國立虎尾科技大學 |

Number Fields

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Number Fields/ by Daniel A. Marcus.
作者:	Marcus, Daniel A.
面頁冊數:	XVIII, 203 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Number theory. -
電子資源:	https://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. 2018. - XVIII, 203 p.online resource. - 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.: QA241-247.5

Dewey Class. No.: 512.7

Number Fields
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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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