Reviews (4)

advanced coverage
This is an advanced treatment of prime numbers. But it is not all abstract number theory. The recurrent theme is how to compute these and how to use primes in other computationally intensive tasks.
Badly Bound
The book content is quite fascinating; the only real readability difficuly is some rather obscure and undefined notation. Standard reference on the subject.
While recently published, this book is shaping to become the standard reference on the theory that surrounds prime numbers in a computational setting, drawing from all branches of number theory, as well as abstract algebra, analysis, combinatorics, statistics, complexity theory and elliptic curves. Surely a multidisciplinary treatise if there ever was one.Read more

Subjects:  1. Functional Analysis    2. Mathematics    3. Number Theory    4. Numbers, Prime    5. Science/Mathematics    6. Mathematics / Number Theory   

Reviews (1)

Extraordinarily Comprensive Review
This book has pretty much anything you could want about the theory of cyclotomic fields: Fermat's Last Theorem(See how it was done before Wiles!), an introduction to iwasawa theory, and a proof of Thaine's theorem for those of you who are interested in Mihailescu's proof of Catalan's conjecture. One thing though, this book is not really an introduction. If you're not familiar with Algebraic Number Theory and p-adic analysis, you will be completely lost in this book. It definitely doesn't hurt to know at least the major statements of Class Field Theory. Other than that, though, a truly great book! ... Read more

Subjects:  1. Algebraic Fields    2. Cyclotomy    3. Group Theory    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. Theory Of Numbers    8. Algebraic number theory    9. Fields    10. Kreiskörper    11. Mathematics / Number Theory   

Subjects:  1. Computer Science    2. Discrete Mathematics    3. Discrete Mathematics (Computer Science)    4. Geometry - Algebraic    5. Mathematics    6. Number Theory    7. Science/Mathematics    8. Theory Of Numbers    9. Mathematics / Number Theory    10. algebraic geometry   

Reviews (1)

A historical juwel
If you want to study mathematics, in particular rational numbers, concepts of infinity and relation with geometry, this book is not very effective, be it only for the tedious style of formulation.
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Subjects:  1. 1616-1703    2. 1616-1703.    3. Arithmetica infinitorum    4. Curves    5. Early works to 1800    6. History & Philosophy    7. Infinity    8. Mathematics    9. Number Theory    10. Rectification and quadrature    11. Science/Mathematics    12. Wallis, John,    13. History of mathematics    14. Mathematics / History   

Reviews (3)

A good start!
You won't find many books on such an out-of-fashion theme as continued fractions, will you? Even less on the arithmetic side of the theory. Yes, it's true, many texts on elementary number theory provide a chapter or so about the subject, but if you want to gain a reasonably thorough picture of the field, without dwelling so much on details, you've got to resort to Kinchin's "Continued fractions": readable (no more mathematic needed than basics of analysis), complete (all fundamental conceptual aspects dealt with, included measure theory and implications on irrational numbers), brief (less than a hundred pages with virtually no applications - not even to Pell's equation!) and LIVELY in style.
I recommend this book to anyone who loves mathematics.
A Y Khinchin was one of the greatest mathematicians of the first half of the twentieth century. His name is is already well-known to students of probability theoryalong with A N Kolmogorov and others from the host of important theorems, inequalites, constants named after them.He was also famous as a teacher and communicator. Several of the books he wrote are still in print in English translations, published by Dover. Like William Feller and Richard Feynman he combines a complete mastery of his subject with an ability to explain clearly without sacrificing mathematical rigour. Classic text, however not suitable for a first exposure.
This is Khinchin's classic work, translated from Russian in the 1930's.Although the book is rich with insight and information, Khinchin stays one nautical mile ahead of the reader at all times, the book moves at a trulyalarming pace, and the book is not suitable to be used ALONE as anintroduction to continued fractions.To supplement this book if this is afirst exposure to continued fractions, I would recommend C.D. Old's book,which has many more examples which can be worked through until the readeris comfortable with the topic.Read more

Subjects:  1. Continued fractions    2. Infinity    3. Mathematical Analysis    4. Mathematical Statistics    5. Mathematics    6. Number Theory    7. Science/Mathematics    8. Mathematics / General    9. Probability & statistics   

Reviews (1)

This is an obsolete edition.
Hasn't this book been replaced by the 2nd edition, 1998, same publisher? ... Read more

Subjects:  1. Mathematics    2. Number Theory    3. Numbers, Prime    4. Science/Mathematics    5. Mathematics / Number Theory   

Subjects:  1. Algebra - General    2. Algebraic fields    3. Ideals (Algebra)    4. Mathematics    5. Number Theory    6. Rings    7. Rings (Algebra)    8. Science/Mathematics    9. Algebraic number theory    10. Fields & rings    11. Groups & group theory    12. Mathematics / Algebra / General    13. Mathematics / Number Theory    14. Mathematics | Pure Mathematics    15. Mathematics-Number Theory   

Editorial Review

Born in 1601, Pierre de Fermat lived a quiet life as a civil servant in Toulouse, France. In his spare time, however, Fermat dabbled in mathematics, and somehow managed to become one of the great mathematical theorists of his century. Around 1637 he scribbled a marginal note in one of his books. In it, he stated that he had solved a celebrated number theory problem: "I have discovered a truly marvelous proof of this, which, however, the margin is not large enough to contain." Read more

Reviews (33)

350 Year Old Detective Story
In 1637 Pierre de Fermat scribbled some notes in a margin of a mathematics book and the world has been talking about it ever since.Was his "last theorem" ever real or did he simply invent a story to boost his ego?Perhaps we will never know, but three centuries later Prof. Andrew Wiles did provide the solution to the greatest mathematical conundrum in history (or at least the most famous).Some people argue that Prof. Wiles used a mathematics unknown to Fermat, but if the Egyptians could build the pyramids in a mere 23 years (a feat that would take us with all our modern technology more than a century, if the money and determination could even be acquired) perhaps the knowledge of Fermat was lost over the centuries as well.We are certainly rediscovering things ancient people knew, so who is to say Fermat did not have a solution?
An Introductory Book
While I did enjoy this book, I believe that it only serves as an introductory preface to the theorem.It does present all of the main ideas, but it fails to provide a network with which to tie them all together.When used with another book, such as Fermats Enigma by Simon Singh, many of the ideas come together so that the reader can see where Andrew Wiles proof came from and how it works.I would recommend this book for those who have very little knowledge of the theorem and would like to know a general outline.

Interesting idea, wrong direction
I think a book about the solution to Fermat's last theorem is an excellent idea.However, I think that this book ultimately fails because Aczel takes too much time discussing the history of the theorem and the developement of mathematics up until the point when the problem was solved in 1993.More than two centuries of mathematics is pigeon-holed into a book that is under 200 pages.In that respect, I think that the author was overly ambitious in his aim; it is simply impossible to explain topology in 3 or 4 pages. I would have rather seen the story approached from the human, rather than the math, side of things. ... Read more

Subjects:  1. Fermat's last theorem    2. History & Philosophy    3. Mathematics    4. Number Theory    5. Science/Mathematics    6. Mathematics / General   

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Algebraic number theory    5. Nonfiction / Education   

Reviews (9)

A Modern Whittaker and Watson, Buy It
This book is great.It is the best overview I have ever seen of the primary special functions, as seen from a modern viewpoint.Buy it and you will spend many happy hours reading the theorems it contains, and doing the excercizes at the end of each chapter.

A book comes close to " A course of modern analysis "
Though this book cannot be compared to Whittaker and Watson's classic book. It comes quite close to it. I just want to comment on the the area covers are too concentrated and the rigorous manner which is the hall mark of " Modern Analysis " is lacking. Anyway, this book deserves 5 stars.

clean and concise
It has a very good style of writing for the nature of mathematics. It is clean, no unnecessary explanation or examples. In a way, one can feel something similar to Axler's.It is an excellent reference book. One should keep this book just as Axler's Linear Algebra Done Right, Numerical Recipe, DE Knuth's Art of Programming. ... Read more

Subjects:  1. Control Theory    2. General    3. Mathematical Analysis    4. Mathematics    5. Number Theory    6. Partial Differential Equations    7. Science/Mathematics    8. Calculus & mathematical analysis    9. Functions, Special    10. Mathematics / Algebra / General   

Features

• Unabridged

Reviews (4)

Three pearls of number theory
A jewel. Highly recommended for students ofnumber theory, expecilally amateurs and teachers.

Truly a pearl.
It is truly a pearl, and pearls have permanence; --they retain their beauty, from one generation to the next.
Come on, professors, write more like this!
This book is actually a letter from a Russian professor to a student sent off to war.It's short, but won't be an easy read. These are "pearls" but getting the oyster open is going to be tough. It's also remarkable for it's candid revelation of the mathematical process of professional practitioners at various universities in different countries.The first pearl is about a young student name van der Waerden. Yep, the guy who went on to prove so many results in Abstract Algebra and wrote the classic text on the subject influencing Artin and Noether. It's interesting to note, van der Waerden used finite differences in his proof recounted in the first pearl, and he's the only author I know that included finite differences in his abstract algebra text book. Both the candid historical confessions and the conversational exposition make this a great book. It's style and methods should be widely imitated. Come on, professors, write more like this! Future archaeologist of the 20th century will be glad this document is available for it's revelation of the habits of homo professorus mathematicus. ... Read more

Subjects:  1. General    2. Mathematics    3. Number Theory    4. Science    5. Science/Mathematics    6. Mathematics / General   

Reviews (2)

Definitely belongs on the shelf of all number theory lovers
This book is an excellent compilation of both the theory and pseudo-code for number theoretic algorithms. The author also takes the time to prove some of the major results as background to the algorithms, in addition to sets of exercises at the end of the book. The book is too large to do a chapter by chapter review, so instead I will list the algorithms in the book that I thought were particularly useful: Excellent!
Cohen (the world renowned expert) starts with the most basic of algorithms(i.e. Euclid & Shanks). He moves seamlessly into Linear Algebra &Polynomials (bedrocks of most CAS). Although meant to be concise, heproves, or sketches a proof of the important results. Finally, the meat ofthe book, C.A.N.T. One important problem is finding the "classnumber" (has to do with unique factorization, which we are allaccustomed to in Z). A detailed description of the continued fractionalgorithm (for finding the fundamental unit), and others made it veryenlightening. He then deals with primality testing and factoring, two veryimportant problems, the latter because of RSA. First, a description of thealgorithm, then the theory behind it. He covered everything, from TrialDivision (Dark Ages) to Pollard Rho to NFS (cutting-edge). Also includedare some useful tables.Read more

Subjects:  1. Algebraic Number Theory    2. Data processing    3. General    4. Mathematics    5. Number Theory    6. Science    7. Science/Mathematics   

Reviews (1)

an introduction to Goppa codes
Coding theory is fundamental to make digital transmission technology work efficiently and usually uses Reed-Solomon codes. The "natural" extension of those codes is to consider riemann surfaces over finite fields.Read more

Subjects:  1. Algebraic fields    2. Algebraic functions    3. Geometry - Algebraic    4. Mathematics    5. Number Theory    6. Science/Mathematics    7. Theory Of Functions   

Subjects:  1. Algebra - Linear    2. Differential Equations    3. Harmonic analysis    4. Homogeneous spaces    5. Lie groups    6. Mathematics    7. Number Theory    8. Science/Mathematics    9. Fourier transfoms    10. Functional analysis    11. Mathematics / Mathematical Analysis    12. several complex variables   

Reviews (1)

discursive look at modern prime number theory
This book gives a survey of some of the top results, methods, and conjectures about the distribution of prime numbers. For many results it gives complete (but very concise) proofs.Read more

Subjects:  1. Mathematics    2. Number Systems    3. Number Theory    4. Numbers, Prime    5. Science/Mathematics    6. Probability & statistics   

Subjects:  1. Children's All Ages - Mathematics    2. Education    3. Number Theory    4. Teaching Methods & Materials - Mathematics   

Subjects:  1. Geometry - General    2. Mathematics    3. Number Theory    4. Science/Mathematics    5. Mathematics / Number Theory   

Subjects:  1. Algebra    2. Algebra - General    3. Arithmetic    4. Mathematics    5. Multiplication, Complex    6. Number Theory    7. Science/Mathematics    8. Komplexe Multiplikation    9. Mathematics / Algebra / General    10. Mathematics / Number Theory    11. Mathematics-Number Theory   

Subjects:  1. Mathematics    2. Number Theory    3. Science/Mathematics    4. Transcendental numbers    5. Mathematics / Number Theory    6. Mathematics and Science   

Subjects:  1. Algebra - General    2. Algebra - Linear    3. Algebras, Linear    4. Geometry - Algebraic    5. Geometry, Algebraic    6. Mathematics    7. Number Theory    8. Science/Mathematics    9. Textbooks    10. Linear algebra