Product Description
Chapters: Thoralf Skolem, Garrett Birkhoff, Henry Wallman, Øystein Ore, Robert P. Dilworth, Alfred Horn, Bjarni Jónsson, Richard J. Wood. Source: Wikipedia. Pages: 33. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Thoralf Albert Skolem (23 May 1887 23 March 1963) (Norwegian pronunciation: ) was a Norwegian mathematician known mainly for his work on mathematical logic and set theory. Although Skolem's father was a primary school teacher, most of his extended family were farmers. Skolem attended secondary school in Kristiania (later renamed Oslo), passing the university entrance examinations in 1905. He then entered Det Kongelige Frederiks Universitet to study mathematics, also taking courses in physics, chemistry, zoology and botany. In 1909, he began working as an assistant to the physicist Kristian Birkeland, known for bombarding magnetized spheres with electrons and obtaining aurora-like effects; thus Skolem's first publications were physics papers written jointly with Birkeland. In 1913, Skolem passed the state examinations with distinction, and completed a dissertation titled Investigations on the Algebra of Logic. He also traveled with Birkeland to the Sudan to observe the zodiacal light. He spent the winter semester of 1915 at the University of Göttingen, at the time the leading research center in mathematical logic, metamathematics, and abstract algebra, fields in which Skolem eventually excelled. In 1916 he was appointed a research fellow at Det Kongelige Frederiks Universitet. In 1918, he became a Docent in Mathematics and was elected to the Norwegian Academy of Science and Letters. Skolem did not at first formally enroll as a Ph.D. candidate, believing that the Ph.D. was unnecessary in Norway. He later changed his mind and submitted a thesis in 1926, titled Some theorems about ...More: http://booksllc.net/?id=453765 ... Read more

Product Description
Les achats comprennent une adhésion à l'essai gratuite au club de livres de l'éditeur, dans lequel vous pouvez choisir parmi plus d'un million d'ouvrages, sans frais. Le livre consiste d'articles Wikipedia sur : Niels Henrik Abel, Sophus Lie, Atle Selberg, Thoralf Skolem, Ludwig Sylow, Kristen Nygaard, Axel Thue, Viggo Brun, Caspar Wessel. Non illustré. Mises à jour gratuites en ligne. Extrait : Niels Henrik Abel (né le 5 août 1802 à Frindoë près de Stavanger et mort le 6 avril 1829 à Christiania, aujourd'hui Oslo) est un mathématicien norvégien. Il est connu pour ses travaux en analyse mathématique sur la semi-convergence des séries numériques, des suites et séries de fonctions, les critères de convergence d'intégrale généralisée, sur la notion d'intégrale elliptique ; en algèbre, sur la résolution des équations. Abel, cadet d'une famille de sept enfants, passa ses premières années dans un pays frappé par la famine du fait du blocus continental, Napoléon ayant contraint les couronnes de Norvège et de Danemark à rejoindre sa coalition contre l'Angleterre. Son père, Sören Georg Abel, éduqua lui-même ses deux fils aînés jusqu'en 1815, puis les envoya au collège paroissial d'Oslo. Dans ce lycée, le latin, le grec et la religion étaient enseignés à l'ancienne, avec punitions et châtiments corporels. La situation évolua en 1817 à la suite du renvoi d'un professeur consécutif au décès d'un élève : le lycée recruta un jeune enseignant ouvert aux idées nouvelles et instruit de mathématiques, Bernt Michael Holmboe. Holmboë enseignait la mécanique céleste d'après Newton et Lalande. Découvrant l'intérêt de Niels Henrik pour les mathématiques, il lui obtint une bourse pour étudier à l'université (1820). Abel fréquenta cet établissement jusqu'en 1823. À la fin de cette année-là, il démontra que l'équation quelconque de degré cinq n'est pas résoluble à partir de combinaisons de racines des coefficients. Ces travaux suffirent à convaincre les...http://booksllc.net/?l=fr ... Read more

Product Description
Albert Thoralf Skolem (* 23. Mai 1887 in Sandsvaer; † 23. März 1963 in Oslo) war ein norwegischer Mathematiker, Logiker und Philosoph. Seine Arbeiten lieferten grundlegende Resultate zur mathematischen Logik, insbesondere zu den Bereichen Modelltheorie und Berechenbarkeit. Aber auch zur mathematischen Grundlagenforschung wie Prädikatenlogik, Klassenlogik, Rekursionstheorie, Mengenlehre und Grundlagen der Arithmetik leistete er wesentliche Beiträge, wie auch in der Algebra und Zahlentheorie. ... Read more

Product Description
High Quality Content by WIKIPEDIA articles! Primitive recursive arithmetic, or PRA, is a quantifier-free formalization of the natural numbers. It was first proposed by Skolem as a formalization of his finitist conception of the foundations of arithmetic, and it is widely agreed that all reasoning of PRA is finitist. Many also believe that all of finitism is captured by PRA, but others believe finitism can be extended to forms of recursion beyond primitive recursion, up to ?0, which is the proof-theoretic ordinal of Peano arithmetic. PRA's proof theoretic ordinal is ??, where ? is the smallest transfinite ordinal. PRA is sometimes called Skolem arithmetic.The language of PRA can express arithmetic propositions involving natural numbers and any primitive recursive function, including the operations of addition, multiplication, and exponentiation. PRA cannot explicitly quantify over the domain of natural numbers. PRA is often taken as the basic metamathematical formal system for proof theory, in particular for consistency proofs such as Gentzen's consistency proof of first-order arithmetic. ... Read more

Product Description
High Quality Content by WIKIPEDIA articles! The primitive recursive functions are defined using primitive recursion and composition as central operations and are a strict subset of the recursive functions. The term was coined by Rózsa Péter.In computability theory, primitive recursive functions are a class of functions which form an important building block on the way to a full formalization of computability. These functions are also important in proof theory.Most of the functions normally studied in number theory are primitive recursive. For example: addition, division, factorial, exponential and the nth prime are all primitive recursive. So are many approximations to real-valued functions. In fact, it is difficult to devise a function that is not primitive recursive, although some are known. The set of primitive recursive functions is known as PR in complexity theory.Every primitive recursive function is a general recursive function. ... Read more

Product Description
High Quality Content by WIKIPEDIA articles! Primitive recursive arithmetic, or PRA, is a quantifier-free formalization of the natural numbers. It was first proposed by Skolem as a formalization of his finitist conception of the foundations of arithmetic, and it is widely agreed that all reasoning of PRA is finitist. Many also believe that all of finitism is captured by PRA, but others believe finitism can be extended to forms of recursion beyond primitive recursion, up to ?0, which is the proof-theoretic ordinal of Peano arithmetic. PRA's proof theoretic ordinal is ??, where ? is the smallest transfinite ordinal. PRA is sometimes called Skolem arithmetic. ... Read more

Product Description
This digital document is an article from Encyclopedia of Philosophy, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 890 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.Explores major marketing and advertising campaigns from 1999-2006. Entries profile recent print, radio, television, billboard and Internet campaigns. Each essay discusses the historical context of the campaign, the target market, the competition, marketing strategy, and the outcome. ... Read more