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Algebraic number theory [electronic resource]

Algebraic number theory [electronic resource]

Material type
E-Book(소장)
Personal Author
Jarvis, Frazer.
Title Statement
Algebraic number theory [electronic resource] / Frazer Jarvis.
Publication, Distribution, etc
Cham :   Springer International Publishing :   Imprint: Springer,   2014.  
Physical Medium
1 online resource (xiii, 292 p.).
Series Statement
Springer undergraduate mathematics series,1615-2085
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.
General Note
Title from e-Book title page.  
Content Notes
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.
Bibliography, Etc. Note
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Algebraic number theory.
Short cut
URL
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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)

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.74 Accession No. E14033031 Availability Loan can not(reference room) Due Date Make a Reservation Service M

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