Gamma Eulers Konstante Primzahlstraende Und Die Riemannsche Vermutung German Edition Book PDF, EPUB Download & Read Online Free

Author: Julian Havil
Publisher: Springer-Verlag
ISBN: 3540484965
Pages: 302
Year: 2007-04-21
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Jeder kennt p = 3,14159..., viele kennen e = 2,71828..., einige i. Und dann? Die "viertwichtigste" Konstante ist die Eulersche Zahl g = 0,5772156... - benannt nach dem genialen Leonhard Euler (1707-1783). Bis heute ist unbekannt, ob g eine rationale Zahl ist. Das Buch lotet die "obskure" Konstante aus. Die Reise beginnt mit Logarithmen und der harmonischen Reihe. Es folgen Zeta-Funktionen und Eulers wunderbare Identität, Bernoulli-Zahlen, Madelungsche Konstanten, Fettfinger in Wörterbüchern, elende mathematische Würmer und Jeeps in der Wüste. Besser kann man nicht über Mathematik schreiben. Was Julian Havil dazu zu sagen hat, ist spektakulär.
Naturwissenschaften im Fokus I
Author: Christian Petersen
Publisher: Springer-Verlag
ISBN: 3658151900
Pages: 205
Year: 2017-07-14
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Dieses fünfbändige Werk gibt eine Einführung in die technischen Disziplinen und ihren naturwissenschaftlichen Grundlagen. Leicht verständlich, angefangen von den Grundlagen bis zum aktuellen Stand der Technik werden die verschiedenen Disziplinen erklärt und anschaulich durch Formeln und Abbildungen ergänzt.
The Theory of Functions
Author: Edward Charles Titchmarsh
Publisher: Oxford University Press
ISBN: 0198533497
Pages: 454
Year: 1939
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The Theory of Functions
The Riemann Zeta-Function
Author: Aleksandar Ivic
Publisher: Courier Corporation
ISBN: 0486140040
Pages: 562
Year: 2012-07-12
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This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.
An Imaginary Tale
Author: Paul J. Nahin
Publisher: Princeton University Press
ISBN: 1400833892
Pages: 296
Year: 2010-02-22
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Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.
Author: Julian Havil
Publisher: Princeton University Press
ISBN: 1400832535
Pages: 296
Year: 2010-01-04
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Among the many constants that appear in mathematics, π, e, and i are the most familiar. Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.
Handbook of Neurochemistry
Author: Abel Lajtha
Publisher: Springer Science & Business Media
ISBN: 1461571723
Pages: 675
Year: 2012-12-06
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Anyone who has any contact with mental patients, old or young, or their families, or just visits a mental hospital or school for the retarded, is aware of the tremendous suffering caused by malfunctioning of the brain. The func tion of no other organ is so crucial for our everyday life, our proper func tioning, indeed our happiness, and no other illness causes as much anguish to patients or their families as mental illness. It is surprising and sad, therefore, how little effort has been devoted to research in this area; more so because such research is the only hope to ameliorate this suffering, or, to speak in the language of politics or economics, to decrease the enormous sums that we spend on trying to help our patients, with what is must generally be agreed are the most primitive and inadequate methods of treatment. Clearly, since functions of the brain are vital not only in illness, but in health, pathology is not the only area of concern to neurochemists, but it is an area that urgently needs neurochemical contributions. Progress in this field has been slower than in other areas of neurochemistry, and it seems that solutions in this field are very elusive. The reason for this is that the experimental approach is especially difficult in conditions specific for humans, or specific for complex behavior.
Bose-Einstein Condensation in Dilute Gases
Author: C. J. Pethick, H. Smith
Publisher: Cambridge University Press
ISBN: 0521665809
Pages: 402
Year: 2002
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In 1925 Einstein predicted that at low temperatures particles in a gas could all reside in the same quantum state. This gaseous state, a Bose–Einstein condensate, was produced in the laboratory for the first time in 1995 and investigating such condensates has become one of the most active areas in contemporary physics. The study of Bose–Einstein condensates in dilute gases encompasses a number of different subfields of physics, including atomic, condensed matter, and nuclear physics. The authors of this graduate-level textbook explain this exciting new subject in terms of basic physical principles, without assuming detailed knowledge of any of these subfields. Chapters cover the statistical physics of trapped gases, atomic properties, cooling and trapping atoms, interatomic interactions, structure of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. Problem sets are also included in each chapter.
Prime Obsession
Author: John Derbyshire
Publisher: Joseph Henry Press
ISBN: 0309141257
Pages: 446
Year: 2003-04-15
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In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark â€" a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic â€" defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark â€" the Riemann Hypothesis â€" that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows â€" subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many â€" the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof â€" and those who have been consumed by it.
Prime Numbers and the Riemann Hypothesis
Author: Barry Mazur, William Stein
Publisher: Cambridge University Press
ISBN: 1107101921
Pages: 150
Year: 2016-04-11
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This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Physics of Thin Films
Author: Ludmila Eckertová
Publisher: Springer Science & Business Media
ISBN: 1461575893
Pages: 254
Year: 2012-12-06
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The investigation of the physical properties of matter has progressed so much during the last hundred years that today physics is divided into a large group of special branches, which are often very distant from each other. These branches arise because of the vast extent of the science itself, and are distinguished by the particular area studied, the method of investigation and so on. An independent and important branch that has developed recently is the physics of thin films. This deals with systems which have only one common property, namely, that one of their dimensions is very small, though all other physical properties of such systems may be different, as well as methods of investigating them. Usually, we investigate the physical characteristics of three-dimensional bodies. Their characteristic prop::!rties are often related to a unit volume, i.e. it is assumed that they are volume-independent. This assumption is legitimate as long as the dimensions are 'normal', i.e. more or less within macroscopic limits; but as soon as one dimension becomes so small that there is a considerable increase in a surface-to-volume ratio, that assumption is no longer valid.
The Riemann Hypothesis
Author: Karl Sabbagh
Publisher: Macmillan
ISBN: 0374250073
Pages: 340
Year: 2003
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An accessible meditation on the ultimate meaning of mathematics draws on the famous eight-page Riemann Hypothesis publication and the ongoing contest to prove his answer true and support his idea about the distribution of prime numbers.
Riemann's Zeta Function
Author: Harold M. Edwards
Publisher: Courier Corporation
ISBN: 0486417409
Pages: 315
Year: 2001
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Superb high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled “On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics. English translation of Riemann's original document appears in the Appendix.
The Riemann Hypothesis
Author: Peter Borwein
Publisher: Springer Science & Business Media
ISBN: 0387721258
Pages: 533
Year: 2008
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This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material is accessible to any senior mathematics student, and much is accessible to anyone with some university mathematics. The appendices include a selection of original papers. This collection is not very large and encompasses only the most important milestones in the evolution of theory connected to the Riemann Hypothesis. The appendices also include some authoritative expository papers. These are the "expert witnesses” whose insight into this field is both invaluable and irreplaceable.
Stalking the Riemann Hypothesis
Author: Dan Rockmore
Publisher: Vintage
ISBN: 0307427943
Pages: 304
Year: 2007-12-18
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For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics. From the Trade Paperback edition.

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