This account of Algebraic Number Theory is written primarily for beginning graduate students in pure mathematics, and encompasses everything that most such students are likely to need; others who need the material will also find it accessible. It assumes no prior knowledge of the subject, but a firm basis in the theory of field extensions at an undergraduate level is required, and an appendix covers other prerequisites. The book covers the two basic methods of approaching Algebraic Number Theory, using ideals and valuations, and includes material on the most usual kinds of algebraic number field, the functional equation of the zeta function and a substantial digression on the classical approach to Fermat's Last Theorem, as well as a comprehensive account of class field theory. Many exercises and an annotated reading list are also included.
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Editorial Reviews
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"This little book would be a good place to find out what the subject is all about...this is not an easy book to read, but it is one that will reward the reader's efforts." MAA Online
"I like short concise yet rigorous books such as this one. You can learn a lot of number theory in 140 pages, and then you have a nice concise reference book when you forget what you learned!" The Bulletin of Mathematical Books
"I like short concise yet rigorous books such as this one. You can learn a lot of number theory in 140 pages, and then you have a nice concise reference book when you forget what you learned!" The Bulletin of Mathematical Books
Book Description
This is an account of Algebraic Number Theory, a field which has grown to touch many other areas of pure mathematics. The book encompasses everything that graduate students and pure mathematicians interested in the subject are likely to need, and assumes only some undergraduate level material and other prerequisites covered in an appendix. The book covers the two basic methods of approaching Algebraic Number Theory and includes a substantial digression on the classical approach to Fermat's Last Theorem. Many exercises and an annotated reading list are also included.
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Inside This Book
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First Sentence:
Unless otherwise stated, throughout this book K and k will be algebraic number fields, even though some results hold more generally. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
classical class field theory, prime which ramifies, minimal monic polynomial, complex conjugacy, ramified primes, fractional ideal, integral ideal, infinite places, ideal class group, residue symbol, algebraic number fields, inertia group, prime ideals, rational primes, abelian extensions, minimal base, cyclotomic field, highest common factor, algebraic number theory, splitting field, ideal classes Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Corollary Let, Proof Suppose, Fermat's Last Theorem, Kronecker-Weber Theorem, Proof Write New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Unless otherwise stated, throughout this book K and k will be algebraic number fields, even though some results hold more generally. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
classical class field theory, prime which ramifies, minimal monic polynomial, complex conjugacy, ramified primes, fractional ideal, integral ideal, infinite places, ideal class group, residue symbol, algebraic number fields, inertia group, prime ideals, rational primes, abelian extensions, minimal base, cyclotomic field, highest common factor, algebraic number theory, splitting field, ideal classes Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Corollary Let, Proof Suppose, Fermat's Last Theorem, Kronecker-Weber Theorem, Proof Write 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 13
books:
See all 13 books this book cites
3
books
cite this book:
- Class Field Theory (Advanced Book Classics) by Emil Artin on page 98
- Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang in Back Matter
- Local Fields (London Mathematical Society Student Texts) by J. W. S. Cassels in Back Matter
- Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) by A. Fröhlich in Back Matter
- Number Theory: An approach through history from Hammurapi to Legendre by André Weil in Back Matter
See all 13 books this book cites
- Algebraic Number Theory and Fermat's Last Theorem: Third Edition by Ian Stewart in Back Matter
- Elementary and Analytic Theory of Algebraic Numbers (Springer Monographs in Mathematics) by Wladyslaw Narkiewicz in Back Matter
- Algebraic Number Theory and Code Design for Rayleigh Fading Channels (Foundations and Trends in Communications and Information The) by F Oggier in Back Matter
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