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Number fields

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Number fields/ by Daniel A. Marcus.
Author:	Marcus, Daniel A.
Published:	Cham :Springer International Publishing : : 2018.,
Description:	xviii, 203 p. :digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Number theory. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-90233-3
ISBN:	9783319902333

Number fields
Marcus, Daniel A.

Number fields[electronic resource] /by Daniel A. Marcus. - 2nd ed. - Cham :Springer International Publishing :2018. - xviii, 203 p. :digital ;24 cm. - Universitext,0172-5939. - Universitext..

1: A Special Case of Fermat's Conjecture -- 2: Number Fields and Number Rings -- 3: Prime Decomposition in Number Rings -- 4: Galois Theory Applied to Prime Decomposition -- 5: The Ideal Class Group and the Unit Group -- 6: The Distribution of Ideals in a Number Ring -- 7: The Dedekind Zeta Function and the Class Number Formula -- 8: The Distribution of Primes and an Introduction to Class Field Theory -- Appendix A: Commutative Rings and Ideals -- Appendix B: Galois Theory for Subfields of C -- Appendix C: Finite Fields and Rings -- Appendix D: Two Pages of Primes -- Further Reading -- Index of Theorems -- List of Symbols.

Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights key arguments. There are several hundred exercises, providing a wealth of both computational and theoretical practice, as well as appendices summarizing the necessary background in algebra. Now in a newly typeset edition including a foreword by Barry Mazur, this highly regarded textbook will continue to provide lecturers and their students with an invaluable resource and a compelling gateway to a beautiful subject. From the reviews: "A thoroughly delightful introduction to algebraic number theory" - Ezra Brown in the Mathematical Reviews "An excellent basis for an introductory graduate course in algebraic number theory" - Harold Edwards in the Bulletin of the American Mathematical Society.

ISBN: 9783319902333

Standard No.: 10.1007/978-3-319-90233-3doiSubjects--Topical Terms:

527883
Number theory.

LC Class. No.: QA241 / .M373 2018

Dewey Class. No.: 512.7

Number fields
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300 $a xviii, 203 p. : $b digital ; $c 24 cm.
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505 0 $a 1: A Special Case of Fermat's Conjecture -- 2: Number Fields and Number Rings -- 3: Prime Decomposition in Number Rings -- 4: Galois Theory Applied to Prime Decomposition -- 5: The Ideal Class Group and the Unit Group -- 6: The Distribution of Ideals in a Number Ring -- 7: The Dedekind Zeta Function and the Class Number Formula -- 8: The Distribution of Primes and an Introduction to Class Field Theory -- Appendix A: Commutative Rings and Ideals -- Appendix B: Galois Theory for Subfields of C -- Appendix C: Finite Fields and Rings -- Appendix D: Two Pages of Primes -- Further Reading -- Index of Theorems -- List of Symbols.
520 $a Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights key arguments. There are several hundred exercises, providing a wealth of both computational and theoretical practice, as well as appendices summarizing the necessary background in algebra. Now in a newly typeset edition including a foreword by Barry Mazur, this highly regarded textbook will continue to provide lecturers and their students with an invaluable resource and a compelling gateway to a beautiful subject. From the reviews: "A thoroughly delightful introduction to algebraic number theory" - Ezra Brown in the Mathematical Reviews "An excellent basis for an introductory graduate course in algebraic number theory" - Harold Edwards in the Bulletin of the American Mathematical Society.
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