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How mathematicians think : using ambiguity, contradiction, and paradox to create mathematics / / William Byers
| How mathematicians think : using ambiguity, contradiction, and paradox to create mathematics / / William Byers |
| Autore | Byers William <1943-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, NJ, : Princeton University Press, c2007 |
| Descrizione fisica | 1 online resource (vii, 415 pages) : illustration |
| Disciplina | 510 |
| Soggetto topico |
Mathematicians - Psychology
Mathematics - Psychological aspects Mathematics - Philosophy |
| ISBN |
9786612531453
1-282-53145-X 1-4008-3395-7 0-691-12738-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Acknowledgments -- INTRODUCTION. Turning on the Light -- Section I. The Light of Ambiguity -- Introduction -- Chapter 1. Ambiguity in Mathematics -- Chapter 2. The Contradictory in Mathematics -- Chapter 3. Paradoxes and Mathematics: Infinity and the Real Numbers -- Chapter 4. More Paradoxes of Infinity: Geometry, Cardinality, and Beyond -- Section II. The Light as Idea -- Introduction -- Chapter 5. The Idea as an Organizing Principle -- Chapter 6. Ideas, Logic, and Paradox -- Chapter 7. Great Ideas -- Section III. The Light and the Eye of the Beholder -- Introduction -- Chapter 8. The Truth of Mathematics -- Chapter 9. Conclusion: Is Mathematics Algorithmic or Creative? -- Notes -- Bibliography -- Index |
| Record Nr. | UNINA-9910808916803321 |
Byers William <1943->
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| Princeton, NJ, : Princeton University Press, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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In praise of mathematics / / Alain Badiou with Gilles Haéri ; translated by Susan Spitzer
| In praise of mathematics / / Alain Badiou with Gilles Haéri ; translated by Susan Spitzer |
| Autore | Badiou Alain |
| Edizione | [New English edition] |
| Pubbl/distr/stampa | Cambridge : , : Polity, , [2016] |
| Descrizione fisica | 1 online volume |
| Disciplina | 510.1 |
| Soggetto topico | Mathematics - Philosophy |
| ISBN | 1-5095-1206-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910156200803321 |
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Badiou Alain
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| Cambridge : , : Polity, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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In pursuit of zeta-3 : the world's most mysterious unsolved math problem / / Paul J. Nahin
| In pursuit of zeta-3 : the world's most mysterious unsolved math problem / / Paul J. Nahin |
| Autore | Nahin Paul J. |
| Pubbl/distr/stampa | Princeton, New Jersey : , : Princeton University Press, , [2021] |
| Descrizione fisica | 1 online resource |
| Disciplina | 510.1 |
| Soggetto topico | Mathematics - Philosophy |
| ISBN |
9780691227597
0-691-22759-4 9780691206073 |
| Classificazione | MAT015000TEC000000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Cover -- Contents -- Preface -- 1. Euler's Problem -- 1.1. Introducing Euler -- 1.2. The Harmonic Series and the Riemann Zeta Function -- 1.3. Euler's Constant, the Zeta Function, and Primes -- 1.4. Euler's Gamma Function, the Reflection Formula, and the Zeta Function -- 1.5. Ramanujan's Master Theorem -- 1.6. Integral Forms for the Harmonic Series and Euler's Constant -- 1.7. Euler's Constant and the Zeta Function Redux (and the Digamma Function, Too) -- 1.8. Calculating ζ(3) -- 2. More Wizard Math and the Zeta Function ζ(s) -- 2.1. Euler's Infinite Series for ζ(2) -- 2.2. The Beta Function and the Duplication Formula -- 2.3. Euler Almost Computes ζ(3) -- 2.4. Integral Forms of ζ(2) and ζ(3) -- 2.5. Zeta Near s = 1 -- 2.6. Zeta Prime at s = 0 -- 2.7. Interlude -- 3. Periodic Functions, Fourier Series, and the Zeta Function -- 3.1. The Concept of a Function -- 3.2. Periodic Functions and Their Fourier Series -- 3.3. Complex Fourier Series and Parseval's Power Formula -- 3.4. Calculating ζ(2n) with Fourier Series -- 3.5. How Fourier Series Fail to Compute ζ(3) -- 3.6. Fourier Transforms and Poisson Summation -- 3.7. The Functional Equation of the Zeta Function -- 4. Euler Sums, the Harmonic Series, and the Zeta Function -- 4.1. Euler's Original Sums -- 4.2. The Algebra of Euler Sums -- 4.3. Euler's Double Sums -- 4.4. Euler Sums after Euler -- Epilogue -- Appendix 1: Solving the Impossible by Changing the Rules -- Appendix 2: Evaluating -- Appendix 3: Proof That Equals Zero -- Appendix 4: Double Integration Reversal Isn't Always Legal -- Appendix 5: Impossibility Results from Computer Science -- Challenge Problem Solutions -- Acknowledgments -- Index. |
| Record Nr. | UNINA-9910554222603321 |
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Nahin Paul J.
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| Princeton, New Jersey : , : Princeton University Press, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The indispensability of mathematics [[electronic resource] /] / Mark Colyvan
| The indispensability of mathematics [[electronic resource] /] / Mark Colyvan |
| Autore | Colyvan Mark |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2001 |
| Descrizione fisica | 1 online resource (183 p.) |
| Disciplina | 510 |
| Soggetto topico |
Mathematics - History
Mathematics - Philosophy |
| Soggetto genere / forma | Electronic books. |
| ISBN |
0-19-983313-3
9786610534012 1-280-53401-X 0-19-803144-0 1-4237-5676-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""1 Mathematics and Its Applications""; ""1.1 Realism and Anti-realism in Mathematics""; ""1.2 Indispensability Arguments""; ""1.3 The Road Ahead""; ""2 The Quinean Backdrop""; ""2.1 Introducing Naturalism""; ""2.2 Quinean Naturalism""; ""2.3 The Methodologies of Philosophy and Science""; ""2.4 The Causal Version of Naturalism""; ""2.5 Holism""; ""2.6 The First Premise Revisited""; ""3 The Eleatic Principle""; ""3.1 The Inductive Argument""; ""3.2 The Epistemic Argument""; ""3.3 The Argument from Causal Explanation""; ""3.4 Causal Relevance""
""3.5 Rejecting Inference to the Best Explanation""""3.6 The Content of Scientific Theories""; ""3.7 The Moral""; ""3.8 Recapitulation""; ""4 Field's Fictionalism""; ""4.1 The Science without Numbers Project""; ""4.2 What Is It to Be Indispensable?""; ""4.3 The Role of Confirmation Theory""; ""4.4 The Role of Mathematics in Physical Theories""; ""4.5 Review of Field's Fictionalism""; ""5 Maddy's Objections""; ""5.1 The Objections""; ""5.2 Maddy's Naturalism""; ""5.3 Defending the Indispensability Argument""; ""5.4 Review of Maddy's Objections"" ""6 The Empirical Nature of Mathematical Knowledge""""6.1 The Obviousness of Some Mathematical Truth""; ""6.2 The Unfalsifiability of Mathematics""; ""6.3 The Sober Objection""; ""6.4 Is Mathematics Contingent?""; ""7 Conclusion""; ""7.1 What the Argument Doesn't Show""; ""7.2 The Benacerraf Challenges""; ""7.3 A Slippery Slope?""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""K""; ""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Z"" |
| Record Nr. | UNINA-9910451898703321 |
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Colyvan Mark
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| Oxford ; ; New York, : Oxford University Press, 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The indispensability of mathematics [[electronic resource] /] / Mark Colyvan
| The indispensability of mathematics [[electronic resource] /] / Mark Colyvan |
| Autore | Colyvan Mark |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2001 |
| Descrizione fisica | 1 online resource (183 p.) |
| Disciplina | 510 |
| Soggetto topico |
Mathematics - History
Mathematics - Philosophy |
| ISBN |
0-19-983313-3
9786610534012 1-280-53401-X 0-19-803144-0 1-4237-5676-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""1 Mathematics and Its Applications""; ""1.1 Realism and Anti-realism in Mathematics""; ""1.2 Indispensability Arguments""; ""1.3 The Road Ahead""; ""2 The Quinean Backdrop""; ""2.1 Introducing Naturalism""; ""2.2 Quinean Naturalism""; ""2.3 The Methodologies of Philosophy and Science""; ""2.4 The Causal Version of Naturalism""; ""2.5 Holism""; ""2.6 The First Premise Revisited""; ""3 The Eleatic Principle""; ""3.1 The Inductive Argument""; ""3.2 The Epistemic Argument""; ""3.3 The Argument from Causal Explanation""; ""3.4 Causal Relevance""
""3.5 Rejecting Inference to the Best Explanation""""3.6 The Content of Scientific Theories""; ""3.7 The Moral""; ""3.8 Recapitulation""; ""4 Field's Fictionalism""; ""4.1 The Science without Numbers Project""; ""4.2 What Is It to Be Indispensable?""; ""4.3 The Role of Confirmation Theory""; ""4.4 The Role of Mathematics in Physical Theories""; ""4.5 Review of Field's Fictionalism""; ""5 Maddy's Objections""; ""5.1 The Objections""; ""5.2 Maddy's Naturalism""; ""5.3 Defending the Indispensability Argument""; ""5.4 Review of Maddy's Objections"" ""6 The Empirical Nature of Mathematical Knowledge""""6.1 The Obviousness of Some Mathematical Truth""; ""6.2 The Unfalsifiability of Mathematics""; ""6.3 The Sober Objection""; ""6.4 Is Mathematics Contingent?""; ""7 Conclusion""; ""7.1 What the Argument Doesn't Show""; ""7.2 The Benacerraf Challenges""; ""7.3 A Slippery Slope?""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""K""; ""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Z"" |
| Record Nr. | UNINA-9910777536103321 |
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Colyvan Mark
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| Oxford ; ; New York, : Oxford University Press, 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The indispensability of mathematics / / Mark Colyvan
| The indispensability of mathematics / / Mark Colyvan |
| Autore | Colyvan Mark |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2001 |
| Descrizione fisica | 1 online resource (183 p.) |
| Disciplina | 510 |
| Soggetto topico |
Mathematics - History
Mathematics - Philosophy |
| ISBN |
0-19-983313-3
9786610534012 1-280-53401-X 0-19-803144-0 1-4237-5676-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""1 Mathematics and Its Applications""; ""1.1 Realism and Anti-realism in Mathematics""; ""1.2 Indispensability Arguments""; ""1.3 The Road Ahead""; ""2 The Quinean Backdrop""; ""2.1 Introducing Naturalism""; ""2.2 Quinean Naturalism""; ""2.3 The Methodologies of Philosophy and Science""; ""2.4 The Causal Version of Naturalism""; ""2.5 Holism""; ""2.6 The First Premise Revisited""; ""3 The Eleatic Principle""; ""3.1 The Inductive Argument""; ""3.2 The Epistemic Argument""; ""3.3 The Argument from Causal Explanation""; ""3.4 Causal Relevance""
""3.5 Rejecting Inference to the Best Explanation""""3.6 The Content of Scientific Theories""; ""3.7 The Moral""; ""3.8 Recapitulation""; ""4 Field's Fictionalism""; ""4.1 The Science without Numbers Project""; ""4.2 What Is It to Be Indispensable?""; ""4.3 The Role of Confirmation Theory""; ""4.4 The Role of Mathematics in Physical Theories""; ""4.5 Review of Field's Fictionalism""; ""5 Maddy's Objections""; ""5.1 The Objections""; ""5.2 Maddy's Naturalism""; ""5.3 Defending the Indispensability Argument""; ""5.4 Review of Maddy's Objections"" ""6 The Empirical Nature of Mathematical Knowledge""""6.1 The Obviousness of Some Mathematical Truth""; ""6.2 The Unfalsifiability of Mathematics""; ""6.3 The Sober Objection""; ""6.4 Is Mathematics Contingent?""; ""7 Conclusion""; ""7.1 What the Argument Doesn't Show""; ""7.2 The Benacerraf Challenges""; ""7.3 A Slippery Slope?""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""K""; ""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Z"" |
| Record Nr. | UNINA-9910823365403321 |
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Colyvan Mark
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| Oxford ; ; New York, : Oxford University Press, 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The infinite in mathematics : logico-mathematical writings / Felix Kaufmann ; edited by Brian McGuinness ; with an introd. by Ernest Nagel ; translated from the German by Paul Foulkes
| The infinite in mathematics : logico-mathematical writings / Felix Kaufmann ; edited by Brian McGuinness ; with an introd. by Ernest Nagel ; translated from the German by Paul Foulkes |
| Autore | Kaufmann, Felix |
| Pubbl/distr/stampa | Boston : D. Reidel Publ. Co., c1978 |
| Descrizione fisica | xvii, 235 p. ; 23 cm |
| Disciplina | 511.3 |
| Collana | Vienna circle collection ; 9 |
| Soggetto topico |
Infinite
Mathematics - Philosophy |
| ISBN | 9027708479 |
| Classificazione | AMS 03A05 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000995459707536 |
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Kaufmann, Felix
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| Boston : D. Reidel Publ. Co., c1978 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Infinitesimal differences [[electronic resource] ] : controversies between leibniz and his contemporaries / / edited by Ursula Goldenbaum and Douglas Jesseph
| Infinitesimal differences [[electronic resource] ] : controversies between leibniz and his contemporaries / / edited by Ursula Goldenbaum and Douglas Jesseph |
| Pubbl/distr/stampa | Berlin ; ; New York, : Walter De Gruyter, c2008 |
| Descrizione fisica | 1 online resource (336 p.) |
| Disciplina | 193 |
| Altri autori (Persone) |
GoldenbaumUrsula
JessephDouglas Michael |
| Soggetto topico |
Physics - Philosophy
Mathematics - Philosophy |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-39828-1
9786613398284 3-11-021186-6 |
| Classificazione | CF 5517 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Table of Contents -- Introduction -- Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals -- Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and his Critics -- Indivisibilia Vera - How Leibniz Came to Love Mathematics -- Indivisibles and Infinitesimals in Early Mathematical Texts of Leibniz -- Archimedes, Infinitesimals and the Law of Continuity: On Leibniz's Fictionalism -- An Enticing (Im)Possibility: Infinitesimals, Differentials, and the Leibnizian Calculus -- Productive Ambiguity in Leibniz's Representation of Infinitesimals -- Generality and Infinitely Small Quantities in Leibniz's Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves -- Leibniz's Calculation with Compendia -- Nieuwentijt, Leibniz, and Jacob Hermann on Infinitesimals -- Truth in Fiction: Origins and Consequences of Leibniz's Doctrine of Infinitesimal Magnitudes -- Rule of Continuity and Infinitesimals in Leibniz's Physics -- Leibniz on Infinitesimals and the Reality of Force -- Dead Force, Infinitesimals, and the Mathematicization of Nature -- Backmatter |
| Record Nr. | UNINA-9910454556703321 |
| Berlin ; ; New York, : Walter De Gruyter, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Infinitesimal differences [[electronic resource] ] : controversies between leibniz and his contemporaries / / edited by Ursula Goldenbaum and Douglas Jesseph
| Infinitesimal differences [[electronic resource] ] : controversies between leibniz and his contemporaries / / edited by Ursula Goldenbaum and Douglas Jesseph |
| Pubbl/distr/stampa | Berlin ; ; New York, : Walter De Gruyter, c2008 |
| Descrizione fisica | 1 online resource (336 p.) |
| Disciplina | 193 |
| Altri autori (Persone) |
GoldenbaumUrsula
JessephDouglas Michael |
| Soggetto topico |
Physics - Philosophy
Mathematics - Philosophy |
| ISBN |
1-283-39828-1
9786613398284 3-11-021186-6 |
| Classificazione | CF 5517 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Table of Contents -- Introduction -- Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals -- Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and his Critics -- Indivisibilia Vera - How Leibniz Came to Love Mathematics -- Indivisibles and Infinitesimals in Early Mathematical Texts of Leibniz -- Archimedes, Infinitesimals and the Law of Continuity: On Leibniz's Fictionalism -- An Enticing (Im)Possibility: Infinitesimals, Differentials, and the Leibnizian Calculus -- Productive Ambiguity in Leibniz's Representation of Infinitesimals -- Generality and Infinitely Small Quantities in Leibniz's Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves -- Leibniz's Calculation with Compendia -- Nieuwentijt, Leibniz, and Jacob Hermann on Infinitesimals -- Truth in Fiction: Origins and Consequences of Leibniz's Doctrine of Infinitesimal Magnitudes -- Rule of Continuity and Infinitesimals in Leibniz's Physics -- Leibniz on Infinitesimals and the Reality of Force -- Dead Force, Infinitesimals, and the Mathematicization of Nature -- Backmatter |
| Record Nr. | UNINA-9910782792403321 |
| Berlin ; ; New York, : Walter De Gruyter, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Infinitesimal differences : controversies between leibniz and his contemporaries / / edited by Ursula Goldenbaum and Douglas Jesseph
| Infinitesimal differences : controversies between leibniz and his contemporaries / / edited by Ursula Goldenbaum and Douglas Jesseph |
| Pubbl/distr/stampa | Berlin ; ; New York, : Walter De Gruyter, c2008 |
| Descrizione fisica | 1 online resource (336 p.) |
| Disciplina | 193 |
| Altri autori (Persone) |
GoldenbaumUrsula
JessephDouglas Michael |
| Soggetto topico |
Physics - Philosophy
Mathematics - Philosophy |
| ISBN |
1-283-39828-1
9786613398284 3-11-021186-6 |
| Classificazione | CF 5517 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Table of Contents -- Introduction -- Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals -- Infinity, Infinitesimals, and the Reform of Cavalieri: John Wallis and his Critics -- Indivisibilia Vera - How Leibniz Came to Love Mathematics -- Indivisibles and Infinitesimals in Early Mathematical Texts of Leibniz -- Archimedes, Infinitesimals and the Law of Continuity: On Leibniz's Fictionalism -- An Enticing (Im)Possibility: Infinitesimals, Differentials, and the Leibnizian Calculus -- Productive Ambiguity in Leibniz's Representation of Infinitesimals -- Generality and Infinitely Small Quantities in Leibniz's Mathematics - The Case of his Arithmetical Quadrature of Conic Sections and Related Curves -- Leibniz's Calculation with Compendia -- Nieuwentijt, Leibniz, and Jacob Hermann on Infinitesimals -- Truth in Fiction: Origins and Consequences of Leibniz's Doctrine of Infinitesimal Magnitudes -- Rule of Continuity and Infinitesimals in Leibniz's Physics -- Leibniz on Infinitesimals and the Reality of Force -- Dead Force, Infinitesimals, and the Mathematicization of Nature -- Backmatter |
| Record Nr. | UNINA-9910807368103321 |
| Berlin ; ; New York, : Walter De Gruyter, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
