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41. 1001 Problems in Classical Number Theory by Jean-Marie De Koninck and Armel Mercier | |
Hardcover: 336
Pages
(2007-04-10)
list price: US$49.00 -- used & new: US$39.20 (price subject to change: see help) Asin: 0821842242 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
42. 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 |
43. Algebraic Number Theory (Grundlehren der mathematischen Wissenschaften) (v. 322) by Jürgen Neukirch | |
Hardcover: 571
Pages
(1999-06-22)
list price: US$169.00 -- used & new: US$94.30 (price subject to change: see help) Asin: 3540653996 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Must have for AN
One of the most beautifully written math books
10 stars if I could. |
44. Integers and Theory of Numbers (Phoenix Edition) by Abraham A. Fraenkel | |
Hardcover: 112
Pages
(2004-06-10)
list price: US$35.00 -- used & new: US$13.08 (price subject to change: see help) Asin: 0486495884 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
45. Essays on the Theory of Numbers by Richard Dedekind | |
Paperback: 66
Pages
(2009-12-26)
list price: US$7.85 -- used & new: US$6.66 (price subject to change: see help) Asin: 1151677787 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 |
46. Class Field Theory: From Theory to Practice (Springer Monographs in Mathematics) by Georges Gras | |
Paperback: 512
Pages
(2010-11-02)
list price: US$129.00 -- used & new: US$129.00 (price subject to change: see help) Asin: 3642079083 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Global class field theory is a major achievement of algebraic number theory based on the functorial properties of the reciprocity map and the existence theorem. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book. |
47. An Adventurer's Guide to Number Theory by Richard Friedberg | |
Paperback: 228
Pages
(1995-01-09)
list price: US$10.95 -- used & new: US$2.49 (price subject to change: see help) Asin: 0486281337 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (8)
An informal introduction to number theory with a historical perspective.
What a carefully written exploration!
Be carefull
"Quirky" is exactly the right word. If b squared were equal to two times a squared, the right side of the equation would contain an odd factor of two, which is obviously impossible by the fundamental theorem of arithmetic.This is the modern way of proving this assertion. Richard Friedberg prefers the old way.He uses Fermat's method. On page 45 we read: "At each point we can prove that the numbers we have reached are even.So we can go on dividing forever. But this is impossible.Eventually we must reach 1, or some other odd number.Since we have proved something that is impossible, we must have assumed something that isn't true.The only thing we assumed was that there are two numbers a and b, such that two times a squared equals b squared.So there can be no such numbers." He continues in this way all the way to quadratic recipocity, and concludes with a Table of Theorems, all rigorously proved in his own quirky way. I continue to be frustrated by Friedberg's approach to number theory.It is historically accurate but very difficult to assimilate or combine into present day orthodoxy.I'm not sure whether he is worth my time, but nevertheless I continue to study his book. I've read it on and off now for more than five years.There is no doubt in my mind that he is a genius . . . hence the five stars. Whether one wants to embark on this slippery slope of classical geometry, historical number theory, the defects in Euler's reasoning and other incredibly obscure topics in number theory, the reader must decide for himself or herself.I don't think I'll ever know as much about the history of number theory as Richard Friedberg does, so I decided to put in my two cents mid-way through the course of my studies.
Not that adventurous |
48. Number theory;: An introduction to proof by Charles Vanden Eynden | |
Hardcover: 158
Pages
(1970)
Isbn: 0700223088 Canada | United Kingdom | Germany | France | Japan | |
49. Introductory Algebraic Number Theory by Saban Alaca, Kenneth S. Williams | |
Paperback: 448
Pages
(2003-11-17)
list price: US$55.00 -- used & new: US$19.70 (price subject to change: see help) Asin: 0521540119 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Grab bag of good and bad |
50. Modern Elementary Theory of Numbers by Leonard E. Dickson | |
Hardcover: 317
Pages
(1939-12)
Isbn: 0226147606 Canada | United Kingdom | Germany | France | Japan | |
51. Biscuits of Number Theory (Dolciani Mathematical Expositions) by Arthur T. Benjamin, Ezra Brown | |
Hardcover: 326
Pages
(2008-12-16)
list price: US$62.50 -- used & new: US$58.50 (price subject to change: see help) Asin: 088385340X Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description In Biscuits of Number Theory, the editors have chosen articles that are exceptionally well-written and that can be appreciated by anyone who has taken (or is taking) a first course in number theory. This book could be used as a textbook supplement for a number theory course, especially one that requires students to write papers or do outside reading. The editors give examples of some of the possibilities. The collection is divided into seven chapters: Arithmetic, Primes, Irrationality, Sums of Squares and Polygonal Numbers, Fibonacci Numbers, Number Theoretic Functions, and Elliptic Curves, Cubes and Fermat's Last Theorem. As with any anthology, you don't have to read the Biscuits in order. Dip into them anywhere: pick something from the Table of Contents that strikes your fancy, and have at it. If the end of an article leaves you wondering what happens next, then by all means dive in and do some research. You just might discover something new! |
52. Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) by A. Fröhlich, M. J. Taylor | |
Paperback: 355
Pages
(1993-02-26)
list price: US$70.00 -- used & new: US$59.43 (price subject to change: see help) Asin: 0521438349 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Technical, but concrete |
53. Three Pearls of Number Theory by A. Y. Khinchin | |
Paperback: 64
Pages
(2010-07-21)
list price: US$6.95 -- used & new: US$4.99 (price subject to change: see help) Asin: 0486400263 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (4)
Three pearls of number theory
Truly a pearl.
Come on, professors, write more like this!
If you like number theory you I think you will enjoy this bo This is a short book of three chapters:Chapter 1. Van der Waerden's theorem on arithmetic progressions. Chapter 2. The Landau-Shnirelmann hypothesis and Mann's theorem. Chapter 3. An elementary solution of Waring's problem. These are all difficult problems from the theory of numbers and I think that the elementary proofs that Khinchin describes here are original.This book is a challenging but enjoyable read. I also recommend his other book on number theory: "Continued Fractions". ... Read more |
54. Number Theory With Applications by James A. Anderson, James M. Bell | |
Hardcover: 566
Pages
(1997-02)
list price: US$73.33 -- used & new: US$55.99 (price subject to change: see help) Asin: 0131901907 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
55. Number Theory: An approach through history from Hammurapi to Legendre (Modern Birkhäuser Classics) by André Weil | |
Paperback: 376
Pages
(2006-12-22)
list price: US$49.95 -- used & new: US$34.58 (price subject to change: see help) Asin: 0817645659 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Number Theory or arithmetic, as some prefer to call it, is the oldest, purest, liveliest, most elementary yet sophisticated field of mathematics. It is no coincidence that the fundamental science of numbers has come to be known as the "Queen of Mathematics." Indeed some of the most complex conventions of the mathematical mind have evolved from the study of basic problems of number theory. André Weil, one of the outstanding contributors to number theory, has written an historical exposition of this subject; his study examines texts that span roughly thirty-six centuries of arithmetical work — from an Old Babylonian tablet, datable to the time of Hammurapi to Legendre’s Essai sur la Théorie des Nombres (1798). Motivated by a desire to present the substance of his field to the educated reader, Weil employs an historical approach in the analysis of problems and evolving methods of number theory and their significance within mathematics. In the course of his study Weil accompanies the reader into the workshops of four major authors of modern number theory (Fermat, Euler, Lagrange and Legendre) and there he conducts a detailed and critical examination of their work. Enriched by a broad coverage of intellectual history, Number Theory represents a major contribution to the understanding of our cultural heritage. Customer Reviews (2)
Weil's Number Theory
Respectable and enjoyable guide to pre-Gaussian number theory |
56. Elementary Number Theory, Cryptography and Codes (Universitext) by M. Welleda Baldoni, Ciro Ciliberto, G.M. Piacentini Cattaneo | |
Paperback: 522
Pages
(2008-12-09)
list price: US$69.95 -- used & new: US$43.70 (price subject to change: see help) Asin: 3540691995 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, continued fractions, etc.) which in recent years have proven to be extremely useful for applications to cryptography and coding theory. Both cryptography and codes have crucial applications in our daily lives, and they are described here, while the complexity problems that arise in implementing the related numerical algorithms are also taken into due account. Cryptography has been developed in great detail, both in its classical and more recent aspects. In particular public key cryptography is extensively discussed, the use of algebraic geometry, specifically of elliptic curves over finite fields, is illustrated, and a final chapter is devoted to quantum cryptography, which is the new frontier of the field. Coding theory is not discussed in full; however a chapter, sufficient for a good introduction to the subject, has been devoted to linear codes. Each chapter ends with several complements and with an extensive list of exercises, the solutions to most of which are included in the last chapter. Though the book contains advanced material, such as cryptography on elliptic curves, Goppa codes using algebraic curves over finite fields, and the recent AKS polynomial primality test, the authors' objective has been to keep the exposition as self-contained and elementary as possible. Therefore the book will be useful to students and researchers, both in theoretical (e.g. mathematicians) and in applied sciences (e.g. physicists, engineers, computer scientists, etc.) seeking a friendly introduction to the important subjects treated here. The book will also be useful for teachers who intend to give courses on these topics. |
57. Transcendental Number Theory (Cambridge Mathematical Library) by Alan Baker | |
Paperback: 176
Pages
(1990-09-28)
list price: US$37.99 -- used & new: US$31.76 (price subject to change: see help) Asin: 052139791X Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
58. Making Transcendence Transparent: An intuitive approach to classical transcendental number theory by Edward B. Burger, Robert Tubbs | |
Paperback: 263
Pages
(2010-11-02)
list price: US$59.95 -- used & new: US$50.35 (price subject to change: see help) Asin: 1441919481 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students. Edward Burger is one of the authors of The Heart of Mathematics, winner of a 2001 Robert W. Hamilton Book Award. He will also be awarded the 2004 Chauvenet Prize, one of the most prestigious MAA prizes for outstanding exposition. Customer Reviews (1)
Review of Making Transcendence Transparent |
59. Elementary Number Theory by Charles Vanden Eynden | |
Hardcover: 288
Pages
(2001-01-12)
list price: US$113.75 -- used & new: US$65.00 (price subject to change: see help) Asin: 0072325712 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Good book on a standard subject
Not a bad book, but horribly expensive
Plenty of choices... |
60. Introduction to Number Theory by Mathew Crawford | |
Paperback: 336
Pages
(2008-06-30)
list price: US$42.00 -- used & new: US$42.00 (price subject to change: see help) Asin: 1934124125 Canada | United Kingdom | Germany | France | Japan | |
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