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The History of Mathematics [electronic resource]: A Brief Course

Roger L. Cooke
Format
EBook; Book; Online
Published
New York : Wiley, 2013.
Edition
3rd ed
Language
English
Related Title
Virtual Library of Virginia EBL DDA purchased title
ISBN
9781118460290 (electronic bk.), 1118460294 (electronic bk.), 9781118217566 (cloth), 111821756X (cloth), 9781118464977, 1118464974
Summary
Aimed at undergraduate students majoring in mathematics, science, engineering, and secondary education, this third edition of "an amazing assemblage of worldwide contributions in mathematics"" (CHOICE) examines the elementary arithmetic, geometry, and algebra of a number of cultures to show how abstract mathematics of the modern world arises from fundamental societal needs.
Contents
  • Cover; 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 Mathematics3.1 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 ComputationProblems 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 Geometry10.1 "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 Elements13.2 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.
Description
1 online resource : illustrations
Notes
  • Chapter 17: Ptolemy's Geography and Astronomy.
  • Includes bibliographical references and index.
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Technical Details
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    a| Cover; 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.
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    a| Chapter 10: Fifth-Century Greek Geometry10.1 "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.
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    a| Chapter 17: Ptolemy's Geography and Astronomy.
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