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Book Title: Bernhard Riemann "Über die Hypothesen, welche der Geometrie zu Grunde liegen" (Klassische Texte der Wissenschaft)|
The author of the book: Bernhard Riemann
Format files: PDF
The size of the: 524 KB
Edition: Springer Berlin Heidelberg
Date of issue: April 23rd 2013
ISBN: No data
ISBN 13: No data
Read full description of the books Bernhard Riemann "Über die Hypothesen, welche der Geometrie zu Grunde liegen" (Klassische Texte der Wissenschaft):Vengono qui raccolti, oltre al testo della famosa prolusione del 1854 sui fondamenti della geometria, alcuni scritti del grande matematico tedesco Bernhard Riemann: a saggi di carattere tecnico-scientifico, i cui compaiono alcuni dei temi più discussi del periodo (la natura dell'etere, la fisiologia, la psicologia della percezione, ecc.), si affiancano scritti metodologici e anche filosofici in senso stretto. Questi ultimi mostrano il grande interesse di Riemann per le idee e i personaggi del dibattito filosofico dell'epoca, e gettano nuova luce sulla sua stessa produzione scientifica. La concezione della scienza offerta da questi scritti è assai significativa del personaggio e della sua epoca. Per Riemann la matematica non è un mero strumento esteriore da applicare, appunto dall' "esterno", ai fenomeni. Al contrario, essa consente di spingersi con rigore necessario oltre la superficie delle cose e di penetrare sempre più a fondo nella realtà, nell'ottica di una concezione unitaria del sapere scientifico.
Read information about the authorGeorg Friedrich Bernhard Riemann [ˈʁiːman] ( listen) (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting contributions to analysis, number theory, and differential geometry, some of them enabling the later development of general relativity.
Riemann was born in Breselenz, a village near Dannenberg in the Kingdom of Hanover in what is the Federal Republic of Germany today. His mother, Charlotte Ebell, died before her children had reached adulthood. Riemann was the second of six children, shy and suffering from numerous nervous breakdowns. Riemann exhibited exceptional mathematical skills, such as calculation abilities, from an early age but suffered from timidity and a fear of speaking in public.
Riemann held his first lectures in 1854, which founded the field of Riemannian geometry and thereby set the stage for Einstein's general theory of relativity. In 1857, there was an attempt to promote Riemann to extraordinary professor status at the University of Göttingen. Although this attempt failed, it did result in Riemann finally being granted a regular salary. In 1859, following Lejeune Dirichlet's death, he was promoted to head the mathematics department at Göttingen. He was also the first to suggest using dimensions higher than merely three or four in order to describe physical reality—an idea that was ultimately vindicated with Albert Einstein's contribution in the early 20th century. In 1862 he married Elise Koch and had a daughter.
Riemann fled Göttingen when the armies of Hanover and Prussia clashed there in 1866. He died of tuberculosis during his third journey to Italy in Selasca (now a hamlet of Verbania on Lake Maggiore) where he was buried in the cemetery in Biganzolo (Verbania). Meanwhile, in Göttingen his housekeeper discarded some of the papers in his office, including much unpublished work. Riemann refused to publish incomplete work and some deep insights may have been lost forever.
Riemann's published works opened up research areas combining analysis with geometry. These would subsequently become major parts of the theories of Riemannian geometry, algebraic geometry, and complex manifold theory. The theory of Riemann surfaces was elaborated by Felix Klein and particularly Adolf Hurwitz. This area of mathematics is part of the foundation of topology, and is still being applied in novel ways to mathematical physics.
Riemann made major contributions to real analysis. He defined the Riemann integral by means of Riemann sums, developed a theory of trigonometric series that are not Fourier series—a first step in generalized function theory—and studied the Riemann–Liouville differintegral.
He made some famous contributions to modern analytic number theory. In a single short paper (the only one he published on the subject of number theory), he investigated the Riemann zeta function and established its importance for understanding the distribution of prime numbers. He made a series of conjectures about properties of the zeta function, one of which is the well-known Riemann hypothesis.
He applied the Dirichlet principle from variational calculus to great effect; this was later seen to be a powerful heuristic rather than a rigorous method. Its justification took at least a generation. His work on monodromy and the hypergeometric function in the complex domain made a great impression, and established a basic way of working with functions by consideration only of their singularities.
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