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# 상세정보 ## Algebraic number theory [electronic resource]

자료유형
E-Book(소장)
개인저자
Jarvis, Frazer.
서명 / 저자사항
Algebraic number theory [electronic resource] / Frazer Jarvis.
발행사항
Cham :   Springer International Publishing :   Imprint: Springer,   2014.
형태사항
1 online resource (xiii, 292 p.).
총서사항
ISBN
9783319075457
요약
The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.
일반주기
Title from e-Book title page.
내용주기
Unique factorisation in the natural numbers -- Number fields -- Fields, discriminants and integral bases -- Ideals -- Prime ideals and unique factorisation -- Imaginary quadratic fields -- Lattices and geometrical methods -- Other fields of small degree -- Cyclotomic fields and the Fermat equation -- Analytic methods -- The number field sieve.
서지주기
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.
일반주제명
Algebraic number theory.
바로가기
 000 00000nam u2200205 a 4500 001 000046046972 005 20200923134405 006 m d 007 cr 008 200916s2014 sz ob 001 0 eng d 020 ▼a 9783319075457 040 ▼a 211009 ▼c 211009 ▼d 211009 050 4 ▼a QA241-247.5 082 0 4 ▼a 512.7/4 ▼2 23 084 ▼a 512.74 ▼2 DDCK 090 ▼a 512.74 100 1 ▼a Jarvis, Frazer. 245 1 0 ▼a Algebraic number theory ▼h [electronic resource] / ▼c Frazer Jarvis. 260 ▼a Cham : ▼b Springer International Publishing : ▼b Imprint: Springer, ▼c 2014. 300 ▼a 1 online resource (xiii, 292 p.). 490 1 ▼a Springer undergraduate mathematics series, ▼x 1615-2085 500 ▼a Title from e-Book title page. 504 ▼a Includes bibliographical references and index. 505 0 ▼a Unique factorisation in the natural numbers -- Number fields -- Fields, discriminants and integral bases -- Ideals -- Prime ideals and unique factorisation -- Imaginary quadratic fields -- Lattices and geometrical methods -- Other fields of small degree -- Cyclotomic fields and the Fermat equation -- Analytic methods -- The number field sieve. 520 ▼a The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level. 530 ▼a Issued also as a book. 538 ▼a Mode of access: World Wide Web. 650 0 ▼a Algebraic number theory. 830 0 ▼a Springer undergraduate mathematics series. 856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-3-319-07545-7 945 ▼a KLPA 991 ▼a E-Book(소장)

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