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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.
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› Consultez la page Harold M. Edwards d'Amazon
› Consultez la page Harold M. Edwards d'Amazon
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Première phrase
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. Lire la première page
Couverture | Copyright | Table des matières | Extrait | Index | Quatrième de couverture
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. Lire la première page
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Concordance
Couverture | Copyright | Table des matières | Extrait | Index | Quatrième de couverture
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Format:Broché
The popular press leaves us with the impression that math is
intimmidating. 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.
intimmidating. 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.
Format:Broché
Malgré son ancienneté, ce livre reste un excellent guide très pédagogique sur l'énigme que reste l'hypothèse de Riemann, véritable sujet de l'ouvrage: le titre peut induire en erreur, il ne s'agit pas en soi d'une étude de la fonction Zeta, c'est bien l'hypothèse de Riemann qui est au centre. Un niveau élevé en mathématiques est nécessaire, mais on peut ne pas entrer dans le détail des démonstrations tout en se faisant une idée suffisante des méthodes et des difficultés du sujet.
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