By Eric Charpentier, Annick LESNE, Nikolaï K. Nikolski
A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was once some of the most very good mathematicians that the area has ever recognized. highly deep and inventive, he was once capable of procedure each one topic with a totally new viewpoint: in a number of superb pages, that are versions of shrewdness and mind's eye, and which astounded his contemporaries, he replaced tremendously the panorama of the subject.Most mathematicians turn out what they could, Kolmogorov used to be of these who end up what they wish. For this publication numerous international specialists have been requested to provide one a part of the mathematical history left to us by way of Kolmogorov.Each bankruptcy treats one in all Kolmogorov's study topics, or a topic that was once invented due to his discoveries. His contributions are offered, his tools, the views he opened to us, the way this study has developed in the past, besides examples of modern purposes and a presentation of the present prospects.This publication might be learn through an individual with a master's (even a bachelor's) measure in arithmetic, machine technological know-how or physics, or extra usually through an individual who likes mathematical principles. instead of current specified proofs, the most principles are defined. A bibliography is equipped if you happen to desire to comprehend the technical details.One can see that usually extremely simple reasoning (with the best interpretation and instruments) can lead in a couple of strains to very monstrous effects.
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Example text
IV. Correspondance A-G. : A formulae-as-types notion of control. Conf. Record 17th Annual ACM Symp. : La math´ematique intuitionniste sans n´egation. Nieuw Arch. : From Frege to G¨ odel. A source book in mathematical logic, 1879–1931. Third printing of the 1967 original, edited by Jean van Heijenoort. : Poincar´e, Russell, Zermelo et Peano. Textes de la discussion (1906–1912) sur les fondements des math´ematiques: des antinomies la pr´edicativit´e. : Gnomes in the fog. The reception of Brouwer’s intuitionism in the 1920s.
Mathematics and its Applications (Soviet Series), 25. : Mathematical logic. Lectures on Modern Mathematics, Vol. III, 95–195. : Functions, ordinals, species. In: Logic, Methodology and Philos. Sci. III, 145–159. : About classical logic and imperative programming. Ann. of Math. and Artif. : Ensembles et preuves. : Typed lambda-calculus in classical Zermelo-Fraenkel set theory. Arch. Math. : Dependent choice, ‘quote’ and the clock. Theoret. Comput. : Intuitionistische Untersuchungen der formalistishen Logik.
B. : Der Minimalkalk¨ ul, ein reduzierter intuitionistischer Formalismus. : Topos theory. London Mathematical Society Monographs, Vol. 10. : Ideas of intuitionism and the struggle for content in contemporary mathematics (Russian). : On the principle of excluded middle (Russian), Matematicheski Sbornik, 32, 646–647 (1925) English translation in [Hei67]. : Contemporary disputes on the nature of mathematics (Russian) Nauch. : Zur Deutung der intuitionistischen Logik. : Grundbegriffe der Wahrscheinlichkeitsrechnung.