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Resources in mathematics.

Mathematics Subject Classification (MSC)

Mathematical Subject Classifications (MSC) are categories created to classify mathematics by the mathematical databases MathSciNet and zbMATH. MSC is made up of codes for 63 different major mathematical disciplines, with multiple levels allowing for even more precision. MSC classifications are five characters long. The first two characters are numbers representing an article's major mathematical discipline. The third character is a letter describing the article's sub-discipline. The final characters are numbers representing the specific focus of the article. For example an an article which was assigned 11D07 would be in Number Theory (11) with focus on Diophantine Equations (D), specifically The Frobenius problem (07). All articles and books indexed in MathSciNet are provided MSC values, more than one if needed, by subject area experts when added to the database. MSC is updated every 10 years to stay on top of changes and trends in mathematics. zbMath provides a browseable page of MSC values for free if you want to dig deeper into the classifications.

About MathSciNet

MathSciNet from the American Mathematical Society is the leading mathematics indexing and abstracting database. It provide abstracts from more than 3100 mathematical journals and many thousands of books, conference proceedings, theses, and technical reports indexes. MathSciNet goes beyond simple bibliographic information, it also incorporates the content of the American Mathematical Society's Mathematical Reviews. These article reviews are written by experts in the article's mathematical content and exist for a significant percentage of the papers in the database, including many from as far back as 1940s.

How to Search MathSciNet

Searching MathSciNet is very similar to using advanced searches in library catalogs or databases. It provides users the ability to search publications, authors, journals, or citations. What sets       MathSciNet's search apart from many other databases, is its unique identification of authors and articles, and its use of the MSC (mathematical subject classification) system.

Screenshot of the front page of MathSciNet with a search bar in the middle, with search tab Publication Highlighted and Authors, Journals, Series, and Search MSC not highlighted

Upon visiting MathSciNet you will be presented with a search bar. If you know the name of an author or an article title you can start typing it into the search bar, but if you are doing a wider search you will have to use field codes.Screenshot of MathSciNet Standard Field Codes: any: anywhere, au: author name, inst: institution name, j: journal name, mr: MR Number, pc: MSC Primary, pcsc: MSC Primary or Secondary, pt: Publication Type, r: Review, rs: Review Status, ti:title, y: Publication Year

For example if you wanted to know what articles Fan Chung wrote about linear algebra and its connections to graph theory then I would use the query: 

au:"Chung Fan" AND pcsc:"05C50" 

Where au:"" is the author field, and when I start typing in Fan Chung's name it provides me with a drop down of author names and I chose Chung Fan.

search bar with au:"fan" typed in and a drop down with Chung Fan, Fan Jishan, Fan Jianqing, Fan Hong Yi, Fan Kai Tai, Wheeler Mary Fannett, Wang Wei Fan, Chan Tony Fan-Cheong, Fangui, and Fan Dashan as options

Then I type AND followed by pcsc:"05C50" to search the Mathematics Subject Classification Primary and Secondary for the subject Graphs and linear algebra. This is the results:

MathSciNet search for au:"Chung Fan" AND pcsc:"05C50" with the top 3 of 48 results shown

Do not worry about having to remember a bunch of field names, clicking on Show All Fields and then clicking on the field you want it will auto-populate in the search bar. You can also click the Show Classic Interface link which brings up a traditional advanced search with drop down menus for field searching.

If you think you will need to do the same search regularly, MathSciNet allows you to Pin any search. Just click on Search History, choose the search you want, and click the Pin button on the right hand side.

MathSciNet Search Interface with the Search History expanded and recent searches selected showing a search for au:"Chung Fan" AND pcsc:"05C50" with the options to Pin or Edit on the right

MathSciNet has also made major progress in solving a major problem in database searching: telling author's with the same name apart from one another. MathSciNet accomplishes this by assigning unique identification numbers to each author. You can search for a specific author by clicking the Author tab on the MathSciNet home page and then use their name or their ID number (if known).

MathSciNet search interface with the Authors option chosen and a search bar with Fan Chung in it with a drop down reading Chung Fan and Chung Ching-Fan

Clicking on an author's name elsewhere in the database will also bring you to their MathSciNet profile. If you are the author of a mathematics paper indexed in MathSciNet, you will also have an author profile which you can log into and add a photo too or otherwise edit.

MathSciNet Author Profile Page for Fan Chung, featuring a black and white picture of her and some data like her author id, publication, and citations.

The Journals tab provides the ability to search for publications by name or ISSN.

MathSciNet Search interface with the Journals option chosen and Michigan in the search bar with a drop down that reads Michigan Mathematical Journal ISSN:0026-2285

The results link to a journal profiles with information about the publisher, previous journal names, dates of publication, and how it is indexed in MathSciNet. You will also find links to issues and articles, citation data, and RSS feeds you can subscribe to which will alert you when MathSciNet adds new articles from the journal.

MathSciNet Journal Page for the Michigan Mathematical Journal featuring links to the recently indexed issues and data about the journal like title, publisher, years of publication,and website

Finding Connections in MathSciNet

MathSciNet also offers a set of unique tools you can use to explore the connections between the authors in the database.

MathSciNet Free Tools page with Collaboration distance chose and Fan Chung and Maryam Mirzakhani as the two mathematicians. The result below is MR Collaboration Distance 3 Chung, Fan coauthored with Alon, Noga and Alon, Noga coauthored with Vondrák, Jan and Vondrák, Jan1 coauthored with Mirzakhani, Maryam

The first tool, available through MathSciNet's free tools and is called collaboration distance. Enter the name of any two mathematicians and the database will find the shortest distance, measure by co-authored papers, between them. 

You can also explore connections through an author's MathSciNet profile page.

Co-Authors box from Fan Chung's Profile page. It says she has 136 Coauthors with Ronald Lewis Graham 96 Collaborations, Linyuan Lu with 23, Shing-Tung Yau with 15, Paul Erdos with 14, and Arnold L Rosenberg listed and Show More and Show All buttons below

All you have to do is click on co-authors. Then you can sort the list of all of the mathematician's co-authors by name, publication count, citation count, or earliest publication.

Mathematics Genealogy Project Page for Fan-Rong King Chung Graham, listing her PhD from University of Pennsylvania in 1974 Dissertation: Ramsey Numbers in Multi-Colors and combinatorial designs Advisor: Herbert Saul Wilf and four of her students Aksoy, Sinan University of California, San Diego 2017 Andersen, Reid University of California, San Diego 2007 Butler, Steve University of California, San Diego 2008 Cooper, Joshua University of California, San Diego 2003

In many cases the profile page also provides a link to an author's mathematical genealogy from the Mathematical Genealogy Project. From there you can explore student advisor connections of over 200,000 mathematicians, with information often going back centuries.