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John Craig (mathematician)
John Craig (1663 – 11 October 1731) was a Scottish mathematician and theologian. Biography Born in Dumfries and educated at the University of Edinburgh, Craig moved to England and became a vicar in the Church of England. A friend of Isaac Newton, he wrote several minor works about the new calculus. He was elected Fellow of the Royal Society in 1711. Mathematical Principles of Christian Theology He is known for his book ''Theologiae Christianae Principia Mathematica'' (''Mathematical Principles of Christian Theology''), published in 1698. In the aforementioned book, Craig presents a formula that describes how the probability of a historical event depends on the number of primary witnesses, on the chain of transmission through secondary witnesses, on the elapsed time and on the spatial distance. Using this formula, Craig derived that the probability of the story of Jesus would reach 0 in the year 3150. This year he interpreted as the Second Coming of Christ because of vers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus and integral calculus; the former concerns instantaneous Rate of change (mathematics), rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence (mathematics), convergence of infinite sequences and Series (mathematics), infinite series to a well-defined limit (mathematics), limit. Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Later work, including (ε, δ)-definition of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Transactions Of The Royal Society
''Philosophical Transactions of the Royal Society'' is a scientific journal published by the Royal Society. In its earliest days, it was a private venture of the Royal Society's secretary. It was established in 1665, making it the first journal in the world exclusively devoted to science, and therefore also the world's longest-running scientific journal. It became an official society publication in 1752. The use of the word ''philosophical'' in the title refers to natural philosophy, which was the equivalent of what would now be generally called ''science''. Current publication In 1887 the journal expanded and divided into two separate publications, one serving the physical sciences ('' Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences'') and the other focusing on the life sciences ('' Philosophical Transactions of the Royal Society B: Biological Sciences''). Both journals now publish themed issues and issues resulting from pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radius Of Convergence
In mathematics, the radius of convergence of a power series is the radius of the largest disk at the center of the series in which the series converges. It is either a non-negative real number or \infty. When it is positive, the power series converges absolutely and uniformly on compact sets inside the open disk of radius equal to the radius of convergence, and it is the Taylor series of the analytic function to which it converges. In case of multiple singularities of a function (singularities are those values of the argument for which the function is not defined), the radius of convergence is the shortest or minimum of all the respective distances (which are all non-negative numbers) calculated from the center of the disk of convergence to the respective singularities of the function. Definition For a power series ''f'' defined as: :f(z) = \sum_^\infty c_n (z-a)^n, where *''a'' is a complex constant, the center of the disk of convergence, *''c''''n'' is the ''n''-th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mercator Series
In mathematics, the Mercator series or Newton–Mercator series is the Taylor series for the natural logarithm: :\ln(1+x)=x-\frac+\frac-\frac+\cdots In summation notation, :\ln(1+x)=\sum_^\infty \frac x^n. The series converges to the natural logarithm (shifted by 1) whenever -1 History The series was discovered independently by and . It was first published by , in his 1668 treatise ''Logarithmotechnia''.Derivation The series can be obtained from |
Proceedings Of The Royal Society
''Proceedings of the Royal Society'' is the main research journal of the Royal Society. The journal began in 1831 and was split into two series in 1905: * Series A: for papers in physical sciences and mathematics. * Series B: for papers in life sciences. Many landmark scientific discoveries are published in the Proceedings, making it one of the most historically significant science journals. The journal contains several articles written by the most celebrated names in science, such as Paul Dirac, Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series ..., Ernest Rutherford, Erwin Schrödinger, William Lawrence Bragg, Lord Kelvin, J.J. Thomson, James Clerk Maxwell, Dorothy Hodgkin and Stephen Hawking. In 2004, the Royal Society began ''The Journal of the Royal Society ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Logarithm
A hyperbolic sector is a region of the Cartesian plane bounded by a hyperbola and two rays from the origin to it. For example, the two points and on the rectangular hyperbola , or the corresponding region when this hyperbola is re-scaled and its orientation is altered by a rotation leaving the center at the origin, as with the unit hyperbola. A hyperbolic sector in standard position has and . Hyperbolic sectors are the basis for the hyperbolic functions. Area The area of a hyperbolic sector in standard position is natural logarithm of ''b'' . Proof: Integrate under 1/''x'' from 1 to ''b'', add triangle , and subtract triangle . When in standard position, a hyperbolic sector corresponds to a positive hyperbolic angle at the origin, with the measure of the latter being defined as the area of the former. Hyperbolic triangle When in standard position, a hyperbolic sector determines a hyperbolic triangle, the right triangle with one vertex at the origin, base on the diag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Log-likelihood Ratio
In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models based on the ratio of their likelihoods, specifically one found by maximization over the entire parameter space and another found after imposing some constraint. If the constraint (i.e., the null hypothesis) is supported by the observed data, the two likelihoods should not differ by more than sampling error. Thus the likelihood-ratio test tests whether this ratio is significantly different from one, or equivalently whether its natural logarithm is significantly different from zero. The likelihood-ratio test, also known as Wilks test, is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent. In the case of comparing two models each of which has no unknown parameters, use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Stigler
Stephen Mack Stigler (born August 10, 1941) is Ernest DeWitt Burton Distinguished Service Professor at the Department of Statistics of the University of Chicago. He has authored several books on the history of statistics; he is the son of the economist George Stigler. Stigler is also known for Stigler's law of eponymy which states that no scientific discovery is named after its original discoverer (whose first formulation he credits to sociologist Robert K. Merton). Biography Stigler was born in Minneapolis. He received his Ph.D. in 1967 from the University of California, Berkeley. His dissertation was on linear functions of order statistics, and his advisor was Lucien Le Cam. His research has focused on statistical theory of robust estimators and the history of statistics. Stigler taught at University of Wisconsin–Madison until 1979 when he joined the University of Chicago. In 2006, he was elected to membership of the American Philosophical Society, and is a p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gospel Of Luke
The Gospel of Luke), or simply Luke (which is also its most common form of abbreviation). tells of the origins, birth, ministry, death, resurrection, and ascension of Jesus Christ. Together with the Acts of the Apostles, it makes up a two-volume work which scholars call Luke–Acts, accounting for 27.5% of the New Testament. The combined work divides the history of first-century Christianity into three stages, with the gospel making up the first two of these – the life of Jesus the Messiah from his birth to the beginning of his mission in the meeting with John the Baptist, followed by his ministry with events such as the Sermon on the Plain and its Beatitudes, and his Passion, death, and resurrection. Most modern scholars agree that the main sources used for Luke were a), the Gospel of Mark, b), a hypothetical sayings collection called the Q source, and c), material found in no other gospels, often referred to as the L (for Luke) source. The author is anonymo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Coming
The Second Coming (sometimes called the Second Advent or the Parousia) is a Christian (as well as Islamic and Baha'i) belief that Jesus will return again after his ascension to heaven about two thousand years ago. The idea is based on messianic prophecies and is part of most Christian eschatologies. Terminology Several different terms are used to refer to the Second Coming of Christ: In the New Testament, the Greek word ἐπιφάνεια (''epiphaneia'', appearing) is used five times to refer to the return of Christ. The Greek New Testament uses the Greek term ''parousia'' (παρουσία, meaning "arrival", "coming", or "presence") twenty-four times, seventeen of them concerning Christ. However, parousia has the distinct reference to a period of time rather than an instance in time. At parousia is used to clearly describe the period of time that Noah lived. The Greek word ''eleusi''s which means "coming" is not interchangeable with parousia. So this parousia or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jesus
Jesus, likely from he, יֵשׁוּעַ, translit=Yēšūaʿ, label=Hebrew/Aramaic ( AD 30 or 33), also referred to as Jesus Christ or Jesus of Nazareth (among other names and titles), was a first-century Jewish preacher and religious leader; he is the central figure of Christianity, the world's largest religion. Most Christians believe he is the incarnation of God the Son and the awaited Messiah (the Christ) prophesied in the Hebrew Bible. Virtually all modern scholars of antiquity agree that Jesus existed historically. Research into the historical Jesus has yielded some uncertainty on the historical reliability of the Gospels and on how closely the Jesus portrayed in the New Testament reflects the historical Jesus, as the only detailed records of Jesus' life are contained in the Gospels. Jesus was a Galilean Jew who was circumcised, was baptized by John the Baptist, began his own ministry and was often referred to as "rabbi". Jesus debated with fellow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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