathematical Experience, Study Edition [documento electrónico] / Davis, Philip J ; SpringerLink (Online service) ; Hersh, Reuben ; Marchisotto, Elena Anne . - Boston : Birkhäuser Boston, 2012 . - XXV, 500 p. 139 illus : online resource. - (Modern Birkhäuser Classics) .ISBN: 978-0-8176-8295-8

Idioma : Inglés (eng)

Palabras clave: Mathematics Philosophy and social sciences science History Mathematical logic Study teaching Mathematics, general Education of Sciences Logic Foundations Science Clasificación: 51 Matemáticas Resumen: Winner of the 1983 National Book Award, The Mathematical Experience presented a highly insightful overview of mathematics that effectively conveyed its power and beauty to a large audience of mathematicians and non-mathematicians alike. The study edition of the work followed about a decade later, supplementing the original material of the book with exercises to provide a self-contained treatment usable for the classroom. This softcover version reproduces the study edition and includes epilogues by the three original authors to reflect on the book's content 15 years after its publication, and to demonstrate its continued applicability to the classroom. Moreover, The Companion Guide to the Mathematical Experience—originally published and sold separately—is freely available online to instructors who use the work, further enhancing its pedagogical value and making it an exceptionally useful and accessible resource for a wide range of lower-level courses in mathematics and mathematics education. A wealth of customizable online course materials for the book can be obtained from Elena Anne Marchisotto (elena.marchisotto@csun.edu) upon request. Reviews [The authors] have tried to provide a book usable in a course for liberal arts students and for future secondary teachers. They have done much more! This course should be required of every undergraduate major employing the mathematical sciences. It differs from the “mathematics appreciation” courses—courses that are merely a collection of amusing puzzles and toy problems giving an illusion of a mathematical encounter—presently found in many institutions. Students of this course are introduced to the context in which mathematics exists and the incredible magnitude of words devoted to communicating mathematics (hundreds of thousands of theorems each year). How much mathematics can there be? they are asked. Instructors in a “Mathematical Experience” course must be prepared to respond to questions from students concerning the fundamental nature of the whole mathematical enterprise. Stimulated by their reading of the text, students will ask about the underlying logical and philosophical issues, the role of mathematical methods and their origins, the substance of contemporary mathematical advances, the meaning of rigor and proof in mathematics, the role of computational mathematics, and issues of teaching and learning. How real is the conflict between “pure” mathematics, as represented by G.H. Hardy’s statements, and “applied” mathematics? they may ask. Are there other kinds of mathematics, neither pure nor applied? This edition of the book provides a source of problems, collateral readings, references, essay and project assignments, and discussion guides for the course. I believe that it is likely that this course would be a challenge to many teachers and students alike, especially those teachers and students who are willing to follow their curiosity beyond the confines of this book and follow up on the many references that are provided. —Notices of the AMS (Kenneth C. Millett) This beautifully written book can be recommended to any cultivated person with a certain sophistication of thought, and also to the practicing mathematician who will find here a vantage point from which to make a tour d'horizon of his science. —Publ. Math. Debrecen This is an unusual book, being more a book about mathematics than a mathematics book. It includes mathematical issues, but also questions from the philosophy of mathematics, the psychology of mathematical discovery, the history of mathematics, and biographies of mathematicians, in short, a book about the mathematical experience broadly considered… The book found its way into "Much for liberal arts students" courses and into education courses directed at future teachers. Term paper topics, essay assignments, problems, computer applications, and suggested readings are included. This new material should greatly enhance the usefulness of this very creative book. The range of topics covered is immense and the contents cannot easily be summarized. The book makes excellent casual reading, would make a good textbook, or could easily be used as a supplement to nearly any course concerned with mathematics. —Zentralblatt MATH Nota de contenido: Preface -- Preface to the Study Edition -- Acknowledgements -- Introduction -- Overture -- 1. The Mathematical Landscape -- 2. Varieties of Mathematical Experience -- 3. Outer Issues -- 4. Inner Issues -- 5. Selected Topics in Mathematics -- 6. Teaching and Learning -- 7. From Certainty to Fallibility -- 8. Mathematical Reality -- Glossary -- Bibliography -- Index -- Epilogue En línea: http://dx.doi.org/10.1007/978-0-8176-8295-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32687 ## Ejemplares

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