Mathematics of the 19th Century

, by Kolmogorov, A. N.; Yushkevich, A. P.; Iushkevich, A. P.

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ISBN: 9780817625528 | 0817625526
Cover: Hardcover
Copyright: 5/1/1992

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Supplemental Materials

Preface
Introduction to the English Translation
Mathematical Logic	p. 1
The Prehistory of Mathematical Logic	p. 1
Leibniz's Symbolic Logic	p. 2
The Quantification of a Predicate	p. 9
The "Formal Logic" of A. De Morgan	p. 10
Boole's Algebra of Logic	p. 14
Jevons' Algebra of Logic	p. 20
Venn's Symbolic Logic	p. 24
Schroder's and Poretskii's Logical Algebra	p. 27
Conclusion	p. 33
Algebra and Algebraic Number Theory	p. 35
Survey of the Evolution of Algebra and of the Theory of Algebraic Numbers During the Period of 1800-1870	p. 35
The Evolution of Algebra	p. 41
Algebraic Proofs of the Fundamental Theorem of Algebra in the 18th Century	p. 41
C.F. Gauss' First Proof	p. 43
C.F. Gauss' Second Proof	p. 44
The Kronecker Construction	p. 47
The Theory of Equations	p. 50
Carl Friedrich Gauss	p. 50
Solution of the Cyclotomic Equation	p. 52
Niels Henrik Abel	p. 55
Evariste Galois	p. 57
The Algebraic Work of Evariste Galois	p. 58
The First Steps in the Evolution of Group Theory	p. 63
The Evolution of Linear Algebra	p. 68
Hypercomplex Numbers	p. 72
William Rowan Hamilton	p. 74
Matrix Algebra	p. 77
The Algebras of Grassmann and Clifford	p. 78
Associative Algebras	p. 79
The Theory of Invariants	p. 80
The Theory of Algebraic Numbers and the Beginnings of Commutative Algebra	p. 86
Disquisitiones Arithmeticae of C.F. Gauss	p. 86
Investigation of the Number of Classes of Quadratic Forms	p. 92
Gaussian Integers and Their Arithmetic	p. 94
Fermat's Last Theorem. The Discovery of E. Kummer	p. 99
Kummer's Theory	p. 102
Difficulties. The Notion of an Integer	p. 106
The Zolotarev Theory. Integral and p-Integral Numbers	p. 108
Dedekind's Ideal Theory	p. 116
On Dedekind's Method. Ideals and Cuts	p. 123
Construction of Ideal Theory in Algebraic Function Fields	p. 125
L. Kronecker's Divisor Theory	p. 131
Conclusion	p. 133
Problems of Number Theory	p. 137
The Arithmetic Theory of Quadratic Forms	p. 137
The General Theory of Forms; Ch. Hermite	p. 137
Korkin's and Zolotarev's Works on the Theory of Quadratic Forms	p. 144
The Investigations of A.A. Markov	p. 151
Geometry of Numbers	p. 154
Origin of the Theory	p. 154
The Work of H.J.S. Smith	p. 159
Geometry of Numbers: Hermann Minkowski	p. 161
The Works of G.F. Voronoi	p. 166
Analytic Methods in Number Theory	p. 171
Lejeune-Dirichlet and the Theorem on Arithmetic Progressions	p. 171
Asymptotic Laws of Number Theory	p. 177
Chebyshev and the Theory of Distribution of Primes	p. 182
The Ideas of Bernhard Riemann	p. 189
Proof of the Asymptotic Law of Distribution of Prime Numbers	p. 192
Some Applications of Analytic Number Theory	p. 194
Arithmetic Functions and Identities. The Works of N.V. Bugaev	p. 196
Transcendental Numbers	p. 201
The Works of Joseph Liouville	p. 201
Charles Hermite and the Proof of the Transcendence of the Number e; The Theorem of Ferdinand Lindemann	p. 205
Conclusion	p. 209
The Theory of Probability	p. 211
Introduction	p. 211
Laplace's Theory of Probability	p. 212
Laplace's Theory of Errors	p. 222
Gauss' Contribution to the Theory of Probability	p. 226
The contributions of Poisson and Cauchy	p. 230
Social and Anthropometric Statistics	p. 242
The Russian School of the Theory of Probability, P.L. Chebyshev	p. 247
New Fields of Application of the Theory of Probability. The Rise of Mathematical Statistics	p. 268
Works of the Second Half of the 19th Century in Western Europe	p. 276
Conclusion	p. 280
Addendum	p. 283
French and German Quotations	p. 283
Notes	p. 285
Additional Bibliography	p. 286
Bibliography	p. 289
Abbreviations	p. 302
Index of Names	p. 304
Table of Contents provided by Blackwell. All Rights Reserved.

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