1、 中文 1120 字 毕业论文（设计）英文文献翻译 学生姓名 : * 专 业 : 数学与应用数学 年 级 : 2008 级 学 号 : 200820404119 本 (专 )科 : 本科 指导教师 : * 外文文献 The development of probability theory Summary This paper consist therefore of two parts: The first is concerned with the development of the calyculus of chance before Bernoulli in order to pro
2、vide a background for the achievement of Ja kob Bernoulli and will emphasize especially the role of Leibniz. The second part deals with the relationship between Leibniz add Bernoulli and with Bernoulli himself, particularly with the question how it came about that he introduced probability into math
3、ematics. First some preliminary remarks: Ja kob Bernoulli is of special interest to me, because he is the founder of a mathematical theory of probability. That is to say that it is mainly due to him that a concept of probability was introduced into a field of mathematics. Text Mathematics could call
4、 the calculus of games of chance before Bernoulli. This has another consequence that makes up for a whole programme: The mathematical tools of this calculus should be applied in the whole realm of areas which used a concept of probability. In other words， the Bernoullian probability theory should be
5、 applied not only to games of chance and mortality questions but also to fields like jurisprudence, medicine, etc. My paper consists therefore of two parts: The first is concerned with the development of the calculus of chance before Bernoulli in order to provide a background or the achievements of
6、Ja kob Bernoulli and will emphasize especially the role of Leibniz. The second part deals with the relationship between Leibniz and Bernoulli and Bernoulli himself, particularly with the question how it came about that he introduced probability into mathematics. Whenever one asks why something like
7、a calculus of probabilities arose in the 17th century, one already assumes several things: for instance that before the 17th century it did not exist, and that only then and not later did such a calculus emerge. If one examines the quite impressive literature on the history of probability, one finds
8、 that it is by no means a foregone conclusion that there was no calculus of probabilities before the 17th century. Even if one disregards numerous references to qualitative and quantitative inquiries in antiquity and among the Arabs and the Jews, which, rather freely interpreted, seem to suggest the
9、 application of a kind of probability-concept or the use of statistical methods, it is nevertheless certain that by the end of the 15th century an attempt was being interpreted. People made in some arithmetic works to solve problems of games of chance by computation. But since similar problems form
10、the major part of the early writings on probability in the 17th century, one may be induced to ask why then a calculus of probabilities did not emerge in the late 15th century. One could say many things: For example, that these early game calculations in fact represent one branch of a development wh
11、ich ultimately resulted in a calculus of probabilities. Then why shouldnt one place the origin of the calculus of probabilities before the 17th after all? Quite simply because a suitable concept of probability was missing from the earlier computations. Once the calculus of probabilities had been dev
12、eloped, it became obvious that the older studies of games of chance formed a part of the new discipline. We need not consider the argument that practically all the solutions of problems of games of chance proposed in the 15th and 16th centuries could have been viewed as inexact, and thus at best as approximate, by Fermat in the middle of the 17th century, that is, before the emergence of a calculus of probabilities. The assertion that no concept of probability was applied to games of chance up to the middle of the 17th century can mean either that there
