Produktbild: The History of Mathematics

The History of Mathematics A Brief Course

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

04.01.2013

Verlag

John Wiley & Sons

Seitenzahl

648

Maße (B/H)

15/25 cm

Gewicht

1275 g

Auflage

3. Auflage

Sprache

Englisch

ISBN

978-1-118-21756-6

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

04.01.2013

Verlag

John Wiley & Sons

Seitenzahl

648

Maße (B/H)

15/25 cm

Gewicht

1275 g

Auflage

3. Auflage

Sprache

Englisch

ISBN

978-1-118-21756-6

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  • Produktbild: The History of Mathematics
  • PREFACE xxiii
     
    Changes from the Second Edition xxiii
     
    Elementary Texts on the History of Mathematics xxiv
     
    PART I. WHAT IS MATHEMATICS?
     
    Contents of Part I 1
     
    1. Mathematics and its History 3
     
    1.1. Two Ways to Look at the History of Mathematics 3
     
    1.2. The Origin of Mathematics 5
     
    1.3. The Philosophy of Mathematics 8
     
    1.4. Our Approach to the History of Mathematics 11
     
    2. Proto-mathematics 14
     
    2.1. Number 14
     
    2.2. Shape 16
     
    2.3. Symbols 18
     
    2.4. Mathematical Reasoning 20
     
    PART II. THE MIDDLE EAST, 2000-1500 BCE
     
    Contents of Part II 25
     
    3. Overview of Mesopotamian Mathematics 27
     
    3.1. A Sketch of Two Millennia of Mesopotamian History 27
     
    3.2. Mathematical Cuneiform Tablets 29
     
    3.3. Systems of Measuring and Counting 30
     
    3.4. The Mesopotamian Numbering System 31
     
    4. Computations in Ancient Mesopotamia 38
     
    4.1. Arithmetic 38
     
    4.2. Algebra 40
     
    5. Geometry in Mesopotamia 46
     
    5.1. The Pythagorean Theorem 46
     
    5.2. Plane Figures 48
     
    5.3. Volumes 49
     
    5.4. Plimpton 322 49
     
    6. Egyptian Numerals and Arithmetic 56
     
    6.1. Sources 56
     
    6.2. The Rhind Papyrus 58
     
    6.3. Egyptian Arithmetic 58
     
    6.4. Computation 59
     
    7. Algebra and Geometry in Ancient Egypt 66
     
    7.1. Algebra Problems in the Rhind Papyrus 66
     
    7.2. Geometry 68
     
    7.3. Areas 69
     
    PART III. GREEK MATHEMATICS FROM 500 BCE TO 500 CE
     
    Contents of Part III 77
     
    8. An Overview of Ancient Greek Mathematics 79
     
    8.1. Sources 80
     
    8.2. General Features of Greek Mathematics 82
     
    8.3. Works and Authors 87
     
    9. Greek Number Theory 91
     
    9.1. The Euclidean Algorithm 92
     
    9.2. The Arithmetica of Nicomachus 93
     
    9.3. Euclid's Number Theory 97
     
    9.4. The Arithmetica of Diophantus 97
     
    10. Fifth-Century Greek Geometry 103
     
    10.1. "Pythagorean" Geometry 103
     
    10.2. Challenge No. 1: Unsolved Problems 106
     
    10.3. Challenge No. 2: The Paradoxes of Zeno of Elea 107
     
    10.4. Challenge No. 3: Irrational Numbers and Incommensurable Lines 108
     
    11. Athenian Mathematics I: The Classical Problems 115
     
    11.1. Squaring the Circle 116
     
    11.2. Doubling the Cube 117
     
    11.3. Trisecting the Angle 122
     
    12. Athenian Mathematics II: Plato and Aristotle 128
     
    12.1. The Influence of Plato 128
     
    12.2. Eudoxan Geometry 130
     
    12.3. Aristotle 134
     
    13. Euclid of Alexandria 140
     
    13.1. The Elements 140
     
    13.2. The Data 144
     
    14. Archimedes of Syracuse 148
     
    14.1. The Works of Archimedes 149
     
    14.2. The Surface of a Sphere 150
     
    14.3. The Archimedes Palimpsest 153
     
    14.4. Quadrature of the Parabola 155
     
    15. Apollonius of Perga 160
     
    15.1. History of the Conics 161
     
    15.2. Contents of the Conics 162
     
    15.3. Foci and the Three- and Four-Line Locus 165
     
    16. Hellenistic and Roman Geometry 169
     
    16.1. Zenodorus 169
     
    16.2. The Parallel Postulate 171
     
    16.3. Heron 172
     
    16.4. Roman Civil Engineering 174
     
    17. Ptolemy's Geography and Astronomy 177
     
    17.1. Geography 177
     
    17.2. Astronomy 180
     
    17.3. The Almagest 184
     
    18. Pappus and the Later Commentators 190
     
    18.1. The Collection of Pappus 190
     
    18.2. The Later Commentators: Theon and Hypatia 196
     
    PART IV. INDIA