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Faà Di Bruno's Formula
Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives. It is named after , although he was not the first to state or prove the formula. In 1800, more than 50 years before Faà di Bruno, the French mathematician Louis François Antoine Arbogast had stated the formula in a calculus textbook, which is considered to be the first published reference on the subject. Perhaps the most well-known form of Faà di Bruno's formula says that f(g(x))=\sum \frac\cdot f^(g(x))\cdot \prod_^n\left(g^(x)\right)^, where the sum is over all ''n''-tuples of nonnegative integers (''m''1, ..., ''m''''n'') satisfying the constraint 1\cdot m_1+2\cdot m_2+3\cdot m_3+\cdots+n\cdot m_n=n. Sometimes, to give it a memorable pattern, it is written in a way in which the coefficients that have the combinatorial interpretation discussed below are less explicit: : f(g(x)) =\sum \frac\cdot f^(g(x))\cdot \prod_^n\left(\frac\right)^. Combining the terms with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reciprocal (mathematics)
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a fraction ''a''/''b'' is ''b''/''a''. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function ''f''(''x'') that maps ''x'' to 1/''x'', is one of the simplest examples of a function which is its own inverse (an involution). Multiplying by a number is the same as dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yields the original number (since the product of the number and its reciprocal is 1). The term ''reciprocal' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birkhäuser Verlag
Birkhäuser was a Swiss publisher founded in 1879 by Emil Birkhäuser. It was acquired by Springer Science+Business Media in 1985. Today it is an imprint used by two companies in unrelated fields: * Springer continues to publish science (particularly: history of science, geosciences, computer science) and mathematics books and journals under the Birkhäuser imprint (with a leaf logo) sometimes called Birkhäuser Science. * Birkhäuser Verlag – an architecture and design publishing company was (re)created in 2010 when Springer sold its design and architecture segment to ACTAR. The resulting Spanish-Swiss company was then called ActarBirkhäuser. After a bankruptcy, in 2012 Birkhäuser Verlag was sold again, this time to De Gruyter. Additionally, the Reinach-based printer Birkhäuser+GBC operates independently of the above, being now owned by ''Basler Zeitung''. History The original Swiss publishers program focused on regional literature. In the 1920s the sons of Emil Birkhà ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proceedings Of The Cambridge Philosophical Society
''Mathematical Proceedings of the Cambridge Philosophical Society'' is a mathematical journal published by Cambridge University Press for the Cambridge Philosophical Society. It aims to publish original research papers from a wide range of pure and applied mathematics. The journal, formerly titled ''Proceedings of the Cambridge Philosophical Society'', has been published since 1843. See also *Cambridge Philosophical Society The Cambridge Philosophical Society (CPS) is a scientific society at the University of Cambridge. It was founded in 1819. The name derives from the medieval use of the word philosophy to denote any research undertaken outside the fields of law ... External linksofficial website Academic journals associated with learned and professional societies Cambridge University Press academic journals Mathematics education in the United Kingdom Mathematics journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harley Flanders
Harley M. Flanders (September 13, 1925 – July 26, 2013) was an American mathematician, known for several textbooks and contributions to his fields: algebra and algebraic number theory, linear algebra, electrical networks, scientific computing. Life Flanders was a sophomore calculus student of Lester R. Ford at the Illinois Institute of Technology and asked for more challenging reading. Ford recommended ''A Course in Mathematical Analysis'' by Edouard Goursat, translated by Earle Hedrick, which included challenging exercises. Flanders recalled in 2001 that the final exercise required a proof of a formula for the derivatives of a composite function, generalizing the chain rule, in a form now called the Faa di Bruno formula.H. Flanders (2001) "From Ford to Faa", American Mathematical Monthly 108(6): 558–61 Flanders received his bachelors (1946), masters (1947) and PhD (1949) at the University of Chicago on the dissertation ''Unification of class field theory'' advised by Ott ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Quarterly Journal Of Pure And Applied Mathematics
''The Quarterly Journal of Pure and Applied Mathematics'' was a mathematics journal that first appeared as such in 1855, but as the continuation of ''The Cambridge Mathematical Journal'' that had been launched in 1836 and had run in four volumes before changing its title to ''The Cambridge and Dublin Mathematical Journal'' for a further nine volumes (these latter volumes carried dual numbering). Papers in the first issue, which carried a preface dated April, 1855, and promised further issues on a quarterly schedule in June, September, December and March, have dates going back to November, 1854; the first volume carried a further preface dated January, 1857. From the outset, keeping the journal up and running was to prove a challenging task. It was edited under the new title by James Joseph Sylvester and Norman Macleod Ferrers, assisted by George G. Stokes and Arthur Cayley, with Charles Hermite as corresponding editor in Paris, an arrangement that remained stable for the first fif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barnaba Tortolini
Barnaba Tortolini (19 November 1808 – 24 August 1874) was a 19th-century Italian priest and mathematician who played an early active role in advancing the scientific unification of the Italian states. He founded the first Italian scientific journal with an international presence and was a distinguished professor of mathematics at the University of Rome for 30 years. As a mathematics researcher, he had more than one hundred mathematical papers to his credit in Italian, French, and German journals. Early years Tortolini was born on 19 November 1808, in Rome and studied literature and philosophy at the Pontifical Gregorian University, especially under Don Andrea Caraffa (1789–1845) who was a mathematical physicist. He continued his mathematical and philosophic studies at the ''Archiginnasio Romano della Sapienza'' in Roma where he obtained the degree of ''laurea ad honorem'' in 1829. Subsequently, he attended the course for engineers before studying theology at the Pont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Books
Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical character recognition (OCR), and stored in its digital database.The basic Google book link is found at: https://books.google.com/ . The "advanced" interface allowing more specific searches is found at: https://books.google.com/advanced_book_search Books are provided either by publishers and authors through the Google Books Partner Program, or by Google's library partners through the Library Project. Additionally, Google has partnered with a number of magazine publishers to digitize their archives. The Publisher Program was first known as Google Print when it was introduced at the Frankfurt Book Fair in October 2004. The Google Books Library Project, which scans works in the collections of library partners and adds them to the digital invent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torino
Turin ( , Piedmontese: ; it, Torino ) is a city and an important business and cultural centre in Northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital from 1861 to 1865. The city is mainly on the western bank of the Po River, below its Susa Valley, and is surrounded by the western Alpine arch and Superga Hill. The population of the city proper is 847,287 (31 January 2022) while the population of the urban area is estimated by Eurostat to be 1.7 million inhabitants. The Turin metropolitan area is estimated by the OECD to have a population of 2.2 million. The city used to be a major European political centre. From 1563, it was the capital of the Duchy of Savoy, then of the Kingdom of Sardinia ruled by the House of Savoy, and the first capital of the Kingdom of Italy from 1861 to 1865. Turin is sometimes called "the cradle of Italian liberty" for having been the political and intellectual cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment (mathematics)
In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph. If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia. If the function is a probability distribution, then the first moment is the expected value, the second central moment is the variance, the third standardized moment is the skewness, and the fourth standardized moment is the kurtosis. The mathematical concept is closely related to the concept of moment in physics. For a distribution of mass or probability on a bounded interval, the collection of all the moments (of all orders, from to ) uniquely determines the distribution (Hausdorff moment problem). The same is not true on unbounded intervals (Hamburger moment problem). In the mid-nineteenth century, Pafnuty Chebyshev became the first person to think systematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
