A few other particular problems on games of chance had been solved fore in the XV-th and XVI-th centuries by Italian mathematicians; however o general theory had been formulated before this famous correspondence In 1655, during his first visit to Paris, the Dutch scientist Christian Huy gens, learns of the work on probability carried out in this correspondence On his return to Holland in 1657, Huygens wrote a small work De ratiociniis in Ludo Aleae the first printed work on the calculus of probabilities. It was a treatise on problems associated with gambling. Because of the inherent appeal of games of chance, probability theory soon became popular, and the subject developed rapidly during the XVIIl-th century The major contributors during this period were Jacob Bernoulli(1654- 1705)and Abraham de Moivre(1667-1754) Jacob(Jacques)Bernoulli was a Swiss mathematician who was the first to use the term integral. He was the first mathematician in the Bernoulli family, a family of famous scientists of the XVIlI-th century. Jacob Bernoulli's most original work was Ars Conjectandi published in Basel in 1713, eight years after his death. The work was incomplete at the time of his death but it was still a work of the greatest significance in the development of the theory of probability. De moivre was a french mathematician who lived most of his life in eng land. A protestant, he was pushed to leave France after Louis XIV revoked the Edict of Nantes in 1685, leading to the expulsion of the Huguenots. De Moivre pioneered the modern approach to the theory of probability, when he published The Doctrine of Chance: A method of calculating the probabilities of events in play in 1718. The definition of statistical independence appears in this book for the first time. The Doctrine of Chance appeared in new ex- panded editions in 1718, 1738 and 1756. The birthday problem(in a slightly different form) appeared in the 1738 edition, the gambler's ruin problem the 1756 edition. The 1756 edition of The Doctrine of Chance contained what is probably de Moivre's most significant contribution to probability, namely the approximation of the binomial distribution by the normal distribution in the case of a large number of trials-which is honored by most probability textbooks as"The First Central Limit Theorem"(we will discuss this the- orem in the course of this semester). He perceives the notion of standard deviation and is the first scientist to write the normal integral A Latin version of the book had been presented earlier to the royal Society and published in the Philosophical Transactions in 1711A few other particular problems on games of chance had been solved be￾fore in the XV-th and XVI-th centuries by Italian mathematicians; however, no general theory had been formulated before this famous correspondence. In 1655, during his first visit to Paris, the Dutch scientist Christian Huy￾gens, learns of the work on probability carried out in this correspondence. On his return to Holland in 1657, Huygens wrote a small work De Ratiociniis in Ludo Aleae the first printed work on the calculus of probabilities. It was a treatise on problems associated with gambling. Because of the inherent appeal of games of chance, probability theory soon became popular, and the subject developed rapidly during the XVIII-th century. The major contributors during this period were Jacob Bernoulli (1654- 1705) and Abraham de Moivre (1667-1754). Jacob (Jacques) Bernoulli was a Swiss mathematician who was the first to use the term integral. He was the first mathematician in the Bernoulli family, a family of famous scientists of the XVIII-th century. Jacob Bernoulli’s most original work was Ars Conjectandi published in Basel in 1713, eight years after his death. The work was incomplete at the time of his death but it was still a work of the greatest significance in the development of the theory of probability. De Moivre was a French mathematician who lived most of his life in Eng￾land. A protestant, he was pushed to leave France after Louis XIV revoked the Edict of Nantes in 1685, leading to the expulsion of the Huguenots. De Moivre pioneered the modern approach to the theory of probability, when he published The Doctrine of Chance: A method of calculating the probabilities of events in play in 17181 . The definition of statistical independence appears in this book for the first time. The Doctrine of Chance appeared in new ex￾panded editions in 1718, 1738 and 1756. The birthday problem (in a slightly different form) appeared in the 1738 edition, the gambler’s ruin problem in the 1756 edition. The 1756 edition of The Doctrine of Chance contained what is probably de Moivre’s most significant contribution to probability, namely the approximation of the binomial distribution by the normal distribution in the case of a large number of trials - which is honored by most probability textbooks as ”The First Central Limit Theorem” (we will discuss this the￾orem in the course of this semester). He perceives the notion of standard deviation and is the first scientist to write the normal integral. 1A Latin version of the book had been presented earlier to the Royal Society and published in the Philosophical Transactions in 1711. 2