東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Number fields

Marcus, Daniel A.

FindBook

Google Book

Amazon

博客來

Number fields

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Number fields/ by Daniel A. Marcus.
作者:	Marcus, Daniel A.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	xviii, 203 p. :digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Number theory. -
電子資源:	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:

515832
Number theory.

LC Class. No.: QA241 / .M373 2018

Dewey Class. No.: 512.7

Number fields
LDR:02549nmm a2200337 a 4500 001 2152505
003 DE-He213
005 20190129164000.0
006 m d
007 cr nn 008maaau
008 190403s2018 gw s 0 eng d
020 $a 9783319902333 $q (electronic bk.)
020 $a 9783319902326 $q (paper)
024 7 $a 10.1007/978-3-319-90233-3 $2 doi
035 $a 978-3-319-90233-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA241 $b .M373 2018
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
082 0 4 $a 512.7 $2 23
090 $a QA241 $b .M322 2018
100 1 $a Marcus, Daniel A. $3 3338889
245 1 0 $a Number fields $h [electronic resource] / $c by Daniel A. Marcus.
250 $a 2nd ed.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a xviii, 203 p. : $b digital ; $c 24 cm.
490 1 $a Universitext, $x 0172-5939
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.
650 0 $a Number theory. $3 515832
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Number Theory. $3 891078
650 2 4 $a Algebra. $3 516203
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Universitext. $3 812115
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-90233-3
950 $a Mathematics and Statistics (Springer-11649)