Algebra : sets, symbols, and the language of thought /
John Tabak.
- New Delhi : Viva Books, 2006
- xiv, 224 p. ill. ; 24 cm.
- History of mathematics 01 .
Includes bibliographical references (p. 203-212) and index.
CONTENTS Acknowledgements ix Introduction: Algebra as Language x 1-The First Algebras 1 Mesopotamia: The Beginnings of Algebra 2 Mesopotamians and Second-Degree Equations 5 Clay Tablets/Electronic Calculators 8 The Mesopotamians and Indeterminate Equations 11 Egyptian Algebra 13 Chinese Algebra 15 Rhetorical Algebra 19 2-Greek Algebra 23 The Discovery of the Pythagoreans 25 The Incommensurability of û2 30 Geometric Algebra 32 Algebra Made Visible 34 Diophantus of Alexandria 39 3-Algebra from India to Northern Africa 43 Brahmagupta and the New Algebra 46 Mahavira 50 Bhaskara and the End of an Era 53 Poetry and Algebra 56 Islamic Mathematics 58 Al-Khwarizmi and a New Concept of Algebra 61 A Problem and a Solution 66 Omar Khayyam, Islamic Algebra at its Best 67 Leonardo of Pisa 72 4-Algebra as a Theory of Equations 74 The New Algorithms 78 Algebra as a Tool in Science 84 François Viète, Algebra as a Symbolic Language 86 Thomas Harriot 92 Albert Girard and the Fundamental Theorem of Algebra 96 Further Attempts at a Proof 101 Using Polynomials 107 5-Algebra in Geometry and Analysis 109 René Descartes 114 Descartes on Multiplication 117 Pierre de Fermat 122 Fermat's Last Theorem 126 The New Approach 129 6-The Search for New Structures 132 Niels Henrik Abel 134 Évariste Galois 137 Galois Theory and the Doubling of the Cube 140 Doubling the Cube with a Straight Edge and Compass Is Impossible 144 The Solution of Algebraic Equations 147 Group Therapy in Chemistry 152 7-The Laws of Thought 154 Aristotle 155 Gottfried Leibniz 159 George Boole and the Laws of Thought 164 Boolean Algebra 168 Aristotle and Boole 171 Refining and Extending Boolean Algebra 175 Boolean Algebra and Computers 179 8-The Theory of Matrices and Determinants 182 Early Ideas 185 Spectral Theory 190 The Theory of Matrices 199 Matrix Multiplication 203 A Computational Application of Matrix Algebra 208 Matrices in Ring Theory 210