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Science and Technology Resources on the Internet

Mathematics Resources on the Internet

Beth A. Roberts
Agricultural Sciences Librarian
University of Maryland Libraries
er100@umail.umd.edu

Scope

This webliography focuses on pure mathematics resources (e.g., algebra, logic, geometry, and analysis) and related subjects such as computer science. It includes electronic databases, WWW gateways, and online mathematical reference sources. This selective webliography focuses on free quality online materials where possible. The primary purpose of this webliography is to assist librarians and researchers with the task of picking quality sites when bombarded with hundreds of sites listed by gateways and in results from search engine queries. I have included older as well as more recent material because mathematicians and mathematics researchers often use older material.

Methods

The resources in this web bibliography were chosen for inclusion based on their relevancy to the intended audience, their authority, usefulness, clarity and ease of use. The intended audience for this resource is primarily graduate students and librarians. I chose many of the resources by looking through gateway sites like the WWW Virtual Library for Mathematics, Academic Info, Argus Clearinghouse, Galaxy, the Open Directory Project and the Internet Public Library mathematics section and then picking the most relevant and useful of those.

Rationale

Mathematics is an area that is often overlooked, looked at only within the context of computer science, or lumped in with general science and technology collections. Mathematicians work as engineers or computer scientists and often use mathematical resources in their work. Because of this, mathematics resources are used by more than just mathematics professors and students. Essentially, "The work of mathematicians falls into two broad classes -- theoretical (pure) mathematics and applied mathematics. These classes, however, are not sharply defined, and often overlap...Theoretical mathematicians advance mathematical knowledge by developing new principles and recognizing previously unknown relationships between existing principles of mathematics...Applied mathematicians, on the other hand, use theories and techniques, such as mathematical modeling and computational methods, to formulate and solve practical problems in business, government, engineering, and in the physical, life, and social sciences" (Bureau of Labor Statistics 2002).

Online Indexes

There are several online indexes to the mathematics literature. The following selection of indexes is not comprehensive but rather a listing of resources that have an especially useful component for researchers in mathematics. Some other databases researchers might want to use for a comprehensive search, especially for applied mathematics topics, include Current Contents, Science Citation Index, Compendex, Web of Science, INSPEC, and Dissertation Abstracts.

Jahrbuch Database
http://www.emis.de/MATH/JFM/JFM.html: This project is from the European Mathematical Society and provides access to articles from the years 1868-1942. It is a database based on the Jahrbuch über die Fortschritte der Mathematik. This database has free citations and some abstracts and contains what the creators of the database describe as "some of the most important mathematical publications of the period" between 1868-1942. There is a limit of three free searches for unregistered users.
MathSciNet
{http://www.ams.org/mathscinet/}: MathSciNet indexes the mathematical literature from 1940 to the present. It provides access to the reviews and bibliographic data from Mathematical Reviews and Current Mathematical Publications. The database has some helpful searching features available such as both full search and a basic search. MathSciNet has the full text of many items but not all. The database will link you to the full text if available on the web. However, you must be a subscriber to access the full text. This database has signed reviews of articles, and contains conference proceedings and books. "MathSciNet is a unique database of a scholarly nature of more utility to faculty and graduate students than to undergraduate students. It has an excellent coverage of current mathematics literature providing signed reviews of math articles, conference proceedings and books of mathematics research" (Dominy and Bhatt 2001).
MATHDI, Mathematics Didactics Database
http://www.emis.de/MATH/DI.html: This web version of the European Mathematical Society's International Reviews on Mathematics Education indexes the mathematics and computer science education journal literature from 1976-present. There is a limit of three free searches allowed for unregistered users.
Zentralblatt MATH
{http://www.zentralblatt-math.org/zmath/en/}: This web version of Zentralblatt Math indexes articles from 1931-present and has full-text reviews from 1985 forward. Zentralblatt indexes articles 3,000 periodicals. There is a list of periodicals covered by the database at {http://www.zentralblatt-math.org/zmath/en/journals/}. There is a limit of three free searches allowed for unregistered users.

Preprint and E-print Servers

Preprints, unpublished articles often referred to now as e-prints, are quite popular with mathematicians for their research. They are useful for those looking to see what the most current research is, or who want to disseminate their research quickly and easily. The articles are free to post and read, but have not been evaluated for quality.

Directory of Mathematics Preprint and e-Print Servers
{http://www.ams.org/global-preprints/}: This is a directory of preprint servers from the American Mathematical Society (AMS). It lists umbrella servers, special subject servers, institute and department servers, as well as retired preprint servers. "The servers are divided into three categories: umbrella servers, which cover all areas of mathematics--such as the mathematics section of the Los Alamos (Ginsparg) e-Print Archive and the MPRESS/MathNet preprints server, special subject servers, and servers administered by mathematics departments and institutes. There is an additional link to retired preprint services" (McMahon 2000).
ArXiv.org e-Print Archive [Mathematics Section]
http://arxiv.org/archive/math: The original preprint archive, long affiliated with the Los Alamos National laboratory; arXiv.org is a "fully automated electronic archive and distribution server for research papers." Currently, mathematics e-prints are available for 1991 to present. Some of the subject areas covered include: algebraic geometry, logic, probability theory, and spectral theory. For the year 2002 alone they already have over 1,200 new articles in their archive. You can browse the articles by author, title, or subject area, or by year. It is also fully searchable.
Mathematics Preprint Server
{http://www.mathpreprints.com/math/Preprint/show/}: This is a preprint server managed by Elsevier. This server allows readers to rank and discuss articles. In order to submit preprints one must register, but searching and browsing is allowed without registration. There are approximately 550 articles on the server.
MPRESS: Mathematics Preprint Search System
{http://MathNet.preprints.org/}: This is an index to preprints and not a full-text archive. It allows both searching and browsing by subject area. It is supported by the Math-Net Project (1997 - 1999) "and was started under the auspices of the European Mathematical Society."

Reference Sources

Following are some selected online reference sources.

Bibliographies

Bibliography of Collected Works and Correspondence of Mathematicians

http://www.math.cornell.edu/~library/collectedwks.html

This bibliography was put together by Steven W. Rockey, mathematics librarian at Cornell University. "The scope includes the collected works and correspondence of mathematicians that were published as monographs and made available for sale. It does not include binders collections, reprint collections or manuscript collections that were put together by individuals, departments or libraries."

Bibliography for Computational Probability and Statistics Resources

{http://home.ubalt.edu/ntsbarsh/statistics/REFSTAT.HTM}

Dr. Hossein Arsham, the Wright Distinguished Research Professor in Decision Science and Statistics at the University of Baltimore compiled this bibliography. The site lists books (print), journal web sites, publishers, societies, and organizations in the areas related to computational probability and statistics.

Also compiled by the same professor are the following bibliographies:

Bibliography for Discrete Event Systems Simulation Resources
{http://home.ubalt.edu/ntsbarsh/ref/RefSim.htm}
Bibliography for Optimization with Sensitivity Analysis Resources
{http://home.ubalt.edu/ntsbarsh/refop/Refop.htm}

Math WWW Virtual Library - Bibliographies

{http://www.math.fsu.edu/Virtual/index.php}

This is a list of bibliographies online maintained by the Florida State University Department of Mathematics. The information is categorized by subject. It includes a list of 19 bibliographies such as a bibliography of Bernoulli numbers.

Biographical Resources

Indexes of Biographies
http://www-groups.dcs.st-andrews.ac.uk/~history/BiogIndex.html: This site is hosted by the School of Mathematics and Statistics at the University of Saint Andrews in Scotland. It is an index of biographies of famous mathematicians. There are presently 1,554 biographies on the site. They are written by two professors at the school, Edmund F. Robertson and John O'Connor. It has biographies on hundreds of mathematicians going back as far as 1680 BC and up to the present day. Some articles on the individuals contain scanned graphics, and they also contain links to more information. The articles include references and sometimes photographs of the mathematicians and are roughly one to two pages in length. One feature that is useful is term hyperlinking. Mathematical terms such as "hyperbola" are linked to definitions. This site is part of the MacTutor History of Mathematics and has won many awards such as 1998 Britannica's Best of the Web award.
Women Mathematicians
http://www.agnesscott.edu/lriddle/women/women.htm: This site contains biographies of famous women mathematicians. "These pages are part of an on-going project by students in mathematics classes at Agnes Scott College, in Atlanta, Georgia, to illustrate the numerous achievements of women in the field of mathematics. There are biographical essays or comments on most of the women mathematicians and some photos." There are over 100 entries. The entries contain references to further information on the mathematicians.
History of Mathematics Links: Sites Relating to Individual Mathematicians
http://www.maths.tcd.ie/pub/HistMath/Links/People.html: This site contains links to sites on specific mathematicians, including such historically significant individuals like Archimedes, and more modern thinkers like Paul Erdös and Robert P. Langlands. The University of Dublin Trinity College hosts the site. There are currently over 70 links.
Mathematicians of the Seventeenth and Eighteenth Centuries
http://www.maths.tcd.ie/pub/HistMath/People/RBallHist.html: "Available here are accounts of the lives and works of seventeenth and eighteenth century mathematicians (and some other scientists), adapted from A Short Account of the History of Mathematics by W. W. Rouse Ball (4th Edition 1908). The ordering of the mathematicians and scientists is approximately chronological. A separate index is provided which lists these people in alphabetical order." There are over 80 entries on this site. Each description is roughly one to two pages in length. There are no additional references or links.

Calculation and Conversion

Martindale's Reference Desk: The Reference Desk: Calculators Online-Mathematics
{http://www.martindalecenter.com/Calculators.html}: This site contains numerous mathematical calculators. It starts with basic math calculators for finding percentages, fractions, etc., and then continues with complex, specific calculators such as those for finding solutions to quadratic equations, and slope field calculators. It is hosted on the University of California, Irvine Science Library's server.
A Dictionary of Measures, Units and Conversions
http://www.ex.ac.uk/cimt/dictunit/dictunit.htm: "This provides a summary of most of the units of measurement to be found in use around the World today (and a few of historical interest), together with the appropriate conversion factors needed to change them into a 'standard' unit of the S I."
Favorite Mathematical Constants
{http://algo.inria.fr/bsolve/}: Constants are listed by associated topic, such as constants associated with number theory. The constants are arranged by topic, such as geometry, "Constants associated with number theory" or, "Constants associated with Analytic Inequalities." There is also a table to aid in locating the constant of interest. The site contains roughly 130 constants.

Dictionaries

Dictionary of Algorithms and Data Structures
http://www.nist.gov/dads/: "This is a dictionary of algorithms, algorithmic techniques, data structures, archetypal problems, and related definitions." The National Institute of Standards and Technology hosts the site. "Some entries have links to further information and implementations". There is an alphabetical index on the main page as well as a search function. Paul Black, computer scientist at NIST, created the page. References on algorithms and data structures are included.

Encyclopedias

Eric Weisstein's World of Mathematics
http://mathworld.wolfram.com/: This contains a well-organized encyclopedia of mathematics. It also has interactive elements such as animated graphics and hyper linked terms, which link to definitions. It contains references at the end of each description as well as hyperlinks to related terms. Eric Weisstein, Internet encyclopedist employed by Wolfram Research, created this resource.
On-line Encyclopedia of Integer Sequences
{https://oeis.org/}: This site identifies integer sequences. "Type in a series of numbers and the database will complete the sequence and provide the name of the sequence, along with its mathematical formula, examples of its classificatory structure, references, and links. Also available in French" (Sonnier 2001).
Mathematical Atlas: A Gateway to Modern Mathematics
{http://www.math.niu.edu/Papers/Rusin/known-math/welcome.html}: This site was created and is managed by Dave Rusin, Associate Professor of Mathematics at Northern Illinois University. It "is a collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information." The material is arranged in a hierarchy of disciplines, each with its own index page ("blue pages"). Dave Rusin originally collected these articles for his own use from various sources and is now making them publicly available on the web. The articles vary in length but are usually substantial, often running roughly three to five pages.

Quotations

Mathematical Quotations Server
http://math.furman.edu/~mwoodard/mquot.html: You can search by keyword or browse for quotations of interest. The browse feature allows browsing by last name of the individual the quote is attributed to. In addition, you can download the entire collection. The site also has a random quote generator. This site is from Furman University.

Historical

Cornell Digital Library Math Collection
{http://historical.library.cornell.edu/math/}: This site has 577 scanned historical books available from the collections of the Cornell University Library. The books are out-of-print or out-of-copyright materials. The collection is indexed by title and by author. These books are part of the library's Digital Math Books Collection. "From 1990 through 1992 Cornell University and Xerox Corporation, with the support of the Commission on Preservation and Access, collaborated on a pilot project to test advanced technology for scanning deteriorating books as digital images, optical storage, and production of high quality paper copies." This is a project in which, "while 'saving' mathematics books from a brittle death, the Library becomes a publisher of out-of-print and out-of-copyright books" (Rockey 1992).
The History of Mathematics
http://www.maths.tcd.ie/pub/HistMath/HistMath.html: This site was created and is maintained by David Wilkins, lecturer in mathematics at Trinity College in Dublin. Some of the articles come from books and also have links to more biographical information on the web. It includes a section on mathematicians of the seventeenth and eighteenth centuries. The rest of the site is devoted to a few mathematicians, such as Sir William Rowan Hamilton and George Berkeley.
MacTutor History of Mathematics
http://www-groups.dcs.st-and.ac.uk/~history/: The School of Mathematics and Statistics host this site at the University of Saint Andrews in Scotland. The site was created and maintained by two professors at the school, Edmund F. Robertson and John O'Connor. There are a number of index pages, such as an index to topics page, an index to female mathematicians, and a quotations index.

Directories

These sites are gateways to collections of mathematics information resources.

Catalogue of Mathematics Internet Resources
{http://bubl.ac.uk/link/m/mathematicslinks.htm}: This web site is from BUBL Link. "BUBL LINK is the name of a catalogue of selected Internet resources covering all academic subject areas and catalogued according to DDC (Dewey Decimal Classification). All items are selected, evaluated, catalogued and described. Links are checked and fixed each month. LINK stands for Libraries of Networked Knowledge." The index to the resources in the mathematics and computing section are in alphabetical order, i.e., fractals, geometry.
Math Archives Topics in Mathematics
http://archives.math.utk.edu/topics/index.html: "The primary emphasis is on materials which are used in the teaching of mathematics. Currently the Archives are particularly strong in its collection of educational software. Other areas, ranging from laboratory notebooks and problem sets to lecture notes and reports on innovative methods, are growing." The resources in this guide are listed by topic. One particularly useful feature on this site is that each article or resource in a subject area is ranked according to level, such as UD for "Upper Division College" level resource or GP for "Graduate and Professional" level. In addition, under each resource heading the site lists the type of resource, such as lecture notes or book.
Mathematics Web Sites Around the World
{http://www.emis.de/PSU-mirror/MathLists/Contents.html}: Provides a search engine and browsing options to help locate mathematics-related web sites. The search engine is not very sophisticated, but the browsing by category is well organized into areas such as mathematics department web servers, mathematics journals, commercial pages, and more.
MathGuide
http://www.mathguide.de/: This is "an Internet-based subject gateway to scholarly relevant information in mathematics, located at the Lower Saxony State- and University Library, Göttingen (Germany). Resources are described and evaluated with a set of Dublin Core metadata." This site has a search engine with simple and advanced search options as well as a subject catalog and a source type catalog (divided by type such as factual reference books, primary sources, etc.). Clicking on a category heading will open a list of more specific category headings to help narrow your subject down. This site presently contains 1,109 records.
The World-Wide Web Virtual Library Mathematics
{http://www.math.fsu.edu/Virtual/index.php}: This site was compiled and is maintained by Florida State University Department of Mathematics as a gateway to mathematics information on the web. The categories include preprints, gophers, online books, and newsgroups.
The World-Wide Web Virtual Library: Statistics
http://www.stat.ufl.edu/vlib/statistics.html: The University of Florida Department of Statistics hosts this page, which is maintained by Mike Conlon, Assistant Vice President for Information Systems and Support, and Chief Information Officer University of Florida Health Science Center. The site contains extensive links to departmental web servers around the world.

Discussion Groups

Mathematics Archives- Electronic Newsgroups and Mailing Lists
http://archives.math.utk.edu/news.html: Directory of electronic newsgroups and e-mail lists on the net in alphabetical order. The University of Tennessee, Knoxville, hosts this site.

Societies

American Mathematical Society: Mathematics Research and Scholarship
http://www.ams.org/: This society was founded to promote mathematical research and scholarship and has members all over the world. The site has a link to the journals that it publishes and a journal article e-mail alert service (alerts you when new content is added to AMS journals). You can also search through the tables of contents and abstracts of their journals. The site also has a link to and information about their database, MathSciNet.
American Statistical Association
http://www.amstat.org/: This society was founded in 1839. It aims to promote statistics "across the wealth of human endeavor." This site has a statistics career center with job listings as well as information on careers for statisticians. Information is also included on meetings and workshops of the ASA and other statistical organizations. There is also a link to government resources such as "Government policies affecting statistics."
Association for Women in Mathematics
http://www.awm-math.org/: This association encourages girls and women in the mathematical sciences. The association has a mentoring network, which matches up mentors and those seeking mentors. There is also a career section with links to articles, employment resources and more information. In addition there is a section with biographies of women mathematicians.
The EMS Homepage: The European Mathematical Information Service
http://www.emis.de/: This site offers access to full-text articles published by the European Mathematical Society. Some of the journals are free to access. It also includes links to projects the EMS is involved, such as the Jahrbuch project. This site is also the host for the Zentralblatt Math database.
IMA: About Us
{http://www.ima.org.uk/about_us.cfm.html}: This site is from the Institute of Mathematics and its Applications (IMA). This UK-based organization was founded in 1964 and aims to promote mathematics in "industry, business, the public sector, education and research." The site lists conferences in mathematics, publications from the society, interest groups, and career information.
Mathematical Association of America: MAA Online
http://www.maa.org/: This association is "devoted to the interests of collegiate mathematics," in particular, the teaching of collegiate mathematics. MAA Online contains articles of interest to mathematicians, book reviews, and information on professional development.
Mathematical Sciences Research Institute
http://www.msri.org/: The Institute aims to further mathematical research and also offers a variety of research programs, workshops and other events. Primary funding for this institute comes from the NSF. The site contains a calendar of events, publications, and a library of books, videos, and journals.
SLA: PAM Division Web Resources
{http://pam.sla.org/subjects/}: PAM is a division of the Special Libraries Association and is geared toward librarians working in physics, astronomy, and mathematics. The division facilitates communication amongst members and others working in these fields. PAM has an online bulletin, a discussion list, and conferences. PAM maintains a list of electronic resources in mathematics on their {web site}. The list includes people, professional societies, preprints, and pathfinders.
Society for Industrial and Applied Mathematics [SIAM]
http://www.siam.org/: It is the policy of SIAM to work to "advance the application of mathematics and computational science to science, engineering, industry, and society;" promote research and provide a way for members to exchange ideas. There is a link to SIAM journals online, books, conferences, and news.

References

U.S. Bureau of Labor Statistics. 2002-2003 Edition. Occupational Outlook Handbook [Online] Available: {https://www.bls.gov/ooh/} [May 1, 2002].

Dominy, Margaret and Bhatt, Jay. 2001. MathSciNet: mathematical reviews on the web, a review. Issues in Science & Technology Librarianship. 31: Summer. [Online]. Available: http://www.istl.org/01-summer/databases2.html [May 1, 2002].

McMahon, Timothy E. 2000. This science isn't just for mathematicians anymore: mathematics resources on the Internet. College & Research Libraries News. 61(5). [Online] Available: {http://www.ala.org/ala/mgrps/divs/acrl/publications/crlnews/2000/may/scienceisntjust.cfm}.

Rockey, Steven. 1992. ARL, the newsletter of the Association of Research Libraries. 161: 11.

Sonnier, Elizabeth. 2001-2002. On-Line Encyclopedia of Integer Sequences. Librarians Index to the Internet [Online] Available: {http://lii.org/search/file/math} [May 1, 2002].

Contents

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Issues in Science and Technology Librarianship		Summer 2002
DOI:10.5062/F4X34VF6