First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it is also eminently suited as a text for self-study.
Algebraic Number Theory and Fermat's Last Theorem
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Editorial Reviews
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"The book remains, as before, an extremely attractive introduction to algebraic number theory, from the ideal-theoretic perspective." -Andrew Bremner, Mathematiacl Reviews, February 2003
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Most Helpful Customer Reviews
16 of 16 people found the following review helpful:
4.0 out of 5 stars
Lucid introduction,
By A Customer
This review is from: Algebraic Number Theory and Fermat's Last Theorem: Third Edition (Hardcover)
Lucid and clear introduction to algebraic number theory, in style very much like the author's other book on Galois theory. Very elementary though, doesn't cover any analytic method, nor gives even a taste of class field theory, besides the problem set is less than challenging. But the book serves its purpose well, strongly recommended for beginners.
14 of 15 people found the following review helpful:
4.0 out of 5 stars
thoughts from an amateur,
This review is from: Algebraic Number Theory and Fermat's Last Theorem: Third Edition (Hardcover)
good overview of algebraic number theory as it applies to FLT, however not exactly pitched at beginners. you'll want to have a grounding in abstract algebra & linear algebra at the minimum. still, even if you don't, you can get a good sense of the "big picture" and a high-level understanding of the advances in mathematics that were directly or indirectly related to attempts to solve FLT. overall a fascinating read if you're a math geek who wants something a little deeper than Simon Singh's pop treatment of Wiles' proof.
14 of 16 people found the following review helpful:
5.0 out of 5 stars
Very clear introduction to Algebraic Number Theory,
By
This review is from: Algebraic Number Theory and Fermat's Last Theorem: Third Edition (Hardcover)
This book is a very clear intoductino to ANT. It is a good first step for many reasons. One: it stays with algebraic number fields that are extensions of Q, the rational numbers. You get a good feel for the subject. When you go to more advanced books Q is replaced by other fields (P-adic, function fields, finite fields,..).
Two: He assumes very little and writes very clearly Three: You only needs to read his Galois theory book for the prerequisite Four: His book is what is usually left for the reader to do as an excersize in more advanced books.
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Inside This Book
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First Sentence:
Fermat's Last Theorem is a special case of the theory of Diophantine equations-integer solutions of polynomial equations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rational conic, factorization into irreducibles, fractional ideals, irregular primes, higher reciprocity laws, projective point, minimum polynomial, projective form, quadratic residue modulo, unique factorization, integral bases, algebraic integers, integral basis, prime ideals, cyclotomic fields, rational integers, quadratic residues, quadratic fields, proper factors, factorization domain, modular functions, elliptic curve, taking norms, highest common factor, algebraic number theory Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fermat's Last Theorem, Taniyama-Shimura-Weil Conjecture, Algebraic Background, Beal Conjecture, Mordell Conjecture New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Fermat's Last Theorem is a special case of the theory of Diophantine equations-integer solutions of polynomial equations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
rational conic, factorization into irreducibles, fractional ideals, irregular primes, higher reciprocity laws, projective point, minimum polynomial, projective form, quadratic residue modulo, unique factorization, integral bases, algebraic integers, integral basis, prime ideals, cyclotomic fields, rational integers, quadratic residues, quadratic fields, proper factors, factorization domain, modular functions, elliptic curve, taking norms, highest common factor, algebraic number theory Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fermat's Last Theorem, Taniyama-Shimura-Weil Conjecture, Algebraic Background, Beal Conjecture, Mordell Conjecture New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 40
books:
See all 40 books this book cites
- Disquisitiones Arithmeticae by Carl F. Gauss in Front Matter, and Back Matter
- Number Theory: An approach through history from Hammurapi to Legendre by André Weil in Back Matter (1), and Back Matter (2)
- A Course in Galois Theory by D. J. H. Garling in Back Matter
- Elementary Linear Algebra by Howard Anton in Back Matter
- Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) by A. Fröhlich in Back Matter
See all 40 books this book cites
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