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Título : 104 Number Theory Problems : From the Training of the USA IMO Team Tipo de documento: documento electrónico Autores: Titu Andreescu ; SpringerLink (Online service) ; Dorin Andrica ; Feng, Zuming Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2007 Número de páginas: XII, 204 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4561-8 Idioma : Inglés (eng) Palabras clave: Mathematics Sequences (Mathematics) Mathematical logic Number theory Theory Sequences, Series, Summability Logic and Foundations Clasificación: 51 Matemáticas Resumen: This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas, conjectures, and conclusions in writing. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory. Key features: * Contains problems developed for various mathematical contests, including the International Mathematical Olympiad (IMO) * Builds a bridge between ordinary high school examples and exercises in number theory and more sophisticated, intricate and abstract concepts and problems * Begins by familiarizing students with typical examples that illustrate central themes, followed by numerous carefully selected problems and extensive discussions of their solutions * Combines unconventional and essay-type examples, exercises and problems, many presented in an original fashion * Engages students in creative thinking and stimulates them to express their comprehension and mastery of the material beyond the classroom 104 Number Theory Problems is a valuable resource for advanced high school students, undergraduates, instructors, and mathematics coaches preparing to participate in mathematical contests and those contemplating future research in number theory and its related areas Nota de contenido: Foundations of Number Theory -- Introductory Problems -- Advanced Problems -- Solutions to Introductory Problems -- Solutions to Advanced Problems En línea: http://dx.doi.org/10.1007/978-0-8176-4561-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34554 104 Number Theory Problems : From the Training of the USA IMO Team [documento electrónico] / Titu Andreescu ; SpringerLink (Online service) ; Dorin Andrica ; Feng, Zuming . - Boston, MA : Birkhäuser Boston, 2007 . - XII, 204 p : online resource.
ISBN : 978-0-8176-4561-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Sequences (Mathematics) Mathematical logic Number theory Theory Sequences, Series, Summability Logic and Foundations Clasificación: 51 Matemáticas Resumen: This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas, conjectures, and conclusions in writing. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory. Key features: * Contains problems developed for various mathematical contests, including the International Mathematical Olympiad (IMO) * Builds a bridge between ordinary high school examples and exercises in number theory and more sophisticated, intricate and abstract concepts and problems * Begins by familiarizing students with typical examples that illustrate central themes, followed by numerous carefully selected problems and extensive discussions of their solutions * Combines unconventional and essay-type examples, exercises and problems, many presented in an original fashion * Engages students in creative thinking and stimulates them to express their comprehension and mastery of the material beyond the classroom 104 Number Theory Problems is a valuable resource for advanced high school students, undergraduates, instructors, and mathematics coaches preparing to participate in mathematical contests and those contemplating future research in number theory and its related areas Nota de contenido: Foundations of Number Theory -- Introductory Problems -- Advanced Problems -- Solutions to Introductory Problems -- Solutions to Advanced Problems En línea: http://dx.doi.org/10.1007/978-0-8176-4561-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34554 Ejemplares
Signatura Medio Ubicación Sección Estado ningún ejemplar The Strength of Nonstandard Analysis / SpringerLink (Online service) ; Imme van den Berg ; Neves, Vítor (2007)
Título : The Strength of Nonstandard Analysis Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Imme van den Berg ; Neves, Vítor Editorial: Vienna : Springer Vienna Fecha de publicación: 2007 Número de páginas: XX, 401 p. 16 illus Il.: online resource ISBN/ISSN/DL: 978-3-211-49905-4 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Partial differential equations History logic Number theory Probabilities Logic and Foundations Probability Theory Stochastic Processes Differential Equations of Sciences Clasificación: 51 Matemáticas Resumen: Nonstandard Analysis enhances mathematical reasoning by introducing new ways of expression and deduction. Distinguishing between standard and nonstandard mathematical objects, its inventor, the eminent mathematician Abraham Robinson, settled in 1961 the centuries-old problem of how to use infinitesimals correctly in analysis. Having also worked as an engineer, he saw not only that his method greatly simplified mathematically proving and teaching, but also served as a powerful tool in modelling, analyzing and solving problems in the applied sciences, among others by effective rescaling and by infinitesimal discretizations. This book reflects the progress made in the forty years since the appearance of Robinson’s revolutionary book Nonstandard Analysis: in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained Nota de contenido: Foundations -- The strength of nonstandard analysis -- The virtue of simplicity -- Analysis of various practices of referring in classical or non standard mathematics -- Stratified analysis? -- ERNA at work -- The Sousa Pinto approach to nonstandard generalised functions -- Neutrices in more dimensions -- Number theory -- Nonstandard methods for additive and combinatorial number theory. A survey -- Nonstandard methods and the Erd?s-Turán conjecture -- Statistics, probability and measures -- Nonstandard likelihood ratio test in exponential families -- A finitary approach for the representation of the infinitesimal generator of a markovian semigroup -- On two recent applications of nonstandard analysis to the theory of financial markets -- Quantum Bernoulli experiments and quantum stochastic processes -- Applications of rich measure spaces formed from nonstandard models -- More on S-measures -- A Radon-Nikodým theorem for a vector-valued reference measure -- Differentiability of Loeb measures -- Differential systems and equations -- The power of Gâteaux differentiability -- Nonstandard Palais-Smale conditions -- Averaging for ordinary differential equations and functional differential equations -- Path-space measure for stochastic differential equation with a coefficient of polynomial growth -- Optimal control for Navier-Stokes equations -- Local-in-time existence of strong solutions of the n-dimensional Burgers equation via discretizations -- Infinitesimals and education -- Calculus with infinitesimals -- Pre-University Analysis En línea: http://dx.doi.org/10.1007/978-3-211-49905-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34591 The Strength of Nonstandard Analysis [documento electrónico] / SpringerLink (Online service) ; Imme van den Berg ; Neves, Vítor . - Vienna : Springer Vienna, 2007 . - XX, 401 p. 16 illus : online resource.
ISBN : 978-3-211-49905-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Partial differential equations History logic Number theory Probabilities Logic and Foundations Probability Theory Stochastic Processes Differential Equations of Sciences Clasificación: 51 Matemáticas Resumen: Nonstandard Analysis enhances mathematical reasoning by introducing new ways of expression and deduction. Distinguishing between standard and nonstandard mathematical objects, its inventor, the eminent mathematician Abraham Robinson, settled in 1961 the centuries-old problem of how to use infinitesimals correctly in analysis. Having also worked as an engineer, he saw not only that his method greatly simplified mathematically proving and teaching, but also served as a powerful tool in modelling, analyzing and solving problems in the applied sciences, among others by effective rescaling and by infinitesimal discretizations. This book reflects the progress made in the forty years since the appearance of Robinson’s revolutionary book Nonstandard Analysis: in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained Nota de contenido: Foundations -- The strength of nonstandard analysis -- The virtue of simplicity -- Analysis of various practices of referring in classical or non standard mathematics -- Stratified analysis? -- ERNA at work -- The Sousa Pinto approach to nonstandard generalised functions -- Neutrices in more dimensions -- Number theory -- Nonstandard methods for additive and combinatorial number theory. A survey -- Nonstandard methods and the Erd?s-Turán conjecture -- Statistics, probability and measures -- Nonstandard likelihood ratio test in exponential families -- A finitary approach for the representation of the infinitesimal generator of a markovian semigroup -- On two recent applications of nonstandard analysis to the theory of financial markets -- Quantum Bernoulli experiments and quantum stochastic processes -- Applications of rich measure spaces formed from nonstandard models -- More on S-measures -- A Radon-Nikodým theorem for a vector-valued reference measure -- Differentiability of Loeb measures -- Differential systems and equations -- The power of Gâteaux differentiability -- Nonstandard Palais-Smale conditions -- Averaging for ordinary differential equations and functional differential equations -- Path-space measure for stochastic differential equation with a coefficient of polynomial growth -- Optimal control for Navier-Stokes equations -- Local-in-time existence of strong solutions of the n-dimensional Burgers equation via discretizations -- Infinitesimals and education -- Calculus with infinitesimals -- Pre-University Analysis En línea: http://dx.doi.org/10.1007/978-3-211-49905-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34591 Ejemplares
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Título : Dual Tableaux: Foundations, Methodology, Case Studies Tipo de documento: documento electrónico Autores: Orlowska, Ewa ; SpringerLink (Online service) ; Golinska Pilarek, Joanna Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2011 Otro editor: Imprint: Springer Colección: Trends in Logic num. 33 Número de páginas: XVI, 523 p Il.: online resource ISBN/ISSN/DL: 978-94-007-0005-5 Idioma : Inglés (eng) Palabras clave: Mathematics Logic Mathematical logic and Foundations Formal Languages Clasificación: 51 Matemáticas Resumen: The book presents logical foundations of dual tableaux together with a number of their applications both to logics traditionally dealt with in mathematics and philosophy (such as modal, intuitionistic, relevant, and many-valued logics) and to various applied theories of computational logic (such as temporal reasoning, spatial reasoning, fuzzy-set-based reasoning, rough-set-based reasoning, order-of magnitude reasoning, reasoning about programs, threshold logics, logics of conditional decisions). The distinguishing feature of most of these applications is that the corresponding dual tableaux are built in a relational language which provides useful means of presentation of the theories. In this way modularity of dual tableaux is ensured. We do not need to develop and implement each dual tableau from scratch, we should only extend the relational core common to many theories with the rules specific for a particular theory Nota de contenido: 1. Dual Tableau for Classical First-Order Logic -- 2. Dual Tableaux for Logics of Classical Algebras of Binary -- 3. Theories of Point Relations and Relational Model Checking -- 4. Dual Tableaux for Peirce Algebras -- 5. Dual Tableaux for Fork Algebras -- 6. Dual Tableaux for Relational Databases -- Part III. Relational Reasoning in Traditional Non-classical Logics -- 7. Dual Tableaux for Classical Modal Logics -- 8. Dual Tableaux for Some Logics Based on Intuitionism -- 9. Dual Tableaux for Relevant Logics -- 10. Dual Tableaux for Many-valued Logics -- Part IV. Relational Reasoning in Logics of Information and Data -- Analysis -- 11. Dual Tableaux for Information Logics of Plain Frames -- 12. Dual Tableaux for Information Logics of Relative Frames -- 13. Dual Tableau for Formal Concept Analysis -- 14. Dual Tableau for a Fuzzy Logic -- 15. Dual Tableaux for Logics of Order of Magnitude Reasoning -- Part V. Relational Reasoning about Time, Space, and Action -- 16. Dual Tableaux for Temporal Logics -- 17. Dual Tableaux for Interval Temporal Logics -- 18. Dual Tableaux for Spatial Reasoning -- 19. Dual Tableaux for Logics of Programs -- Part VI. Beyond Relational Theories -- 20. Dual Tableaux for Threshold Logics -- 21. Signed Dual Tableau for G¨odel-Dummett Logic -- 22. Dual Tableaux for First-Order Post Logics -- 23. Dual Tableau for Propositional Logic with Identity -- 24. Dual Tableaux for Logics of Conditional Decisions -- 25. Methodological Principles of Dual Tableaux -- References -- Index En línea: http://dx.doi.org/10.1007/978-94-007-0005-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33486 Dual Tableaux: Foundations, Methodology, Case Studies [documento electrónico] / Orlowska, Ewa ; SpringerLink (Online service) ; Golinska Pilarek, Joanna . - Dordrecht : Springer Netherlands : Imprint: Springer, 2011 . - XVI, 523 p : online resource. - (Trends in Logic; 33) .
ISBN : 978-94-007-0005-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Logic Mathematical logic and Foundations Formal Languages Clasificación: 51 Matemáticas Resumen: The book presents logical foundations of dual tableaux together with a number of their applications both to logics traditionally dealt with in mathematics and philosophy (such as modal, intuitionistic, relevant, and many-valued logics) and to various applied theories of computational logic (such as temporal reasoning, spatial reasoning, fuzzy-set-based reasoning, rough-set-based reasoning, order-of magnitude reasoning, reasoning about programs, threshold logics, logics of conditional decisions). The distinguishing feature of most of these applications is that the corresponding dual tableaux are built in a relational language which provides useful means of presentation of the theories. In this way modularity of dual tableaux is ensured. We do not need to develop and implement each dual tableau from scratch, we should only extend the relational core common to many theories with the rules specific for a particular theory Nota de contenido: 1. Dual Tableau for Classical First-Order Logic -- 2. Dual Tableaux for Logics of Classical Algebras of Binary -- 3. Theories of Point Relations and Relational Model Checking -- 4. Dual Tableaux for Peirce Algebras -- 5. Dual Tableaux for Fork Algebras -- 6. Dual Tableaux for Relational Databases -- Part III. Relational Reasoning in Traditional Non-classical Logics -- 7. Dual Tableaux for Classical Modal Logics -- 8. Dual Tableaux for Some Logics Based on Intuitionism -- 9. Dual Tableaux for Relevant Logics -- 10. Dual Tableaux for Many-valued Logics -- Part IV. Relational Reasoning in Logics of Information and Data -- Analysis -- 11. Dual Tableaux for Information Logics of Plain Frames -- 12. Dual Tableaux for Information Logics of Relative Frames -- 13. Dual Tableau for Formal Concept Analysis -- 14. Dual Tableau for a Fuzzy Logic -- 15. Dual Tableaux for Logics of Order of Magnitude Reasoning -- Part V. Relational Reasoning about Time, Space, and Action -- 16. Dual Tableaux for Temporal Logics -- 17. Dual Tableaux for Interval Temporal Logics -- 18. Dual Tableaux for Spatial Reasoning -- 19. Dual Tableaux for Logics of Programs -- Part VI. Beyond Relational Theories -- 20. Dual Tableaux for Threshold Logics -- 21. Signed Dual Tableau for G¨odel-Dummett Logic -- 22. Dual Tableaux for First-Order Post Logics -- 23. Dual Tableau for Propositional Logic with Identity -- 24. Dual Tableaux for Logics of Conditional Decisions -- 25. Methodological Principles of Dual Tableaux -- References -- Index En línea: http://dx.doi.org/10.1007/978-94-007-0005-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33486 Ejemplares
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Título : Logical Foundations of Mathematics and Computational Complexity : A Gentle Introduction Tipo de documento: documento electrónico Autores: Pudlák, Pavel ; SpringerLink (Online service) Editorial: Heidelberg : Springer International Publishing Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XIV, 695 p. 49 illus., 4 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-319-00119-7 Idioma : Inglés (eng) Palabras clave: Mathematics Algorithms Mathematical logic Logic and Foundations of Algorithmic Complexity Algorithm Analysis Problem Clasificación: 51 Matemáticas Resumen: The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory Nota de contenido: Mathematician’s world -- Language, logic and computations -- Set theory -- Proofs of impossibility -- The complexity of computations -- Proof complexity -- Consistency, Truth and Existence -- References En línea: http://dx.doi.org/10.1007/978-3-319-00119-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32452 Logical Foundations of Mathematics and Computational Complexity : A Gentle Introduction [documento electrónico] / Pudlák, Pavel ; SpringerLink (Online service) . - Heidelberg : Springer International Publishing : Imprint: Springer, 2013 . - XIV, 695 p. 49 illus., 4 illus. in color : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-3-319-00119-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Algorithms Mathematical logic Logic and Foundations of Algorithmic Complexity Algorithm Analysis Problem Clasificación: 51 Matemáticas Resumen: The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory Nota de contenido: Mathematician’s world -- Language, logic and computations -- Set theory -- Proofs of impossibility -- The complexity of computations -- Proof complexity -- Consistency, Truth and Existence -- References En línea: http://dx.doi.org/10.1007/978-3-319-00119-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32452 Ejemplares
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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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