A数学体系概述、主要分支、学科分类(MSC)、构成联系和应用数学简介(62k字)
I. 数学体系分支概述
II. 数学体系主要分支
III. 美国数学会(AMS)官网《2010年数学学科分类》
IV. 数学体系的构成和各分支间的联系
V. 应用数学
数学体系概述、主要分支、学科分类(MSC)、构成联系和应用数学简介
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III. 美国数学会(AMS)官网《2010年数学学科分类》
- 美国数学会(AMS)的MSC2010分类
美国数学会(American MathematicalSociety, AMS)官网的《 2010年数学学科分类》包括MSC2000数据库、MSC2010数据库、如何使用MSC，和PDF中的整个MSC、2000年至2010年转换、2010年至2000年转换等内容。目前的2010年数学学科分类(MSC2010)，是自2000年以来MR和Zbl使用的MSC2000的修订版.MSC2010是MR和Zbl的编辑共同努力更新其共享分类的结果。这些编辑承认在两年多的修订过程中，数学界提出了许多有用的建议。
(详情见官网https://mathscinet.ams.org/msc/msc2010.html)
MSC2000 database, MSC2010 database, How to use the MSC
2010Mathematics Subject Classification
Thecurrent 2010 Mathematics Subject Classification (MSC2010) is a revision of theMSC2000 that has been used by MR and Zbl since 2000. MSC2010 is the result of acollaborative effort by the editors of MR and Zbl to update their sharedclassification. These editors acknowledge the many helpful suggestions from themathematical community during the revision process over more than two years.
| Entire MSC in PDF| 2000 to 2010 Conversion| 2010 to 2000 Conversion|
下载其中的主要文件MSC2010(47 pages pdf)，翻译如下。
这份MSC2010(47页pdf)文件是MSC2010的印刷版，MSC修订版由数学评论(MR)和Zentralblatt furMathematik(Zbl)的编辑人员与数学界协商共同制作。本次修订的数学学科分类(MSC)的目标载于其公告中，并于2006年8月征求MR执行编辑和Zbl主编的意见。本文件结果从那时起一直在进行的MSC修订过程。MSC2010将于2010年7月全面部署。
Thisdocument is a printed form of MSC2010, an MSC revision produced jointly by theeditorial staffs of Mathematical Reviews (MR) and Zentralblatt fur Mathematik(Zbl) in consultation with the mathematical community. The goals of thisrevision of the Mathematics Subject Classication (MSC) were set out in the wereset out in the announcement of it and call for comments by the Executive Editorof MR and the the Chief Editor of Zbl in August 2006. This document resultsfrom the MSC revision process that has been going on since then. MSC2010 willbe fully deployed from July 2010.
因此，部署此修订版的MR和Zbl的编辑会要求提供有关剩余错误的反馈，以帮助完成这项工作，最好在网站http://msc2010.org上提供，或者，如果没有互联网，通过电子邮件发送到[email protected]。他们感谢以前收到的许多建议，这些建议对我们所拥有的东西有很大影响。
Theeditors of MR and Zbl deploying this revision therefore ask for feedback onremaining errors to help in this work, which should be given, preferably, onthe Web site at http://msc2010.org or, if the internet is not available,through e-mail to [email protected]. They are grateful for the manysuggestions that were received previously which have much in uenced what wehave.
如何使用数学科目分类[MSC]
How touse the Mathematics Subject Classication [MSC]
使用数学主题分类方案对数学文献中项目进行分类的主要目的是帮助用户尽可能容易地找到他们现有或潜在感兴趣的项目|来自数学评论数据库(MRDB)的产品，如MathSciNet，Zentralblatt MATH(ZMATH)，或使用此分类方案的任何其他地方。数学文献中的一个项目应该被分类，以吸引所有可能对它感兴趣的人的注意。该项目可能正好落在MSC的一个明确区域内，或者可能涉及多个区域。理想情况下，附加到项目的MSC代码应代表项目包含贡献的主题。分类应该为那些与特定主题领域密切相关的人和那些熟悉主题的人提供服务，以便将他们的结果和方法应用于数学内外的其他地方。对于用户和班级用户来说，熟悉整个分类系统并因此了解他们可能感兴趣的所有分类将是非常有用的。
Themain purpose of the classication of items in the mathematical literature usingthe Mathematics Subject Classication scheme is to help users find the items ofpresent or potential interest to them as readily as possible|in productsderived from the Mathematical Reviews Database (MRDB) such as MathSciNet, inZentralblatt MATH (ZMATH), or anywhere else where this classication scheme isused. An item in the mathematical literature should be classied so as toattract the attention of all those possibly interested in it. The item may besomething which falls squarely within one clear area of the MSC, or it mayinvolve several areas. Ideally, the MSC codes attached to an item shouldrepresent the subjects to which the item contains a contribution. Theclassi_cation should serve both those closely concerned with speci_c subjectareas, and those familiar enough with subjects to apply their results andmethods elsewhere, inside or outside of mathematics. It will be extremelyuseful for both users and classi_ers to familiarize themselves with the entire classificationsystem and thus to become aware of all the classifications of possible interestto them.
MRDB或ZMATH中的每个项目只接收一个主要分类，它只是描述其主要贡献的MSC代码。当一个项目包含对不同领域的若干主要贡献时，主要分类应涵盖其中最重要的分类。可以为纸质或书籍分配一个或多个二级分类号，以涵盖所讨论事项的任何剩余主要贡献，辅助结果，动机或来源，预期或潜在的应用领域，或值得注意的其他重要方面。
Everyitem in the MRDB or ZMATH receives precisely one primary classification, whichis simply the MSC code that describes its principal contribution. When an itemcontains several principal contributions to different areas, the primaryclassification should cover the most important among them. A paper or book maybe assigned one or several secondary classification numbers to cover anyremaining principal contributions, ancillary results, motivation or origin ofthe matters discussed, intended or potential field of application, or othersignificant aspects worthy of notice.
主要贡献是包括该项目中实际完成的工作中最重要部分的贡献。例如，一篇论文的主要内容是图论中的一个问题的解决方案，它出现在计算机科学中，并且其解决方案(可能)目前只对计算机科学家感兴趣，将在05C(图论)中进行初步分类。)68(计算机科学)中的一个或多个二级分类;相反，一篇总体内容主要在计算机科学中的论文应该在68中得到一个主要的分类，即使它大量使用图论并在此过程中证明了几个新的图论理论结果。
Theprincipal contribution is meant to be the one including the most important partof the work actually done in the item. For example, a paper whose main overallcontent is the solution of a problem in graph theory, which arose in computerscience and whose solution is (perhaps) at present only of interest to computerscientists, would have a primary classification in 05C (Graph Theory) with oneor more secondary classifications in 68 (Computer Science); conversely, a paperwhose overall content lies mainly in computer science should receive a primaryclassification in 68, even if it makes heavy use of graph theory and provesseveral new graph-theoretic results along the way.
在MSC的许多条目的末尾给出了两种类型的交叉引用。第一种类型是括号：“{For A，see X}”;如果这出现在Y部分，则意味着A描述的贡献通常应该被分配分类代码X，而不是Y.另一种类型的交叉引用仅指出相关的分类;它在括号中：“[另见…]”，“[主要参见…]”等，括号中列出的分类代码可以但不一定要包括在分类代码中可以使用它们来代替交叉引用的分类。分类器必须判断哪种分类最适合于手头的纸张。
Thereare two types of cross-references given at the end of many of the entries inthe MSC. The first type is in braces: “{For A, see X}“; if this appears insection Y, it means that contributions described by A should usually beassigned the classification code X, not Y. The other type of cross-referencemerely points out related classifications; it is in brackets: “[See also…]”, “[See mainly …]", etc., and the classification codes listed inthe brackets may, but need not, be included in the classification codes of apaper, or they may be used in place of the classification where thecross-reference is given. The classifier must judge which classification is themost appropriate for the paper at hand.
- 美国数学会(AMS)的MSC2020分类
MSC2020
公布修订数学科目分类的计划
数学评论(MR)和zbMATH合作维护数学学科分类(MSC)，这些评论服务，出版商和其他人使用MSC对数学科学文献中的项目进行分类。当前版本MSC2010由63个区域组成，分为两个数字，分为5000多个三位和五位分类。有关MSC2010的详细信息，请访问www.msc2010.org或www.ams.org/msc/msc2010.html和zbmath.org/classification/。
MSC2020
Announcementof the plan to revise the Mathematics Subject Classification
MathematicalReviews (MR) and zbMATH cooperate in maintaining the Mathematics Subject Classification(MSC), which is used by these reviewing services, publishers, and others tocategorize items in the mathematical sciences literature. The current version,MSC2010, consists of 63 areas classified with two digits refined into over 5000three- and five-digit classifications. Details of MSC2010 can be found at www.msc2010.orgor www.ams.org/msc/msc2010.htmland zbmath.org/classification/.
MSC2010是对zbMATH编辑和MR的编辑共同努力开发的2000年主题分类方案的修订版，得到了社区的大量投入。zbMATH和MR已启动修订MSC2010的过程，期望从2020年开始使用该版本。从MR和zbMATH的角度来看，五位数分类方案MSC是一个非常重要的设备，允许编辑和审阅者处理文献。zbMATH和MR的出版物的用户使用MSC按主题区域搜索文献。自上次修订以来的十年中，关键字搜索变得越来越普遍，可搜索数据库得到了显着改进。然而，分类方案仍然很重要。许多出版商在提交文章时，作为对编辑的帮助，或在出版时使用主题类，作为对读者的帮助。arXiv使用作者提供的MSC代码对提交进行分类，并作为为每日列表创建警报的选项。使用两位或三位数分类搜索浏览MR或zbMATH数据库是跟上特定领域研究的有效方法。
MSC2010was a revision of the 2000 subject classification scheme developed through thecollaborative efforts of the editors of zbMATH and MR with considerable inputfrom the community. zbMATH and MR have initiated the process of revisingMSC2010 with an expectation that the revision will be used beginning in 2020.From the perspective of MR and zbMATH, the five-digit classification scheme MSCis an extremely important device that allows editors and reviewers to processthe literature. Users of the publications of zbMATH and MR employ the MSC tosearch the literature by subject area. In the decade since the last revision,keyword searching has become increasingly prevalent, with remarkableimprovements in searchable databases. Yet, the classification scheme remainsimportant. Many publishers use the subject classes at either the time ofsubmission of an article, as an aid to the editors, or at the time ofpublication, as an aid to readers. The arXiv uses author-supplied MSC codes toclassify submissions, and as an option in creating alerts for the dailylistings. Browsing the MR or zbMATH database using a two- or three-digitclassification search is an effective method of keeping up with research inspecific areas.
部分基于社区成员的一些深思熟虑的建议，MR和zbMATH的编辑初步考虑了MSC的修订范围。我们预计不会有两位数的变化;但是，预计将会改进三位和五位数级别。
Basedin part on some thoughtful suggestions from members of the community, theeditors of MR and zbMATH have given preliminary consideration to the scope ofthe revision of the MSC. We do not foresee any changes at the two-digit level;however, it is anticipated that there will be refinement of the three- and five-digitlevels.
此时，zbMATH和MR欢迎其他社区输入进入该流程。应通过在msc2020.org创建帐户，通过网络提交评论。您可以点击此处创建一个帐户。要联系编辑，或者如果您不能使用网络界面，您可以发送电子邮件至[email protected]。有关MSC修订的所有信息由MR和zbMATH共同共享。随着流程的推进，这一输入将具有重要价值。
At thispoint, zbMATH and MR welcome additional community input into the process.Comments should be submitted through the Web by creating an account atmsc2020.org. You may create an account by clicking here. Tocontact the editors or if you cannot use the web interface, you may send emailto [email protected]. All information about the MSC revision is jointlyshared by MR and zbMATH. This input will be of great value as the process movesforward.
Edward Dunne，数学评论执行编辑
Klaus Hulek，ZbMATH主编
EdwardDunne, Executive Editor, Mathematical Reviews
KlausHulek, Editor-in-Chief, zbMATH
(注：所引相关素材[1-7]图文版权归原作者所有。)
素材(1.2k字)
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