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Ars Conjectandi
(Latin for "The Art of Conjecturing") is a book on combinatorics and mathematical probability written by Jacob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre. Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Bla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as or \mathbb. History The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes ''in a fair way'' between two players, who have to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johan De Witt
Johan de Witt (; 24 September 1625 – 20 August 1672), ''lord of Zuid- en Noord-Linschoten, Snelrewaard, Hekendorp en IJsselvere'', was a Dutch statesman and a major political figure in the Dutch Republic in the mid-17th century, the First Stadtholderless Period, when its flourishing sea trade in a period of globalization made the republic a leading European trading and seafaring power – now commonly referred to as the Dutch Golden Age. De Witt controlled the Dutch political system from around 1650 until shortly before his murder and cannibalisation by a pro-Orangist mob in 1672. As a leading republican of the Dutch States Party, de Witt opposed the House of Orange-Nassau and the Orangists and preferred a shift of power from the central government to the regenten. However, his neglect of the Dutch army (as the regents focused only on merchant vessels, thinking they could avoid war) proved disastrous when the Dutch Republic suffered numerous early defeats in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Demography
Demography () is the statistical study of populations, especially human beings. Demographic analysis examines and measures the dimensions and dynamics of populations; it can cover whole societies or groups defined by criteria such as education, nationality, religion, and ethnicity. Educational institutions usually treat demography as a field of sociology, though there are a number of independent demography departments. These methods have primarily been developed to study human populations, but are extended to a variety of areas where researchers want to know how populations of social actors can change across time through processes of birth, death, and migration. In the context of human biological populations, demographic analysis uses administrative records to develop an independent estimate of the population. Demographic analysis estimates are often considered a reliable standard for judging the accuracy of the census information gathered at any time. In the lab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Graunt
John Graunt (24 April 1620 – 18 April 1674) has been regarded as the founder of demography. Graunt was one of the first demographers, and perhaps the first epidemiologist, though by profession he was a haberdasher. He was bankrupted later in life by losses suffered during Great Fire of London and the discrimination he faced following his conversion to Catholicism. Biography Born in London, John Graunt was the eldest of the seven or eight children of Henry and Mary Graunt. Graunt's father was a draper who had moved to London from Hampshire. In February 1641, Graunt married Mary Scott, with whom he had one son (Henry) and three daughters. He became a freeman of the Drapers' Company at age 21. Graunt worked in his father's shop until his father died in 1662, and Graunt became influential in the City. He was able to secure the post of professor of music for his friend William Petty in 1650. He served in various ward offices in Cornhill ward, becoming a common councilman about 166 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jansenists
Jansenism was an Early modern period, early modern Christian theology, theological movement within Catholicism, primarily active in the Kingdom of France, that emphasized original sin, human Total depravity, depravity, the necessity of divine grace, and predestination. It was declared a Heresy in Christianity, heresy by the Catholic Church. The movement originated in the posthumously published work of the Dutch theologian Cornelius Jansen, who died in 1638. It was first popularized by Jansen's friend, Abbot Jean du Vergier de Hauranne of Saint-Cyran-en-Brenne Abbey, and after du Vergier's death in 1643, the movement was led by Antoine Arnauld. Through the 17th and into the 18th centuries, Jansenism was a distinct movement away from the Catholic Church. The theological center of the movement was Port-Royal-des-Champs Abbey, which was a haven for writers including du Vergier, Arnauld, Pierre Nicole, Blaise Pascal, and Jean Racine. Jansenism was opposed by many within the Catholic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Nicole
Pierre Nicole (19 October 1625 – 16 November 1695) was one of the most distinguished of the French Jansenists. Life Born in Chartres, he was the son of a provincial barrister, who took in charge his education. Sent to Paris in 1642 to study theology, he soon entered into relations with the Jansenist community at Port-Royal through his aunt, Marie des Anges Suireau, who was for a short time abbess of the convent, and he taught for a while at the Petites écoles de Port-Royal. Some scruple of conscience forbade him to proceed to the priesthood, and he remained throughout life a "clerk in minor orders," although a profound theological scholar. For some years he was a master in the "little school" for boys established at Port Royal, and had the honour of teaching Greek to young Jean Racine, the future poet. But his chief duty was to act, in collaboration with Antoine Arnauld, as general editor of the controversial literature put forth by the Jansenists. He had a large share in co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antoine Arnauld
Antoine Arnauld (6 February 16128 August 1694) was a French Catholic theologian, philosopher and mathematician. He was one of the leading intellectuals of the Jansenist group of Port-Royal and had a very thorough knowledge of patristics. Contemporaries called him ''le Grand'' to distinguish him from his father. Biography Antoine Arnauld was born in Paris to the Arnauld family. The twentieth and youngest child of the original Antoine Arnauld, he was originally intended for the bar, but decided instead to study theology at the Sorbonne. Here he was brilliantly successful, and his career was flourishing when he came under the influence of Jean du Vergier de Hauranne, the spiritual director and leader of the convent of Port-Royal, and was drawn in the direction of Jansenism. His book, ''De la fréquente Communion'' (1643), was an important step in making the aims and ideals of this movement intelligible to the general public. It attracted controversy by being against frequen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Port-Royal Logic
''Port-Royal Logic'', or ''Logique de Port-Royal'', is the common name of ''La logique, ou l'art de penser'', an important textbook on logic first published anonymously in 1662 by Antoine Arnauld and Pierre Nicole, two prominent members of the Jansenist movement, centered on Port-Royal. Blaise Pascal likely contributed considerable portions of the text. Its linguistic companion piece is the ''Port-Royal Grammar'' (1660) by Arnauld and Lancelot. Written in French, it became quite popular and was in use up to the twentieth century, introducing the reader to logic, and exhibiting strong Cartesian elements in its metaphysics and epistemology (Arnauld having been one of the main philosophers whose objections were published, with replies, in Descartes' '' Meditations on First Philosophy''). The ''Port-Royal Logic'' is sometimes cited as a paradigmatic example of traditional term logic. The philosopher Louis Marin particularly studied it in the 20th century (''La Critique du discou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encyclopædia Britannica Inc
An encyclopedia (American English) or encyclopædia (British English) is a reference work or compendium providing summaries of knowledge either general or special to a particular field or discipline. Encyclopedias are divided into articles or entries that are arranged alphabetically by article name or by thematic categories, or else are hyperlinked and searchable. Encyclopedia entries are longer and more detailed than those in most dictionaries. Generally speaking, encyclopedia articles focus on ''factual information'' concerning the subject named in the article's title; this is unlike dictionary entries, which focus on linguistic information about words, such as their etymology, meaning, pronunciation, use, and grammatical forms.Béjoint, Henri (2000)''Modern Lexicography'', pp. 30–31. Oxford University Press. Encyclopedias have existed for around 2,000 years and have evolved considerably during that time as regards language (written in a major international or a verna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pascal's Triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in India, Persia, China, Germany, and Italy. The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top (the 0th row). The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows. The triangle may be constructed in the following manner: In row 0 (the topmost row), there is a unique nonzero entry 1. Each entry of each subsequent row is constructed by adding the number above and to the left with the number above and to the right, treating blank entries as 0. For example, the initial number of row 1 (or any other row) is 1 (the sum of 0 and 1), whereas the numbers 1 and 3 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Problem Of Points
The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory. One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value. The problem concerns a game of chance with two players who have equal chances of winning each round. The players contribute equally to a prize pot, and agree in advance that the first player to have won a certain number of rounds will collect the entire prize. Now suppose that the game is interrupted by external circumstances before either player has achieved victory. How does one then divide the pot fairly? It is tacitly understood that the division should depend somehow on the number of rounds won by each player, such that a player who is close to winning will get a larger part of the pot. But the problem is not merely one of calculation; it also involves dec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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