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1. Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang | |
Hardcover: 376
Pages
(1994-06-24)
list price: US$69.95 -- used & new: US$49.00 (price subject to change: see help) Asin: 0387942254 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Classic |
2. A Course in Computational Algebraic Number Theory (Graduate Texts in Mathematics) by Henri Cohen | |
Paperback: 550
Pages
(2010-11-02)
list price: US$89.95 -- used & new: US$71.97 (price subject to change: see help) Asin: 3642081428 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Great book for computational aspects
Definitely belongs on the shelf of all number theory lovers 1. Most of the algorithms on elliptic curves. The author reminds the reader that number-theoretical experiments resulted in the famous Swinnerton-Dyer Conjecture and the Birch Conjecture. (a) the reduction algorithm, which for a given point in the upper half plane, gives the unique point in the half plane equivalent to this point under the action of the special linear group along with the matrix that maps these two points to each other. (b) The computation of the coefficient g2 and g3 of the Weierstrass equation of an elliptic curve. (c) The computation of the Weierstrass function and its derivative. (d) Determination of the periods of an elliptic curve over the real numbers. (e) The determination of the elliptic logarithm. (f) The reduction of a general cubic (f) The Shanks-Mestre algorithm for computing the order of an elliptic curve over a finite field F(p), where p is prime and greater than 457. (g) The reduction of an elliptic curve modulo p for p > 3. (h) The reduction of an elliptic curve modulo 2 or 3. (i) Reduction of an elliptic curve over the rational numbers. (j) Determination of the rational torsion points of an elliptic curve. (k) Computation of the Hilbert class polynomials and thus a determination of the j-function of an elliptic curve. 2. A few of the algorithms on factoring. (a) The Pollard algorithm for finding non-trivial factors of composites. (The author does not give the improved algorithm due to P. Montgomery, but does give references) (b) Shanks Square Form Factorization algorithm for finding a non-trivial factor of an odd integer. (c) Lenstra's Elliptic Curve test for compositeness. 3. Primality tests (a) The Jacobi Sum Primality Test for a positive integer. (b) Goldwasser-Killian elliptic curve test for a positive integer not equal to 1 and coprime to 6. The author gives an overview of the computer packages used for number theory, including Pari, which was written by him and his collaborators. I have not used this package, but instead use Lydia and Mathematica for most of the number theoretic computations I need to do.
Excellent! Of course, CAS information from 1993, won't bethat helpful (look in his newest, Advanced Topics inC.A.N.T.). Excellent. Also try Knuth's "Semi-numericalAlgorithms" for a more computer oriented approach. ... Read more |
3. Algebraic Number Theory and Fermat's Last Theorem: Third Edition by Ian Stewart, David Tall | |
Hardcover: 250
Pages
(2001-12-01)
list price: US$59.00 -- used & new: US$57.13 (price subject to change: see help) Asin: 1568811195 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (7)
Not bad, but much to be improved.
Great Introductory Book to Algebraic Number Theory
skips too much
tough problems => good for the student
Very clear introduction to Algebraic Number Theory |
4. 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. |
5. Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger (Dover Books on Mathematics) by Pierre Samuel | |
Paperback: 112
Pages
(2008-05-19)
list price: US$10.95 -- used & new: US$5.79 (price subject to change: see help) Asin: 0486466663 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Algebraic number theory introduces students to new algebraic notions as well as related concepts: groups, rings, fields, ideals, quotient rings, and quotient fields. This text covers the basics, from divisibility theory in principal ideal domains to the unit theorem, finiteness of the class number, and Hilbert ramification theory. 1970 edition. Customer Reviews (4)
Crystal clear
Samuel Knows Numbers
Good service
A gem of a book |
6. Algebraic Number Theory | |
Paperback: 392
Pages
(2010-03-12)
list price: US$55.00 -- used & new: US$49.50 (price subject to change: see help) Asin: 0950273422 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Hallelujah!Back in print at last!
The best place to learn Class Field Theory |
7. 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 |
8. 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 |
9. Algebraic Number Theory by Edwin Weiss | |
Paperback: 288
Pages
(1998-01-29)
list price: US$15.95 -- used & new: US$7.00 (price subject to change: see help) Asin: 0486401898 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Uncompromising and difficult
A high level book |
10. The Theory of Algebraic Numbers by Harry Pollard, Harold G. Diamond | |
Paperback: 192
Pages
(2010-08-19)
list price: US$9.95 -- used & new: US$6.25 (price subject to change: see help) Asin: 0486404544 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
underdeveloped and outdated It's quite apparent that the 40 years that have passed since this book was printed have very much dated it's content. The definitions of many key concepts (such as an ideal) contain the right ideas, but are not formulated in the modern viewpoint.These, however are only minor setbacks. The main flaw of this book is its subject matter. There are 11 chapters, and it was not until the eighth that the ideas start getting deeper. Even these last 4 chapters do not delve very far into the heart of things. The text is written with the reader in mind (almost excessively so). Useful equations are clearly labeled and the steps in the proof are clearly outlined, though sometimes to an unnecessary degree. I would recommend this book for a mathematics hobbyist, or perhaps an undergraduate number theory course. For anyone with a stronger background, they wil not glean much.
A Strong Introduction |
11. Algebraic number theory: 2nd edition by Ian Stewart | |
Paperback: 220
Pages
(1979-05-31)
list price: US$104.50 -- used & new: US$104.50 (price subject to change: see help) Asin: 0412138409 Canada | United Kingdom | Germany | France | Japan | |
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12. Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Graduate Texts in Mathematics) by Harold M. Edwards | |
Paperback: 407
Pages
(2000-01-14)
list price: US$59.95 -- used & new: US$28.55 (price subject to change: see help) Asin: 0387950028 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Old school algebraic number theory with heavy Kummer bias
great book
Read this if you're seriously interested in math. The answer, of course, is that attacks on the problem revealed deep and important connections between elementary number theory and various other branches of mathematics, such as the theory of rings. Thus, as so often in mathematics, the importance of the problem lies in where it leads the mind, rather than in the problem itself. Harold M. Edwards' book is a minor classic of exposition, showing how the instincts of top-flight research mathematicians lead them to fruitful work from a seemingly unimportant starting point. I'm only sorry that Professor Edwards seems never to have completed the second volume he had hoped to write. Thus book deserves to be read by a much larger audience than it has gotten; in particular, I believe every graduate student in math who hopes to do good research, regardless of specialty, would benefit from reading it. Beyond that, any mathematically inclined reader with a modicum of training in math, is likely to find this a fascinating book. ... Read more |
13. Elementary Number Theory: An Algebraic Approach (Dover Books on Mathematics) by Ethan D. Bolker | |
Paperback: 208
Pages
(2007-03-15)
list price: US$13.95 -- used & new: US$8.83 (price subject to change: see help) Asin: 0486458075 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and the Fermat conjecture for exponents three and four. The text contains abundant numerical examples and a particularly helpful collection of exercises. |
14. Elementary and Analytic Theory of Algebraic Numbers (Springer Monographs in Mathematics) by Wladyslaw Narkiewicz | |
Paperback: 708
Pages
(2010-11-02)
list price: US$179.00 -- used & new: US$142.21 (price subject to change: see help) Asin: 3642060102 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems. |
15. Number Theory: Algebraic Numbers and Functions (Graduate Studies in Mathematics) by Helmut Koch | |
Hardcover: 368
Pages
(2000-06-06)
list price: US$65.00 -- used & new: US$65.00 (price subject to change: see help) Asin: 0821820540 Canada | United Kingdom | Germany | France | Japan | |
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16. A Course in Algebraic Number Theory (Dover Books on Mathematics) by Robert B. Ash | |
Paperback: 128
Pages
(2010-06-17)
list price: US$10.95 -- used & new: US$6.71 (price subject to change: see help) Asin: 0486477541 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This text for a graduate-level course covers the general theory of factorization of ideals in Dedekind domains as well as the number field case. It illustrates the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition. |
17. A Brief Guide to Algebraic Number Theory by H. P. F. Swinnerton-Dyer, Peter Swinnerton-Dyer | |
Paperback: 200
Pages
(2001-07-15)
list price: US$45.99 -- used & new: US$21.99 (price subject to change: see help) Asin: 0521004233 Canada | United Kingdom | Germany | France | Japan | |
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18. Algebraic Number Theory by H. Koch | |
Paperback: 280
Pages
(1997-10-16)
list price: US$149.00 -- used & new: US$87.38 (price subject to change: see help) Asin: 3540630031 Canada | United Kingdom | Germany | France | Japan | |
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19. Problems in Algebraic Number Theory (Graduate Texts in Mathematics) by M. Ram Murty, Jody (Indigo) Esmonde | |
Paperback: 352
Pages
(2010-11-02)
list price: US$74.95 -- used & new: US$60.14 (price subject to change: see help) Asin: 1441919678 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved Customer Reviews (3)
Excellent book on problems
Amazing!!
Won't become a classic. |
20. Number Theory II: Algebraic Number Theory (Encyclopaedia of Mathematical Sciences) by A. N. Parshin | |
Hardcover: 262
Pages
(1992-10)
list price: US$120.00 -- used & new: US$183.13 (price subject to change: see help) Asin: 0387533869 Canada | United Kingdom | Germany | France | Japan | |
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