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21. Number Theory: Volume II: Analytic andModern Tools (Graduate Texts in Mathematics) by Henri Cohen | |
Paperback: 596
Pages
(2010-11-02)
list price: US$64.95 -- used & new: US$64.95 (price subject to change: see help) Asin: 1441923888 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject. |
22. Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity by Manfred R. Schroeder | |
Paperback: 456
Pages
(2009-12-09)
list price: US$99.00 -- used & new: US$79.11 (price subject to change: see help) Asin: 3642099017 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Good mix of theory and mathematics
could have included some problems |
23. Advanced Number Theory with Applications (Discrete Mathematics and Its Applications) by Richard A. Mollin | |
Hardcover: 440
Pages
(2009-08-26)
list price: US$89.95 -- used & new: US$54.99 (price subject to change: see help) Asin: 1420083287 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and more than 1,500 entries in the index so that students can easily cross-reference and find the appropriate data. With numerous examples throughout, the text begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes in arithmetic progression. It then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. The text also presents an overview of Fermat’s Last Theorem (FLT) and numerous consequences of the ABC conjecture, including Thue–Siegel–Roth theorem, Hall’s conjecture, the Erdös–Mollin-–Walsh conjecture, and the Granville–Langevin Conjecture. In the appendix, the author reviews sieve methods, such as Eratothesenes’, Selberg’s, Linnik’s, and Bombieri’s sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring. By focusing on salient techniques in number theory, this textbook provides the most up-to-date and comprehensive material for a second course in this field. It prepares students for future study at the graduate level. Customer Reviews (1)
Number Theory applied ! |
24. Number Theory by Helmut Hasse | |
Paperback: 658
Pages
(2002-02-26)
list price: US$69.95 -- used & new: US$35.47 (price subject to change: see help) Asin: 354042749X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Number Theory |
25. Recreations in the Theory of Numbers by Albert H. Beiler | |
Paperback: 349
Pages
(1964-06-01)
list price: US$14.95 -- used & new: US$6.34 (price subject to change: see help) Asin: 0486210960 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (8)
Full of info
Full of info, but poorly written.
Recreational Mathematics Is NotA Contradiction In Terms This book is well-organized, beginning with topics that are easy to grasp, then going on to more complicated ideas. The contents include such terms as prime numbers, perfect numbers, amicable pairs, sociable numbers, divisors, congruences, cyclical numbers, repunits (a term the author coined) and logarithms. The book reveals many curiosities about common artcles such as squares, triangles and circles. More complex topics such as a resolution of a number into prime factors and Pell equalities are shown in a manner that is informative and easy to comprehend. The grand climax of the book is a stirring discussionof Fermat's Last Theorem. This volume remains a 'good read' despite the fact that it is almost forty years old. Although much of what it in this book has been superceded over the course of time, this boof is not obsolete. If you have any interest in numbers, buy this book if you do not already possess a copy of it.
A classic
Lots of examples, lots of tables, lots of fun |
26. Excursions in Number Theory (Dover books explaining science) by C. Stanley Ogilvy | |
Paperback: 168
Pages
(1988-11-01)
list price: US$8.95 -- used & new: US$5.45 (price subject to change: see help) Asin: 0486257789 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (8)
An understandable journey through one of the most fascinating areas of human endeavor
Great service
An Enjoyable Romp Through Number Theory, Skipping from Topic to Topic
Fantastic Journey
A Wonderful Trip I found the author's annotations helpful and I did not mind the occasional use of British vernacular.At many points in the text, Ogilvy & Anderson prompt the reader to pursue a question on their own, rather than walk through a full proof or explanation.This may seem abrupt, but it keeps the text focused and leaves the reader wanting to know more about number theory. I hope Dover continues to reach out to a general audience with books like this.It condenses a difficult subject into everyday language without condescending to the reader. ... Read more |
27. Topics in Number Theory, Volumes I and II by William J. LeVeque | |
Paperback: 496
Pages
(2002-11-07)
list price: US$24.95 -- used & new: US$17.00 (price subject to change: see help) Asin: 0486425398 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
28. Basic Number Theory (Classics in Mathematics) by Andre Weil | |
Paperback: 315
Pages
(1995-02-15)
list price: US$59.95 -- used & new: US$42.91 (price subject to change: see help) Asin: 3540586555 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
A warning to beginners As Weil says at the start of the book, it has few prerequisites in algebra or number theory, except that the reader is presumed familiar with the standard theorems on locally compact Abelian groups, and Pontryagin duality and Haar measures on those groups. This part is not a joke. If you want to really understand class field theory this may be a good book. (I am reliably told it is.) But Weil deliberately avoids using many ideas that are now standard: geometric ideas such as group schemes, and especially cohomological methods. Beginners studying algebraic numbers do not need this book. Weil recommends Hecke ALGEBRAIC NUMBERS for such readers, and that is a terrific book. To learn class field theory today you'd probably do better with and Cassels and Frohlich ALGEBRAIC NUMBER THEORY, which Weil also recommends in a note to the second edition of this book. ... Read more |
29. 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 |
30. Multiplicative Number Theory by Harold Davenport | |
Hardcover: 177
Pages
(2000-10-31)
list price: US$79.95 -- used & new: US$45.00 (price subject to change: see help) Asin: 0387950974 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
If you want to be an analytic number theorist
An extraordinary Book
A good historical approach to Analytic Number Theory The book works up gradually to each result, for example proving Dirichlet's theorem first for a prime modulus (as Dirichlet did himself), then the general modulus. In most cases it proves first the result for all primes (zeta function) and then the generalization for primes in an arithmetic progression (L function), pointing out which parts generalize easily and which cause special difficulties. Some of the more advanced results covered are exponential sums, Vinogradov's theorem that every large odd number is the sum of three primes, and Bombieri's theorem about the average distribution of primes in arithmetic progressions. I haven't seen the previous (1980) edition; this new edition seems to be lightly revised from the previous one. The last chapter is up-to-date and gives a brief survey of new results and of new books on the subject. ... Read more |
31. A Guide To Elementary Number Theory (Dolciani Mathematical Expositions) by Underwood Dudley | |
Hardcover: 141
Pages
(2009-11-19)
list price: US$49.95 -- used & new: US$45.63 (price subject to change: see help) Asin: 0883853477 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description A Guide to Elementary Number Theory is a 140 pages exposition of the topics considered in a first course in number theory. It is intended for those who may have seen the material before but have half-forgotten it, and also for those who may have misspent their youth by not having a course in number theory and who want to see what it is about without having to wade through a traditional text, some of which approach 500 pages in length. It will be especially useful to graduate student preparing for the qualifying exams. Though Plato did not quite say, He is unworthy of the name of man who does not know which integers are the sums of two squares he came close. This Guide can make everyone more worthy. |
32. Boethian Number Theory: A Translation of the De Institutione Arithmetica (Studies in Classical Antiquity) by Michael Masi | |
Paperback: 200
Pages
(1983-01)
list price: US$30.00 -- used & new: US$22.14 (price subject to change: see help) Asin: 9062037852 Canada | United Kingdom | Germany | France | Japan | |
33. 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 |
34. A Computational Introduction to Number Theory and Algebra by Victor Shoup | |
Hardcover: 598
Pages
(2009-02-16)
list price: US$64.00 -- used & new: US$40.00 (price subject to change: see help) Asin: 0521516447 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Really a treasure
The background you really need, clear and sweet |
35. 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 |
36. A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics) by Kenneth Ireland, Michael Rosen | |
Paperback: 389
Pages
(2010-11-02)
list price: US$94.95 -- used & new: US$64.00 (price subject to change: see help) Asin: 1441930949 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves. Customer Reviews (7)
This is not a book for learning number theory for the first time!
Best book on the subject
Great Book
Covers many important areas
Simply Amazing |
37. Unsolved Problems in Number Theory (Problem Books in Mathematics) (v. 1) by Richard K. Guy | |
Hardcover: 300
Pages
(1994-07)
list price: US$54.95 -- used & new: US$21.75 (price subject to change: see help) Asin: 0387942890 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
An excursion into the labyrinths carved by numbers
Outstanding source of intersting problems in number theory |
38. Advanced Number Theory by Harvey Cohn | |
Paperback: 288
Pages
(1980-08-01)
list price: US$12.95 -- used & new: US$7.47 (price subject to change: see help) Asin: 048664023X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (6)
All about quadratric number fields, but little else Cohn is clearly quite keen on the subject, and is not just writing a textbook on some arbitrary topic for which he thinks there might be a market. And he has no fear of including pedagogical remarks in a textbook. The English is a bit awkward in places, but that is a minor thing. The basics about characters and Dirichlet L-series are developed, but only to the extent needed to give Dirichlet's original proof of his theorem on arithmetic progressions. That proof, unlike later ones, uses Dirichlet's class number formula for quadratic fields, and is worth a look. There is a lengthy but now dated bibliography. An unusual feature is a table (from Sommer's 1911 book) describing the structure of Z[sqrt(n)] for all nonsquare n from -99 to 99.
Advanced, but now dated. Still useful. Be warned there is some dated material in this book. It is prior to Alan Baker's 1966 proofabout d=-163 and imaginary quadratic fields, and such is still only conjectured in the text.And of course, FLT wasn't on Wiles' check list when this book was published. It doesn't cover prime-producing polynomials or transcendental functions and their relation to class field theory, like one would hope (I guess the world had to wait for Baker for that). And forget about rational points on elliptic curves, none at all. It's from the period when elliptic equations were poo-pooed as relics before being brought to the fore again by recent developments. Despite all the short-comings, I can still recommend the book as a worthy edition to your number theory library. Just don't put it at the top of your lists (unless you're short on cash and Dover is all you can afford).
Not advanced enough for Fermat's last theorm
Not advanced enough for Fermat's last theorm
A book only for advanced students ! |
39. An Introduction to Number Theory (Graduate Texts in Mathematics) by G. Everest, Thomas Ward | |
Hardcover: 302
Pages
(2005-05-06)
list price: US$59.95 -- used & new: US$19.91 (price subject to change: see help) Asin: 1852339179 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The book aims to take readers to a deeper understanding of the patterns of thought that have shaped the modern understanding of number theory. It begins with the fundamental theorem of arithmetic and shows how it echoes through much of number theory over the last two hundred years. One of the main strengths of this book is the narrative. Everest and Ward present number theory as a living subject, showing how various new developments have drawn upon older traditions. The authors concentrate on the underlying ideas instead of working out the most general and complete version of a result. They select material from both the algebraic and analytic disciplines and sometimes present several different proofs of a single result to show the differing viewpoints and also to capture the imagination of the reader and help them to discover their own tastes. They also cover important topics of significant interest, eg. elliptic functions and the new primality test, which are often omitted from other books at this level. |
40. A Course in Computational Number Theory (Key Curriculum Press) by David Bressoud, Stan Wagon | |
Hardcover: 384
Pages
(2008-06-10)
-- used & new: US$60.00 (price subject to change: see help) Asin: 0470412151 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Typesetting ruins a great book |
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