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Kurzbeschreibung
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.
Synopsis
Edwards elaborates on Bernard Riemann's eight-page paper On the Number of Primes Less Than a Given Magnitude, published in German in 1859. His goal is not to supplant the classic work, but to provide mathematics students access to it. Indeed an English translation of the original is appended. Academic Press published the 1974 edition. Cited in Book
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Einleitungssatz
This book is a study of Bernhard Riemann's epoch-making 8-page paper "On the Number of Primes Less Than a Given Magnitude," and of the subsequent developments in the theory which this paper inaugurated. Lesen Sie die erste Seite
Buchdeckel | Copyright | Inhaltsverzeichnis | Auszug | Stichwortverzeichnis | Rückseite
This book is a study of Bernhard Riemann's epoch-making 8-page paper "On the Number of Primes Less Than a Given Magnitude," and of the subsequent developments in the theory which this paper inaugurated. Lesen Sie die erste Seite
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Buchdeckel | Copyright | Inhaltsverzeichnis | Auszug | Stichwortverzeichnis | Rückseite
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Die hilfreichsten Kundenrezensionen
13 von 13 Kunden fanden die folgende Rezension hilfreich:
5.0 von 5 Sternen
New and old.,
Von Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - Alle meine Rezensionen ansehen (REAL NAME)
Rezension bezieht sich auf: Riemann's Zeta Function (Dover Books on Mathematics) (Taschenbuch)
The popular press leaves us with the impression that math isintimmidating. This wasn't always the case. In my time, the approach to how we teach math went thru cycles: (1) The boot-camp approach with its endless drills, (2) The New-Math approach, (3) The back-to-basics trend, and (4) The Make-it-Seem-Easy-and Fun approach and the motivational speakers.---Finally Edwards suggests, following Eric Temple Bell, that we rather begin with the classics when approaching a subject in math. It was thought that later books based on the classics had more effective ways of doing it, and few took the trouble of looking at the original and central papers of the great masters. The landmark papers. All the while, they collected dust on the shelves in the back rooms of libraries. Of the classics, the true landmarks, one stands out: It is Riemann's paper on the prime numbers, what later turned into the prime number theorem. It is also the paper with the Riemann hypothesis, still unproved, now generations later. So it is a delightful idea including Riemann's paper, in translation, in an appendix. It would have been nice had Edwards also reproduced the original German text. Now the RH is one of the Million-Dollar problems in math. It is anyone's guess when it will be cracked, but in the mean time, it continues to inspire generations of mathematicians and students. This lovely Dover edition is came out in 2001. The original first 1974 edition, Academic Press, had gone out of print. This lovely book seems still to be a model that we can measure other books against. Edwards' presentation is both engaging and deep, and the book contains the gems in a subject that continues to be central in math, the subject of analytic number theory. Helfen Sie anderen Kunden bei der Suche nach den hilfreichsten Rezensionen
4 von 4 Kunden fanden die folgende Rezension hilfreich:
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This is where you should start your study,
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Rezension bezieht sich auf: Riemann's Zeta Function (Dover Books on Mathematics) (Taschenbuch)
This book gives a detailed overview of the Riemann Zeta function. It covers both the theoretical as well as practical applications of the function. Recommended as a starter for your study of this wonderful function. It misses recent results (it has been written 35 years ago), but once you get through it your ready for what comes after.
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