The Beginnings and Evolution of Algebra

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Cambridge University Press, Apr 27, 2000 - Mathematics - 179 pages
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The elements of algebra were known to the ancient Mesopotamians at least 4000 years ago. Today algebra stands as one of the cornerstones of modern mathematics. How then did the subject evolve? How did its constituent ideas and concepts arise, and how have they changed over the years? These are the questions that the authors address in this work. The authors challenge the existing view that the development of algebra was driven by the investigation of determinate equations and in particular their solution by radicals. In short they claim that the study of indeterminate equations was no less important. Historians of mathematics, as well as working algebraists who want to look into the history of their subject, will find this an illuminating read.
 

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Contents

Chapter
11
Chapter 3
35
Chapter 4
49
The first advances in algebra in Europe
55
Algebraic symbolism in Europe The German cossists and the development of algebra in Italy
59
Chapter 5
67
The Algebra of Rafael Bombelli Introduction of complex numbers
71
François Viète
75
The fundamental theorem of algebra
94
Gauss criticism
98
The problem of solution of equations by radicals
100
Proof of the unsolvability of the general quintic by radicals
102
Chapter 7
109
Equations with an Abelian group
114
Galois theory
115
The evolution of group theory in the 19th century
120

Creation of a literal calculus
77
Genesis triangulorum
80
Indeterminate equations in the work of Viète
85
Beginning of the theory of determinate equations
87
Chapter 6
91
Descartes treatment of determinate equations
93
The victorious march of group theory
125
Chapter 8
129
Chapter 9
149
Conclusion
161
References
175
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