跳到内容
Elementary number theory : primes, congruences, and secrets : a computational approach 预览资料
关闭预览资料
正在查...

Elementary number theory : primes, congruences, and secrets : a computational approach

著者: William A Stein
出版商: New York, NY : Springer, ©2009.
丛书: Undergraduate texts in mathematics.
版本/格式:   电子图书 : 文献 : 英语查看所有的版本和格式
数据库:WorldCat
提要:
The systematic study of number theory was initiated around 300B.C. when Euclid proved that there are infinitely many prime numbers. At the same time, he also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over 1000 years later (around 972A.D.) Arab mathematicians formulated the congruent number problem that asks for a way to  再读一些...
评估:

(尚未评估) 0 附有评论 - 争取成为第一个。

主题
更多类似这样的

 

在图书馆查找

&AllPage.SpinnerRetrieving; 正在查找有这资料的图书馆...

详细书目

类型/形式: Electronic books
附加的形体格式: Print version:
Stein, William A., 1974-
Elementary number theory.
New York, NY : Springer, ©2009
(OCoLC)268798336
材料类型: 文献, 互联网资源
文件类型: 互联网资源, 计算机文档
所有的著者/提供者: William A Stein
ISBN: 9780387855257 0387855254 0387855246 9780387855240 1281850969 9781281850966
OCLC号码: 317545887
描述: 1 online resource (x, 166 pages) : illustrations.
内容: Prime numbers --
The ring of integers modulo n --
Public-key cryptography --
Quadratic reciprocity --
Continued fractions --
Elliptic curves.
丛书名: Undergraduate texts in mathematics.
责任: William Stein.
更多信息:

摘要:

Classical number theory and elliptic curves are examined in this textbook, which moves on from elementary topics such as primes, continued fractions, and quadratic forms, to elliptic curves and their  再读一些...

评论

社评

出版商概要

From the reviews: "This one treats topics that have become standard in recent years ... and it has exercises with selected solutions. ... it gives the students a tool to do calculations that 再读一些...

 
用户提供的评论
正在获取GoodReads评论...
正在检索DOGObooks的评论

标签

争取是第一个!
确认申请

你可能已经申请过这份资料。如果还是想申请,请选确认。

链接数据


Primary Entity

<http://www.worldcat.org/oclc/317545887> # Elementary number theory : primes, congruences, and secrets : a computational approach
    a schema:MediaObject, schema:CreativeWork, schema:Book ;
   library:oclcnum "317545887" ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/890884167#Place/new_york_ny> ; # New York, NY
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/nyu> ;
   schema:about <http://id.worldcat.org/fast/1041214> ; # Number theory
   schema:about <http://dewey.info/class/512.7/e22/> ;
   schema:about <http://id.worldcat.org/fast/885455> ; # Curves, Elliptic
   schema:about <http://experiment.worldcat.org/entity/work/data/890884167#Topic/mathematics> ; # Mathematics
   schema:about <http://experiment.worldcat.org/entity/work/data/890884167#Topic/mathematics_number_theory> ; # MATHEMATICS--Number Theory
   schema:bookFormat schema:EBook ;
   schema:copyrightYear "2009" ;
   schema:creator <http://viaf.org/viaf/86017564> ; # William A. Stein
   schema:datePublished "2009" ;
   schema:description "Prime numbers -- The ring of integers modulo n -- Public-key cryptography -- Quadratic reciprocity -- Continued fractions -- Elliptic curves."@en ;
   schema:description "The systematic study of number theory was initiated around 300B.C. when Euclid proved that there are infinitely many prime numbers. At the same time, he also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over 1000 years later (around 972A.D.) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another 1000 years later (in 1976), Diffie and Hellman introduced the first ever public-key cryptosystem, which enabled two people to communicate secretly over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, public-key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles' resolution of Fermat's Last Theorem. Today, pure and applied number theory is an exciting mix of simultaneously broad and deep theory, which is constantly informed and motivated by algorithms and explicit computation. Active research is underway that promises to resolve the congruent number problem, deepen our understanding into the structure of prime numbers, and both challenge and improve our ability to communicate securely. The goal of this book is to bring the reader closer to this world. Each chapter contains exercises, and throughout the text there are examples of calculations done using the powerful free open source mathematical software system Sage. The reader should know how to read and write mathematical proofs and must know the basics of groups, rings, and fields. Thus, the prerequisites for this book are more than the prerequisites for most elementary number theory books, while still being aimed at undergraduates. William Stein is an Associate Professor of Mathematics at the University of Washington. He is also the author of Modular Forms, A Computational Approach (AMS 2007), and the lead developer of the open source software, Sage."@en ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/890884167> ;
   schema:genre "Electronic books"@en ;
   schema:inLanguage "en" ;
   schema:isPartOf <http://worldcat.org/issn/0172-6056> ; # Undergraduate texts in mathematics,
   schema:isPartOf <http://experiment.worldcat.org/entity/work/data/890884167#Series/undergraduate_texts_in_mathematics> ; # Undergraduate texts in mathematics.
   schema:isSimilarTo <http://www.worldcat.org/oclc/268798336> ;
   schema:name "Elementary number theory : primes, congruences, and secrets : a computational approach"@en ;
   schema:productID "317545887" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/317545887#PublicationEvent/new_york_ny_springer_2009> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/890884167#Agent/springer> ; # Springer
   schema:url <http://dx.doi.org/10.1007/b13279> ;
   schema:url <http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=261571> ;
   schema:url <http://www.myilibrary.com?id=185096> ;
   schema:url <http://site.ebrary.com/id/10257911> ;
   schema:url <http://www.myilibrary.com?id=185096&ref=toc> ;
   schema:url <http://0-dx.doi.org.skyline.cudenver.edu/10.1007/b13279> ;
   schema:workExample <http://dx.doi.org/10.1007/b13279> ;
   schema:workExample <http://worldcat.org/isbn/9780387855257> ;
   schema:workExample <http://worldcat.org/isbn/9781281850966> ;
   schema:workExample <http://worldcat.org/isbn/9780387855240> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/317545887> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/890884167#Series/undergraduate_texts_in_mathematics> # Undergraduate texts in mathematics.
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/317545887> ; # Elementary number theory : primes, congruences, and secrets : a computational approach
   schema:name "Undergraduate texts in mathematics." ;
    .

<http://experiment.worldcat.org/entity/work/data/890884167#Topic/mathematics_number_theory> # MATHEMATICS--Number Theory
    a schema:Intangible ;
   schema:name "MATHEMATICS--Number Theory"@en ;
    .

<http://id.worldcat.org/fast/1041214> # Number theory
    a schema:Intangible ;
   schema:name "Number theory"@en ;
    .

<http://id.worldcat.org/fast/885455> # Curves, Elliptic
    a schema:Intangible ;
   schema:name "Curves, Elliptic"@en ;
    .

<http://viaf.org/viaf/86017564> # William A. Stein
    a schema:Person ;
   schema:birthDate "1974" ;
   schema:familyName "Stein" ;
   schema:givenName "William A." ;
   schema:name "William A. Stein" ;
    .

<http://worldcat.org/isbn/9780387855240>
    a schema:ProductModel ;
   schema:isbn "0387855246" ;
   schema:isbn "9780387855240" ;
    .

<http://worldcat.org/isbn/9780387855257>
    a schema:ProductModel ;
   schema:isbn "0387855254" ;
   schema:isbn "9780387855257" ;
    .

<http://worldcat.org/isbn/9781281850966>
    a schema:ProductModel ;
   schema:isbn "1281850969" ;
   schema:isbn "9781281850966" ;
    .

<http://worldcat.org/issn/0172-6056> # Undergraduate texts in mathematics,
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/317545887> ; # Elementary number theory : primes, congruences, and secrets : a computational approach
   schema:issn "0172-6056" ;
   schema:name "Undergraduate texts in mathematics," ;
    .

<http://www.worldcat.org/oclc/268798336>
    a schema:CreativeWork ;
   rdfs:label "Elementary number theory." ;
   schema:description "Print version:" ;
   schema:isSimilarTo <http://www.worldcat.org/oclc/317545887> ; # Elementary number theory : primes, congruences, and secrets : a computational approach
    .

<http://www.worldcat.org/title/-/oclc/317545887>
    a genont:InformationResource, genont:ContentTypeGenericResource ;
   schema:about <http://www.worldcat.org/oclc/317545887> ; # Elementary number theory : primes, congruences, and secrets : a computational approach
   schema:dateModified "2017-04-01" ;
   void:inDataset <http://purl.oclc.org/dataset/WorldCat> ;
    .


Content-negotiable representations

关闭窗口

请登入WorldCat 

没有张号吗?很容易就可以 建立免费的账号.