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