The Beginnings and Evolution of AlgebraCambridge University Press, 27 d’abr. 2000 - 179 pàgines 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. |
Continguts
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 | 106 |
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 |
Frases i termes més freqüents
19th century al-Karaji algebraic integers algebraic numbers ancient Arabic arbitrary Archimedes arithmetic Arithmetica Babylonians Bombelli Book century BCE classes coefficients commutative complex numbers composition considered construction cube cubic equations curve Dedekind defined denoted Descartes determinate Diophantus domain equation of degree Euclid's Elements Euler evolution of algebra expressed factors Fermat's Fermat's last theorem fields of algebraic formula Galois theory Gauss geometric algebra given hypotenuse ideal indeterminate equations integers introduced investigations irreducible Lagrange linear literal calculus magnitudes mathematicians mathematics matrices memoir method multiplication negative numbers normal subgroup notation number theory obtained operations polynomial powers prime problem proof propositions proved Pythagoreans quadratic equations quartic equations quintic rational function rational numbers real numbers reduced right triangle ruler and compass rules segments showed solution of equations solvable by radicals solve squarable square subgroup substitution symbols theorem transformation treatise unknown Viète Viète's
Referències a aquest llibre
Episodes in the History of Modern Algebra (1800-1950) Jeremy Gray,Karen Hunger Parshall Previsualització no disponible - 2007 |