Mathematics of the 19th Century: Mathematical Logic Algebra Number Theory Probability TheoryBirkhäuser, 11 nov 2013 - 308 páginas This multi-authored effort, Mathematics of the nineteenth century (to be fol lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics fram antiquity to the early nineteenth century, published in three 1 volumes from 1970 to 1972. For reasons explained below, our discussion of twentieth-century mathematics ends with the 1930s. Our general objectives are identical with those stated in the preface to the three-volume edition, i. e. , we consider the development of mathematics not simply as the process of perfecting concepts and techniques for studying real-world spatial forms and quantitative relationships but as a social process as weIl. Mathematical structures, once established, are capable of a certain degree of autonomous development. In the final analysis, however, such immanent mathematical evolution is conditioned by practical activity and is either self-directed or, as is most often the case, is determined by the needs of society. Proceeding from this premise, we intend, first, to unravel the forces that shape mathe matical progress. We examine the interaction of mathematics with the social structure, technology, the natural sciences, and philosophy. Throughan anal ysis of mathematical history proper, we hope to delineate the relationships among the various mathematical disciplines and to evaluate mathematical achievements in the light of the current state and future prospects of the science. The difficulties confronting us considerably exceeded those encountered in preparing the three-volume edition. |
Índice
1 | |
Chapter | 35 |
The Evolution of Algebra | 41 |
The Theory of Algebraic Numbers and | 72 |
Beginnings of Commutative Algebra | 86 |
Kummers Theory | 102 |
Conclusion | 133 |
Geometry of Numbers | 154 |
Analytic Methods in Number Theory | 171 |
Transcendental Numbers | 201 |
Chapter Four | 210 |
Addendum by O B Sheĭnin | 283 |
Bibliography by F A Medvedev | 289 |
Abbreviations | 302 |
Otras ediciones - Ver todo
Mathematics of the 19th Century: Mathematical Logic, Algebra, Number Theory ... A.N. Kolmogorov,Adolʹf Pavlovich I︠U︡shkevich Vista previa restringida - 2001 |
Mathematics of the 19th Century: Mathematical Logic Algebra Number Theory ... A.N. Kolmogorov,A.P. Yushkevich No hay ninguna vista previa disponible - 2001 |
Mathematics of the 19th Century: Mathematical Logic Algebra Number Theory ... A.N. Kolmogorov,A.P. Yushkevich No hay ninguna vista previa disponible - 2001 |
Términos y frases comunes
19th century algebraic numbers analytic applications arithmetic arithmetic derivative Berlin binary biquadratic reciprocity Boole Bugaev calculus Cauchy Cayley Chebyshev coefficients complex numbers congruences considered construction Dedekind defined determinant Dirichlet Disquisitiones arithmeticae distribution divisible divisors equation Euler field finite formula fundamental Galois Gauss geometry Göttingen Hermite Ibid ideas integers introduced invariants investigations Jevons Korkin Korkin and Zolotarev Kronecker Kummer Laplace large numbers law of large lectures Leibniz limit theorem linear Markov Math mathematical logic mathematicians memoir method minima Minkowski Moscow notion number of classes number theory obtained paper Paris Petersburg Poisson polynomial prime ideal prime numbers probabilités problem proof properties proposition proved published quadratic forms quaternions random variables rational representation Riemann roots Russian solution statistical symbols teorii ternary ternary forms theory of algebraic theory of numbers theory of probability theory of quadratic tion values Venn Voronoi Werke