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 |
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