Maistrov / Kotz Probability Theory

A Historical Sketch
1. Auflage 2014
ISBN: 978-1-4832-1863-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 292 Seiten, Web PDF

Probability Theory: A Historical Sketch covers the probability theory, mainly axiomatization problems. The book discusses the prehistory of the probability theory; the first stage in the development of probability theory; and the development of probability theory to the middle of the 19th century. The text also describes the probability theory in the second half of the 19th century; and the axiomatic foundations of the probability theory. Historians and mathematicians will find the book invaluable.

Autoren/Hrsg.

Maistrov, L. E.

Kotz, Samuel

Inhaltsverzeichnis

1;Front Cover;1
2;Probability Theory: A Historical Sketch;4
3;Copyright Page;5
4;Table of Contents;6
5;Foreword;8
6;Translator's Preface;10
7;Author's Preface;14
8;Introduction;16
9;Chapter I. Prehistory of Probability Theory;18
9.1;1 Basic stimuli in the rise of probability theory;18
9.2;2 The role of gambling in the rise of probability theory;22
9.3;3 The first problems;30
9.4;4 Cardano and Tartaglia;33
9.5;5 Elements of probability theory in Galileo's works;43
9.6;6 Basic stages in the development of combinatorics;49
10;Chapter II. The First Stage in the Development of Probability Theory;54
10.1;1 De Mere's legend;55
10.2;2 Letters between Fermat and Pascal;58
10.3;3 Contributions of Huygens to probability theory;63
11;Chapter III. The Development of Probability Theory to the Middle of the Nineteenth Century;71
11.1;1 James Bernoulli and his treatise "Ars Conjectandi";71
11.2;2 The development of probability theory in the first half of the eighteenth century;91
11.3;3 Simpson's contributions to probability theory;97
11.4;4 Thomas Bayes and his theorem;102
11.5;5 Euler's and Daniel Bernoulli's contributions;116
11.6;6 G. L. Buffon;133
11.7;7 Opposition from d'Alembert;138
11.8;8 Jean Antoine de Caritat, Marquis de Condorcet;144
11.9;9 Laplace and his contributions to probability theory;150
11.10;10 Distribution of random errors;163
11.11;11 The state of probability theory in Europe prior to the advent of the Russian (St. Petersburg) school;173
11.12;12 Probability theory in Russia prior to the advent of the St. Petersburg school;176
12;Chapter IV. Probability Theory in the Second Half of the Nineteenth Century;203
12.1;1 Chebyshev—The originator of the Russian school of probability theory;203
12.2;2 Prominent representatives of the St. Petersburg school;223
12.3;3 Probability in physics;240
12.4;4 Bertrand's paradoxes;249
13;Chapter V. The Axiomatic Foundations of Probability Theory;255
13.1;1 The need for axiomatization;255
13.2;2 Prerequisites for axiomatization;263
13.3;3 Bernstein's contributions;264
13.4;4 The frequency approach of R. von Mises;269
13.5;5 The beginning of a new stage in the development of probability theory;274
14;Bibliography;280
15;Index;290