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1. Essays on the Theory of Numbers: I. Continuity and Irrational Numbers, II. The Nature and Meaning of Numbers [ 1901 ] by Richard Dedekind | |
Paperback: 142
Pages
(2009-08-10)
list price: US$16.98 -- used & new: US$16.98 (price subject to change: see help) Asin: B002MCYM1W Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
Foundations of the reals, foundations of the integers
Will Appeal to Students of Mathematics and Philosophy
An interesting pair of historical essays There are two difficulties with the book, which I found serious enough to warrant only four stars. First, the terminology is rather antiquated, so that the descriptions are clear only once you are able to translate Dedekind's phrases; for instance, "a system S is compounded from the systems A and B" would today be written "the set S is the union of sets A and B." Second, there are a fairly large number of typos in the book, given its importance and the rigorousness of the work; for example, in the proof in paragraph 42 of The Meaning of Numbers, the phrase (not in Dedekind's shorthand) "the transformation of A is contained in B" should read "the transformation of A is contained in A." Most typos are as minor as this, but annoying in the unnecessary effort needed to bull ones way through them. A couple errors are more significant. I blame the translator and proofreader, not Dedekind. All in all, the book is well worth the price and the effort to understand it.
Accessible genius Probably the main value of the book is as an introduction to Dedekind's way of thinking about mathematics: his clarity, precision, and way of cutting to the bare core of a subject. You can find the same genius in Dedekind's THEORY OF ALGEBRAIC INTEGERS (available in a fine English translation by John Stillwell) but of course that is a more advanced text. The same style of thought works powerfully in all of Dedekind's mathematics. But most of it is very hard stuff. Here you see it in easily accessible form, suitable for even a smart high school student willing to think hard.
A very good Introduction to Number Theory |
2. Richard Dedekind, 1831-1981: Eine Wurdigung zu seinem 150. Geburtstag (German Edition) | |
Perfect Paperback: 146
Pages
(1981)
Isbn: 3528084987 Canada | United Kingdom | Germany | France | Japan | |
3. Theory of Algebraic Integers (Cambridge Mathematical Library) by Richard Dedekind | |
Paperback: 168
Pages
(1996-09-28)
list price: US$39.99 -- used & new: US$33.57 (price subject to change: see help) Asin: 0521565189 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
An antidote against too much modernistic algebra
Emmy Noether called it a must-read Dedekind (most of the time) explicitly limits himself to modules of algebraic numbers, but Noether correctly saw that Dedekind already knew (many of) his theorems held for the whole abstract range she would explicate and develop. Benefitting from her, we can even see this generality peeking through in some of his remarks. Anyone knowing the basic modern ideas of rings and modules can read this with pleasure, both as the origins of abstract algebra with many fine insights to offer, and as a connection to the concrete motives. Of course Dedekind wrote for people who did not know such things. But he assumed they would think very, very hard. He also assumed some arithmetic ideas not widely taught today, but nicely explained in Stillwell's preface. Dedekind is a wonderful writer, well served here by a clear translation. You are apt to fall in love with this book, and want to accompany it with Dirichlet's own LECTURES ON NUMBER THEORY, written up by Dedekind, and also translated to english by Stillwell.
Emmy Noether called it a must-read |
4. Lectures on Number Theory (History of Mathematics Source Series, V. 16) by Peter Gustav Lejeune Dirichlet, Richard Dedekind, P. G. L. Dirichlet | |
Paperback: 275
Pages
(1999-08-04)
list price: US$54.00 -- used & new: US$36.45 (price subject to change: see help) Asin: 0821820176 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions. The book is suitable as a textbook, yet it also offers a fascinating historical perspective that links Gauss with modern number theory. The legendary story is told how Dirichlet kept a copy of Gauss's Disquisitiones Arithmeticae with him at all times and how Dirichlet strove to clarify and simplify Gauss's results. Dedekind's footnotes document what material Dirichlet took from Gauss, allowing insight into how Dirichlet transformed the ideas into essentially modern form. Also shown is how Gauss built on a long tradition in number theory--going back to Diophantus--and how it set the agenda for Dirichlet's work. This important book combines historical perspective with transcendent mathematical insight. The material is still fresh and presented in a very readable fashion. This volume is one of an informal sequence of works within the History of Mathematics series. Volumes in this subset, "Sources", are classical mathematical works that served as cornerstones for modern mathematical thought. (For another historical translation by Professor Stillwell, see Sources of Hyperbolic Geometry, Volume 10 in the History of Mathematics series.) Customer Reviews (1)
Gauss and then some |
5. Essays On the Theory of Numbers: I. Continuity and Irrational Numbers, Ii. the Nature and Meaning of Numbers by Richard Dedekind | |
Paperback: 132
Pages
(2010-03-26)
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6. Festschrift Zur Feier Des Hundertfünfzigjährigen Bestehens Der Königlichen Gesellschaft Der Wissenschaften Zu Göttingen (German Edition) by Richard Dedekind, David Hilbert | |
Paperback: 378
Pages
(2010-04-02)
list price: US$33.75 -- used & new: US$19.48 (price subject to change: see help) Asin: 1148319883 Canada | United Kingdom | Germany | France | Japan | |
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7. Essays on the theory of numbers: I. Continuity and irrational numbers. II. The nature and meaning of number by Richard Dedekind | |
Unknown Binding: 115
Pages
(1963)
Asin: B0007DONMQ Canada | United Kingdom | Germany | France | Japan | |
8. Vorlesungen Über Zahlentheorie, Volume 1 (German Edition) by Richard Dedekind, Peter Gustav Lejeune Dirichlet | |
Paperback: 646
Pages
(2010-03-16)
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9. Uber Die Elemente Der Theorie Der Euler'schen Integrale (1852) (German Edition) by Richard Dedekind | |
Hardcover: 24
Pages
(2010-05-23)
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10. Was Sind Und Was Sollen Die Zahlen? (German Edition) by Richard Dedekind | |
Paperback: 82
Pages
(2010-02-22)
list price: US$17.75 -- used & new: US$11.05 (price subject to change: see help) Asin: 1145125328 Canada | United Kingdom | Germany | France | Japan | |
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11. What Are Numbers and What Should They Be? by Richard Dedekind, W. Snyder | |
Hardcover: 91
Pages
(1995-01)
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Customer Reviews (1)
Come on . . . it's Dedekind. |
12. Vorlesungen Über Zahlentheorie (German Edition) by Richard Dedekind, Peter Gustav Lejeune Dirichlet | |
Paperback: 524
Pages
(2010-04-02)
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13. Bernhard Riemann's Gesammelte Mathematische Werke Und Wissenschaftlicher Nachlass (German Edition) by Heinrich Weber, Bernhard Riemann, Richard Dedekind | |
Paperback: 712
Pages
(2010-02-23)
list price: US$49.75 -- used & new: US$27.11 (price subject to change: see help) Asin: 1145165052 Canada | United Kingdom | Germany | France | Japan | |
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14. Frege, Dedekind, and Peano on the Foundation of Arithmetic (Methodology and Science Foundation : No. 2) by Dee Ann Gillies, Donald Gillies | |
Paperback: 116
Pages
(1982-06)
list price: US$9.00 Isbn: 9023218884 Canada | United Kingdom | Germany | France | Japan | |
15. La notion de nombre chez Dedekind, Cantor, Frege: Theories, conceptions et philosophie (Mathesis) (French Edition) by Jean-Pierre Belna | |
Paperback: 376
Pages
(1996)
-- used & new: US$85.98 (price subject to change: see help) Asin: 2711612929 Canada | United Kingdom | Germany | France | Japan | |
16. Julius Wilhelm Richard Dedekind: An entry from Gale's <i>Science and Its Times</i> by P. Andrew Karam | |
Digital: 2
Pages
(2000)
list price: US$2.90 -- used & new: US$2.90 (price subject to change: see help) Asin: B0027UWT5A Canada | United Kingdom | Germany | France | Japan | |
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17. Tu Braunschweig Faculty: Richard Dedekind, Kurt Tank, Manfred Eigen, Georg Wittig, Nikolaus Hofreiter, Henning Kagermann, Herbert Freundlich | |
Paperback: 42
Pages
(2010-09-15)
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18. People From Braunschweig: Carl Friedrich Gauss, Caroline of Brunswick, Karl Andree, Karl Fiehler, Richard Dedekind, Louis Spohr | |
Paperback: 234
Pages
(2010-09-15)
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19. Richard Dedekind | |
Paperback: 76
Pages
(2010-08-23)
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20. Bernhard Riemann's Gesammelte mathematische Werke und Wissenschaftlicher Nachlass, Hrsg. unter Mitwirkung von Richard Dedekind, von Heinrich Weber. by Bernhard Riemann | |
Hardcover: 576
Pages
(1899-01-01)
list price: US$39.95 -- used & new: US$37.91 (price subject to change: see help) Asin: 1418169706 Canada | United Kingdom | Germany | France | Japan | |
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