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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, Nicolaus I 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 B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean, mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would expect to get in reality. 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 Integral, 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johan De Witt
Johan de Witt (24 September 1625 – 20 August 1672) was a Dutch statesman and mathematician who was a major political figure during the First Stadtholderless Period, when flourishing global trade in a period of rapid European colonial expansion made the Dutch a leading trading and seafaring power in Europe, commonly referred to as the Dutch Golden Age. De Witt was elected Grand Pensionary of Holland, and together with his uncle Cornelis de Graeff, he controlled the Dutch political system from around 1650 until the (Disaster Year) of 1672. This progressive cooperation between the two statesmen, and the consequent support of Amsterdam under the rule of De Graeff, was an important political axis that organized the political system within the republic. 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, the Dutch Republic su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Demography
Demography () is the statistical study of human populations: their size, composition (e.g., ethnic group, age), and how they change through the interplay of fertility (births), mortality (deaths), and migration. 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 estima ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jansenists
Jansenism was a 17th- and 18th-century theological movement within Roman Catholicism, primarily active in France, which arose as an attempt to reconcile the theological concepts of free will and divine grace in response to certain developments in the Catholic Church, but later developed political and philosophical aspects in opposition to royal absolutism. It was based on the ideas of Cornelius Jansen, (1585-1638), a Dutch bishop, and his book '' Augustinus''. Jansenists believed that God’s grace was the only way to salvation and that human free will had no role. Jansenists provoked lively debates, particularly in France, where five propositions, including the doctrines of limited atonement and irresistible grace, were extracted from the work and declared heretical by theologians hostile to Jansen. In 1653, Pope Innocent X condemned five ideas from Jansenism in the apostolic constitution '' Cum occasione''. Although Jansenists had some protection under Clement XI, they la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Nicole
Pierre Nicole (; 19 October 1625 – 16 November 1695) was a French writer and one of the most distinguished of the French Jansenists. Life Born in Chartres in 1625, Nicole 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 Jans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antoine Arnauld
Antoine Arnauld (; 6 February 16128 August 1694) was a French Catholic theologian, priest, 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 ag ... [...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. The book helped popularize the concept that a definition with more qualifications or features (the intension) denotes a class with fewer members (the extension), and vice versa. It was based on Aristotle's ideas about ''genus'' and ''species''. The same concept would later become a fundamental element in the works of Gottfried Wilhelm Leibniz. Use as a textbook on Cartesian metaphysics and epistemology Written in French, it became quite popular and was in use up to the twentieth century, introducing the reader to logic, and exhibiting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encyclopædia Britannica Inc
An encyclopedia is a reference work or compendium providing summaries of knowledge, either general or special, in 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 vernacular language), size (few or many volumes), intent ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pascal's Triangle
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role 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 Persia, India, 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 ... [...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] |
