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The History of Mathematics : A Brief Course
The History of Mathematics : A Brief Course
Autore Cooke Roger L
Edizione [3rd ed.]
Pubbl/distr/stampa New York : , : John Wiley & Sons, Incorporated, , 2012
Descrizione fisica 1 online resource (730 pages)
Disciplina 510/.9
Altri autori (Persone) CookeRoger L
Soggetto topico Mathematics - History
Soggetto genere / forma Electronic books.
ISBN 9781118460290
9781118217566
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Title Page -- Copyright -- Preface -- Changes from the Second Edition -- Elementary Texts on the History of Mathematics -- Part I: What is Mathematics? -- Contents of Part I -- Chapter 1: Mathematics and its History -- 1.1 Two Ways to Look at the History of Mathematics -- 1.2 The Origin of Mathematics -- 1.3 The Philosophy of Mathematics -- 1.4 Our Approach to the History of Mathematics -- Questions for Reflection -- Chapter 2: Proto-mathematics -- 2.1 Number -- 2.2 Shape -- 2.3 Symbols -- 2.4 Mathematical Reasoning -- Problems and Questions -- Part II: The Middle East, 2000-1500 BCE -- Contents of Part II -- Chapter 3: Overview of Mesopotamian Mathematics -- 3.1 A Sketch of Two Millennia of Mesopotamian History -- 3.2 Mathematical Cuneiform Tablets -- 3.3 Systems of Measuring and Counting -- 3.4 The Mesopotamian Numbering System -- Problems and Questions -- Chapter 4: Computations in Ancient Mesopotamia -- 4.1 Arithmetic -- 4.2 Algebra -- Problems and Questions -- Chapter 5: Geometry in Mesopotamia -- 5.1 The Pythagorean Theorem -- 5.2 Plane Figures -- 5.3 Volumes -- 5.4 Plimpton 322 -- Problems and Questions -- Chapter 6: Egyptian Numerals and Arithmetic -- 6.1 Sources -- 6.2 The Rhind Papyrus -- 6.3 Egyptian Arithmetic -- 6.4 Computation -- Problems and Questions -- Chapter 7: Algebra and Geometry in Ancient Egypt -- 7.1 Algebra Problems in the Rhind Papyrus -- 7.2 Geometry -- 7.3 Areas -- Problems and Questions -- Part III: Greek Mathematics From 500 BCE to 500 CE -- Contents of Part III -- Chapter 8: An Overview of Ancient Greek Mathematics -- 8.1 Sources -- 8.2 General Features of Greek Mathematics -- 8.3 Works and Authors -- Questions -- Chapter 9: Greek Number Theory -- 9.1 The Euclidean Algorithm -- 9.2 The Arithmetica of Nicomachus -- 9.3 Euclid's Number Theory -- 9.4 The Arithmetica of Diophantus -- Problems and Questions.
Chapter 10: Fifth-Century Greek Geometry -- 10.1 "Pythagorean" Geometry -- 10.2 Challenge No. 1: Unsolved Problems -- 10.3 Challenge No. 2: The Paradoxes of Zeno of Elea -- 10.4 Challenge No. 3: Irrational Numbers and Incommensurable Lines -- Problems and Questions -- Chapter 11: Athenian Mathematics I: The Classical Problems -- 11.1 Squaring the Circle -- 11.2 Doubling the Cube -- 11.3 Trisecting the Angle -- Problems and Questions -- Chapter 12: Athenian Mathematics II: Plato and Aristotle -- 12.1 The Influence of Plato -- 12.2 Eudoxan Geometry -- 12.3 Aristotle -- Problems and Questions -- Chapter 13: Euclid of Alexandria -- 13.1 The Elements -- 13.2 The Data -- Problems and Questions -- Chapter 14: Archimedes of Syracuse -- 14.1 The Works of Archimedes -- 14.2 The Surface of a Sphere -- 14.3 The Archimedes Palimpsest -- 14.4 Quadrature of the Parabola -- Problems and Questions -- Chapter 15: Apollonius of Perga -- 15.1 History of the Conics -- 15.2 Contents of the Conics -- 15.3 Foci and the Three-and Four-line Locus -- Problems and Questions -- Chapter 16: Hellenistic and Roman Geometry -- 16.1 Zenodorus -- 16.2 The Parallel Postulate -- 16.3 Heron -- 16.4 Roman Civil Engineering -- Problems and Questions -- Chapter 17: Ptolemy's Geography and Astronomy -- 17.1 Geography -- 17.2 Astronomy -- 17.3 The Almagest -- Problems and Questions -- Part IV: India, China, and Japan 500 BCE-1700 CE -- Contents of Part IV -- Chapter 18: Pappus and the Later Commentators -- 18.1 The Collection of Pappus -- 18.2 The Later Commentators: Theon and Hypatia -- Problems and Questions -- Chapter 19: Overview of Mathematics in India -- 19.1 The Sulva Sutras -- 19.2 Buddhist and Jain Mathematics -- 19.3 The Bakshali Manuscript -- 19.4 The Siddhantas -- 19.5 Hindu-Arabic Numerals -- 19.6 Aryabhata I -- 19.7 Brahmagupta -- 19.8 Bhaskara II -- 19.9 Muslim India.
19.10 Indian Mathematics in the Colonial Period and After -- Questions -- Chapter 20: From the Vedas to Aryabhata I -- 20.1 Problems from the Sulva Sutras -- 20.2 Aryabhata I: Geometry and Trigonometry -- Problems and Questions -- Chapter 21: Brahmagupta, the Kuttaka, and Bhaskara II -- 21.1 Brahmagupta's Plane and Solid Geometry -- 21.2 Brahmagupta's Number Theory and Algebra -- 21.3 The Kuttaka -- 21.4 Algebra in the Works of Bhaskara II -- 21.5 Geometry in the Works of Bhaskara II -- Problems and Questions -- Chapter 22: Early Classics of Chinese Mathematics -- 22.1 Works and Authors -- 22.2 China's Encounter with Western Mathematics -- 22.3 The Chinese Number System -- 22.4 Algebra -- 22.5 Contents of the Jiu Zhang Suan Shu -- 22.6 Early Chinese Geometry -- Problems and Questions -- Chapter 23: Later Chinese Algebra and Geometry -- 23.1 Algebra -- 23.2 Later Chinese Geometry -- Problems and Questions -- Chapter 24: Traditional Japanese Mathematics -- 24.1 Chinese Influence and Calculating Devices -- 24.2 Japanese Mathematicians and Their Works -- 24.3 Japanese Geometry and Algebra -- 24.4 Sangaku -- Problems and Questions -- Part V: Islamic Mathematics, 800-1500 -- Contents of Part V -- Chapter 25: Overview of Islamic Mathematics -- 25.1 A Brief Sketch of the Islamic Civilization -- 25.2 Islamic Science in General -- 25.3 Some Muslim Mathematicians and their Works -- Questions -- Chapter 26: Islamic Number Theory and Algebra -- 26.1 Number Theory -- 26.2 Algebra -- Problems and Questions -- Chapter 27: Islamic Geometry -- 27.1 The Parallel Postulate -- 27.2 Thabit ibn-Qurra -- 27.3 Al-Biruni: Trigonometry -- 27.4 Al-Kuhi -- 27.5 Al-Haytham and Ibn-Sahl -- 27.6 Omar Khayyam -- 27.7 Nasir al-Din al-Tusi -- Problems and Questions -- Part VI: European Mathematics, 500-1900 -- Contents of Part VI -- Chapter 28: Medieval and Early Modern Europe.
28.1 From the Fall of Rome to the Year 1200 -- 28.2 The High Middle Ages -- 28.3 The Early Modern Period -- 28.4 Northern European Advances -- Questions -- Chapter 29: European Mathematics: 1200-1500 -- 29.1 Leonardo of Pisa (Fibonacci) -- 29.2 Hindu-Arabic numerals -- 29.3 Jordanus Nemorarius -- 29.4 Nicole d'Oresme -- 29.5 Trigonometry: Regiomontanus and Pitiscus -- 29.6 A Mathematical Skill: ProsthaphÆresis -- 29.7 Algebra: Pacioli and Chuquet -- Problems and Questions -- Chapter 30: Sixteenth-Century Algebra -- 30.1 Solution of Cubic and Quartic Equations -- 30.2 Consolidation -- 30.3 Logarithms -- 30.4 Hardware: slide rules and calculating machines -- Problems and Questions -- Chapter 31: Renaissance Art and Geometry -- 31.1 The Greek Foundations -- 31.2 The Renaissance Artists and Geometers -- 31.3 Projective Properties -- Problems and Questions -- Chapter 32: The Calculus Before Newton and Leibniz -- 32.1 Analytic Geometry -- 32.2 Components of the Calculus -- Problems and Questions -- Chapter 33: Newton and Leibniz -- 33.1 Isaac Newton -- 33.2 Gottfried Wilhelm von Leibniz -- 33.3 The Disciples of Newton and Leibniz -- 33.4 Philosophical Issues -- 33.5 The Priority Dispute -- 33.6 Early Textbooks on Calculus -- Problems and Questions -- Chapter 34: Consolidation of the Calculus -- 34.1 Ordinary Differential Equations -- 34.2 Partial Differential Equations -- 34.3 Calculus of Variations -- 34.4 Foundations of the Calculus -- Problems and Questions -- Part VII: Special Topics -- Contents of Part VII -- Chapter 35: Women Mathematicians -- 35.1 Sof'ya Kovalevskaya -- 35.2 Grace Chisholm Young -- 35.3 Emmy Noether -- Questions -- Chapter 36: Probability -- 36.1 Cardano -- 36.2 Fermat and Pascal -- 36.3 Huygens -- 36.4 Leibniz -- 36.5 The Ars Conjectandi of James Bernoulli -- 36.6 De Moivre -- 36.7 The Petersburg Paradox -- 36.8 Laplace.
36.9 Legendre -- 36.10 Gauss -- 36.11 Philosophical Issues -- 36.12 Large Numbers and Limit Theorems -- Problems and Questions -- Chapter 37: Algebra from 1600 to 1850 -- 37.1 Theory of Equations -- 37.2 Euler, D'Alembert, and Lagrange -- 37.3 The Fundamental Theorem of Algebra and Solution by Radicals -- Problems and Questions -- Chapter 38: Projective and Algebraic Geometry and Topology -- 38.1 Projective Geometry -- 38.2 Algebraic Geometry -- 38.3 Topology -- Problems and Questions -- Chapter 39: Differential Geometry -- 39.1 Plane Curves -- 39.2 The Eighteenth Century: Surfaces -- 39.3 Space Curves: The French Geometers -- 39.4 Gauss: Geodesics and Developable Surfaces -- 39.5 The French and British Geometers -- 39.6 Grassmann and Riemann: Manifolds -- 39.7 Differential Geometry and Physics -- 39.8 The Italian Geometers -- Problems and Questions -- Chapter 40: Non-Euclidean Geometry -- 40.1 Saccheri -- 40.2 Lambert and Legendre -- 40.3 Gauss -- 40.4 The First Treatises -- 40.5 Lobachevskii's Geometry -- 40.6 János Bólyai -- 40.7 The Reception of Non-Euclidean Geometry -- 40.8 Foundations of Geometry -- Problems and Questions -- Chapter 41: Complex Analysis -- 41.1 Imaginary and Complex Numbers -- 41.2 Analytic Function Theory -- 41.3 Comparison of the Three Approaches -- Problems and Questions -- Chapter 42: Real Numbers, Series, and Integrals -- 42.1 Fourier Series, Functions, and Integrals -- 42.2 Fourier Series -- 42.3 Fourier Integrals -- 42.4 General Trigonometric Series -- Problems and Questions -- Chapter 43: Foundations of Real Analysis -- 43.1 What Is a Real Number? -- 43.2 Completeness of the Real Numbers -- 43.3 Uniform Convergence and Continuity -- 43.4 General Integrals and Discontinuous Functions -- 43.5 The Abstract and the Concrete -- 43.6 Discontinuity as a Positive Property -- Problems and Questions -- Chapter 44: Set Theory.
44.1 Technical Background.
Record Nr. UNINA-9910795812003321
Cooke Roger L  
New York : , : John Wiley & Sons, Incorporated, , 2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The History of Mathematics : A Brief Course
The History of Mathematics : A Brief Course
Autore Cooke Roger L
Edizione [3rd ed.]
Pubbl/distr/stampa New York : , : John Wiley & Sons, Incorporated, , 2012
Descrizione fisica 1 online resource (730 pages)
Disciplina 510/.9
Altri autori (Persone) CookeRoger L
Soggetto topico Mathematics - History
Soggetto genere / forma Electronic books.
ISBN 9781118460290
9781118217566
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Title Page -- Copyright -- Preface -- Changes from the Second Edition -- Elementary Texts on the History of Mathematics -- Part I: What is Mathematics? -- Contents of Part I -- Chapter 1: Mathematics and its History -- 1.1 Two Ways to Look at the History of Mathematics -- 1.2 The Origin of Mathematics -- 1.3 The Philosophy of Mathematics -- 1.4 Our Approach to the History of Mathematics -- Questions for Reflection -- Chapter 2: Proto-mathematics -- 2.1 Number -- 2.2 Shape -- 2.3 Symbols -- 2.4 Mathematical Reasoning -- Problems and Questions -- Part II: The Middle East, 2000-1500 BCE -- Contents of Part II -- Chapter 3: Overview of Mesopotamian Mathematics -- 3.1 A Sketch of Two Millennia of Mesopotamian History -- 3.2 Mathematical Cuneiform Tablets -- 3.3 Systems of Measuring and Counting -- 3.4 The Mesopotamian Numbering System -- Problems and Questions -- Chapter 4: Computations in Ancient Mesopotamia -- 4.1 Arithmetic -- 4.2 Algebra -- Problems and Questions -- Chapter 5: Geometry in Mesopotamia -- 5.1 The Pythagorean Theorem -- 5.2 Plane Figures -- 5.3 Volumes -- 5.4 Plimpton 322 -- Problems and Questions -- Chapter 6: Egyptian Numerals and Arithmetic -- 6.1 Sources -- 6.2 The Rhind Papyrus -- 6.3 Egyptian Arithmetic -- 6.4 Computation -- Problems and Questions -- Chapter 7: Algebra and Geometry in Ancient Egypt -- 7.1 Algebra Problems in the Rhind Papyrus -- 7.2 Geometry -- 7.3 Areas -- Problems and Questions -- Part III: Greek Mathematics From 500 BCE to 500 CE -- Contents of Part III -- Chapter 8: An Overview of Ancient Greek Mathematics -- 8.1 Sources -- 8.2 General Features of Greek Mathematics -- 8.3 Works and Authors -- Questions -- Chapter 9: Greek Number Theory -- 9.1 The Euclidean Algorithm -- 9.2 The Arithmetica of Nicomachus -- 9.3 Euclid's Number Theory -- 9.4 The Arithmetica of Diophantus -- Problems and Questions.
Chapter 10: Fifth-Century Greek Geometry -- 10.1 "Pythagorean" Geometry -- 10.2 Challenge No. 1: Unsolved Problems -- 10.3 Challenge No. 2: The Paradoxes of Zeno of Elea -- 10.4 Challenge No. 3: Irrational Numbers and Incommensurable Lines -- Problems and Questions -- Chapter 11: Athenian Mathematics I: The Classical Problems -- 11.1 Squaring the Circle -- 11.2 Doubling the Cube -- 11.3 Trisecting the Angle -- Problems and Questions -- Chapter 12: Athenian Mathematics II: Plato and Aristotle -- 12.1 The Influence of Plato -- 12.2 Eudoxan Geometry -- 12.3 Aristotle -- Problems and Questions -- Chapter 13: Euclid of Alexandria -- 13.1 The Elements -- 13.2 The Data -- Problems and Questions -- Chapter 14: Archimedes of Syracuse -- 14.1 The Works of Archimedes -- 14.2 The Surface of a Sphere -- 14.3 The Archimedes Palimpsest -- 14.4 Quadrature of the Parabola -- Problems and Questions -- Chapter 15: Apollonius of Perga -- 15.1 History of the Conics -- 15.2 Contents of the Conics -- 15.3 Foci and the Three-and Four-line Locus -- Problems and Questions -- Chapter 16: Hellenistic and Roman Geometry -- 16.1 Zenodorus -- 16.2 The Parallel Postulate -- 16.3 Heron -- 16.4 Roman Civil Engineering -- Problems and Questions -- Chapter 17: Ptolemy's Geography and Astronomy -- 17.1 Geography -- 17.2 Astronomy -- 17.3 The Almagest -- Problems and Questions -- Part IV: India, China, and Japan 500 BCE-1700 CE -- Contents of Part IV -- Chapter 18: Pappus and the Later Commentators -- 18.1 The Collection of Pappus -- 18.2 The Later Commentators: Theon and Hypatia -- Problems and Questions -- Chapter 19: Overview of Mathematics in India -- 19.1 The Sulva Sutras -- 19.2 Buddhist and Jain Mathematics -- 19.3 The Bakshali Manuscript -- 19.4 The Siddhantas -- 19.5 Hindu-Arabic Numerals -- 19.6 Aryabhata I -- 19.7 Brahmagupta -- 19.8 Bhaskara II -- 19.9 Muslim India.
19.10 Indian Mathematics in the Colonial Period and After -- Questions -- Chapter 20: From the Vedas to Aryabhata I -- 20.1 Problems from the Sulva Sutras -- 20.2 Aryabhata I: Geometry and Trigonometry -- Problems and Questions -- Chapter 21: Brahmagupta, the Kuttaka, and Bhaskara II -- 21.1 Brahmagupta's Plane and Solid Geometry -- 21.2 Brahmagupta's Number Theory and Algebra -- 21.3 The Kuttaka -- 21.4 Algebra in the Works of Bhaskara II -- 21.5 Geometry in the Works of Bhaskara II -- Problems and Questions -- Chapter 22: Early Classics of Chinese Mathematics -- 22.1 Works and Authors -- 22.2 China's Encounter with Western Mathematics -- 22.3 The Chinese Number System -- 22.4 Algebra -- 22.5 Contents of the Jiu Zhang Suan Shu -- 22.6 Early Chinese Geometry -- Problems and Questions -- Chapter 23: Later Chinese Algebra and Geometry -- 23.1 Algebra -- 23.2 Later Chinese Geometry -- Problems and Questions -- Chapter 24: Traditional Japanese Mathematics -- 24.1 Chinese Influence and Calculating Devices -- 24.2 Japanese Mathematicians and Their Works -- 24.3 Japanese Geometry and Algebra -- 24.4 Sangaku -- Problems and Questions -- Part V: Islamic Mathematics, 800-1500 -- Contents of Part V -- Chapter 25: Overview of Islamic Mathematics -- 25.1 A Brief Sketch of the Islamic Civilization -- 25.2 Islamic Science in General -- 25.3 Some Muslim Mathematicians and their Works -- Questions -- Chapter 26: Islamic Number Theory and Algebra -- 26.1 Number Theory -- 26.2 Algebra -- Problems and Questions -- Chapter 27: Islamic Geometry -- 27.1 The Parallel Postulate -- 27.2 Thabit ibn-Qurra -- 27.3 Al-Biruni: Trigonometry -- 27.4 Al-Kuhi -- 27.5 Al-Haytham and Ibn-Sahl -- 27.6 Omar Khayyam -- 27.7 Nasir al-Din al-Tusi -- Problems and Questions -- Part VI: European Mathematics, 500-1900 -- Contents of Part VI -- Chapter 28: Medieval and Early Modern Europe.
28.1 From the Fall of Rome to the Year 1200 -- 28.2 The High Middle Ages -- 28.3 The Early Modern Period -- 28.4 Northern European Advances -- Questions -- Chapter 29: European Mathematics: 1200-1500 -- 29.1 Leonardo of Pisa (Fibonacci) -- 29.2 Hindu-Arabic numerals -- 29.3 Jordanus Nemorarius -- 29.4 Nicole d'Oresme -- 29.5 Trigonometry: Regiomontanus and Pitiscus -- 29.6 A Mathematical Skill: ProsthaphÆresis -- 29.7 Algebra: Pacioli and Chuquet -- Problems and Questions -- Chapter 30: Sixteenth-Century Algebra -- 30.1 Solution of Cubic and Quartic Equations -- 30.2 Consolidation -- 30.3 Logarithms -- 30.4 Hardware: slide rules and calculating machines -- Problems and Questions -- Chapter 31: Renaissance Art and Geometry -- 31.1 The Greek Foundations -- 31.2 The Renaissance Artists and Geometers -- 31.3 Projective Properties -- Problems and Questions -- Chapter 32: The Calculus Before Newton and Leibniz -- 32.1 Analytic Geometry -- 32.2 Components of the Calculus -- Problems and Questions -- Chapter 33: Newton and Leibniz -- 33.1 Isaac Newton -- 33.2 Gottfried Wilhelm von Leibniz -- 33.3 The Disciples of Newton and Leibniz -- 33.4 Philosophical Issues -- 33.5 The Priority Dispute -- 33.6 Early Textbooks on Calculus -- Problems and Questions -- Chapter 34: Consolidation of the Calculus -- 34.1 Ordinary Differential Equations -- 34.2 Partial Differential Equations -- 34.3 Calculus of Variations -- 34.4 Foundations of the Calculus -- Problems and Questions -- Part VII: Special Topics -- Contents of Part VII -- Chapter 35: Women Mathematicians -- 35.1 Sof'ya Kovalevskaya -- 35.2 Grace Chisholm Young -- 35.3 Emmy Noether -- Questions -- Chapter 36: Probability -- 36.1 Cardano -- 36.2 Fermat and Pascal -- 36.3 Huygens -- 36.4 Leibniz -- 36.5 The Ars Conjectandi of James Bernoulli -- 36.6 De Moivre -- 36.7 The Petersburg Paradox -- 36.8 Laplace.
36.9 Legendre -- 36.10 Gauss -- 36.11 Philosophical Issues -- 36.12 Large Numbers and Limit Theorems -- Problems and Questions -- Chapter 37: Algebra from 1600 to 1850 -- 37.1 Theory of Equations -- 37.2 Euler, D'Alembert, and Lagrange -- 37.3 The Fundamental Theorem of Algebra and Solution by Radicals -- Problems and Questions -- Chapter 38: Projective and Algebraic Geometry and Topology -- 38.1 Projective Geometry -- 38.2 Algebraic Geometry -- 38.3 Topology -- Problems and Questions -- Chapter 39: Differential Geometry -- 39.1 Plane Curves -- 39.2 The Eighteenth Century: Surfaces -- 39.3 Space Curves: The French Geometers -- 39.4 Gauss: Geodesics and Developable Surfaces -- 39.5 The French and British Geometers -- 39.6 Grassmann and Riemann: Manifolds -- 39.7 Differential Geometry and Physics -- 39.8 The Italian Geometers -- Problems and Questions -- Chapter 40: Non-Euclidean Geometry -- 40.1 Saccheri -- 40.2 Lambert and Legendre -- 40.3 Gauss -- 40.4 The First Treatises -- 40.5 Lobachevskii's Geometry -- 40.6 János Bólyai -- 40.7 The Reception of Non-Euclidean Geometry -- 40.8 Foundations of Geometry -- Problems and Questions -- Chapter 41: Complex Analysis -- 41.1 Imaginary and Complex Numbers -- 41.2 Analytic Function Theory -- 41.3 Comparison of the Three Approaches -- Problems and Questions -- Chapter 42: Real Numbers, Series, and Integrals -- 42.1 Fourier Series, Functions, and Integrals -- 42.2 Fourier Series -- 42.3 Fourier Integrals -- 42.4 General Trigonometric Series -- Problems and Questions -- Chapter 43: Foundations of Real Analysis -- 43.1 What Is a Real Number? -- 43.2 Completeness of the Real Numbers -- 43.3 Uniform Convergence and Continuity -- 43.4 General Integrals and Discontinuous Functions -- 43.5 The Abstract and the Concrete -- 43.6 Discontinuity as a Positive Property -- Problems and Questions -- Chapter 44: Set Theory.
44.1 Technical Background.
Record Nr. UNINA-9910815547603321
Cooke Roger L  
New York : , : John Wiley & Sons, Incorporated, , 2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui