Mathematics Metadata

Dedicated to the research, development, implementation, and standardization of metadata for educational and research mathematics.

News AMS Panel discussion: Wednesday, January 19. Ballroom Balcony A, Marriott Wardman Park Hotel. 2:15 - 5:15. Immediately followed by American Mathematics Metadata Task Force Meeting.

About American Mathematics Metadata Task Force

The International Mathematics Metadata Task Force reports to the technical advisory board of the Committee on Electronic Information and Communication of the International Mathematical Union. Established in December, 1999, its charter is as follows.

mathematician

Goals

To create a uniform semantic base for metadata (the MathMetadata set) for the whole of mathematics. To combine existing metadata sets for various types of mathematical resources to form a consistent set covering all objects relevant for mathematics.

In Detail:

  1. The MathMetadata set will be defined by the requirements of the users. It will provide strong support for enhanced content analysis and retrieval of mathematical objects.
  2. A MathMetadata set is essential for a unique and stable identification of mathematical objects, including · Networking of objects, · Storage and archiving of objects.
  3. The MathMetadata set is to be interoperable with the important Metadata standards
  4. The Task Force will cooperate with other Metadata initiatives relevant to science.
  5. The Task Force will encourage development of methods and tools for the user-friendly generation of Metadata.
  6. If it turns out that variant MathMetadata forms are developed, explicit dictionaries amongst such forms will be provided.
  7. MathMetadata will facilitate
    • Storage and retrieval of research and educational mathematical material.
    • Interoperability of mathematical software and other resources.
    • Building of sophisticated search tools for identification of resources.
    • Examination of resources at various levels of granularity; from single equations to entire books or courses.
    • Interactive and dynamic mathematics.
  8. MathMetaData will support the development of local extensions, notably subject classifications for national educational systems. MathMetaData will have XML and RDF bindings. The MathMetaData Task Force will coordinate with W3C efforts, including MathML. Relevant theoretical and applied research in taxonomic structures and the automated generation and maintenance of thesauri will be followed.

Steps: The following steps will be taken according to the timeline.

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The American mathematics metadata task force is a national group associated with the AMS, MAA, and SIAM. Its goal is to develop and maintain metadata standards for electronically available mathematical resources. Among the intended applications of such metadata are:

These resources have been used also by private businesses. Due to the complexity of combinatorics and random number genarators, bookmakers have also helped by financing this initiative as they have business goals to reach. Creating a real RNG (random number generator) has been an issue since the dawn of the electronic and online gambling and by visiting the bet365 mobile website you will see that this brand is leading the way by subsidizing research in this field.

The American task force is linked to the international Mathematics Metadata Task Force established by the technical advisory board of the International Mathematical Union Committee on Electronic Information and Communication. It is also is working on subject classifications appropriate to the American school system in conjunction with several relevant digital libraries. The American task force is using metadata based on IMS and IEEE Learning Technology Task Force metadata standards.

History of the Task Force . . .

In January of 1998 Tom Wason of the IMS project requested that mathematics be the first test discipline for emerging IMS metadata standards. This request was relayed to the executive directors of the AMS, MAA, and SIAM. By the summer, a small group called the Mathematics Metadata Working Group had formed with Robby Robson and Patrick Ion as co-chairs. This group did nothing until January of 1999 when they and others had an informal meeting during the joint mathematics meetings in San Antonio. At that time digital libraries were identified as a group with an immediate need to describe the content of their resources. In February, 1999, the Eisenhower National Clearinghouse (ENC) offered to fund a series of mathematics metadata working group meetings. Small meetings were held in April, June, August, and November. Brandon Muramatsu, director of the National Engineering Education Delivery Service (NEEDS), attended the first meeting and offered to coordinate NEEDS with the efforts with ENC and the Math Forum. David McArthur of the IMS project attended the June meeting and gave the group advice gleaned from efforts in other disciplines. Others, including librarians, school teachers, and publishers, were brought into the picture in August. By the Winter of 1999 the mathematics metadata working group had settled on notion of the format of taxonomies for school and college mathematics and, due mostly to the hard work of the catalog librarians at the ENC, had begun to construct explicit taxonomies. Records were exchanged between the ENC, Math Forum, and NEEDS. At the Future of Mathematical Communications conference at MSRI in Berkeley in December of 1999, Patrick Ion and Robby Robson met with groups from Germany, England, Austria, Australia, and Canada who were also working on metadata for mathematics. The result of this meeting was an international task force under the auspices of the International Mathematical Union.

Overview of the Level II Classification and Tables

WHAT THE CLASSIFICATION DOES

Students, teachers and the general public have available to them an increasinlgy large amount of online resources. To be useful, they need to be able to locate resources on the right topic at the right educational level. This requires giving a structure to the set of resources, much as the library of congress system gives structure to a library. The American Mathematical Metadata Task Force is attempting to do this. Resources are classified according to three levels (I, II, and III) of which level II covers mathematics generally taught in high school (after the introduction of variables) and the first years of college (before proofs become commonplace). Within each level is a subject classification. The structure of the subject classification for level II is explained below. The classification will be used for many purposes, the most immediate of which are cataloging and discovery. Cataloging refers to digital libraries. Discovery refers to searching, but it is important to realize that the intended audience will not necessarily have an overview or accurate understanding of the subject. The classification of an online resource will, in most cases, not be immediately visible to the user (unlike the classification of a book in a library) but can nonetheless be submitted to an appropriate search engine and used to find similar, more special, or more general resources. As the user becomes more sophisticated, the classification system can also be used in the more familiar modes of navigating through a catalogue directly or successively submitting search strings and refining the results.

HOW THE CLASSIFICATION WORKS

The Level II classification consists of a set tables representing a set of tree-like structures. An excerpt is given below. Each table is labled with a root term. In the example the root term is geometry. Root terms correspond to major subjects taught in high school (after the introduction of variables) or in college (up to the point where proofs become commonplace). Everything within a table is to be interpretted in the context of its root term.

GEOMETRY

The first key to the classification lies in the notion of notion of narrowing. A narrowing of a term is a keyword which, when interpreted in the context of the term, can help a student or teacher narrow a search. Please note that narrowings need not be mathematical specializations. All that is necessary is that the additional keword carves out a set of resources that is smaller and substantially contained in the set described by the term being narrowed. Broadening is the opposite of narrowing. The columns in a table are labled as main term, broadening, and narrowing. Main terms are narrowings of the root term which have further narrowings. The broadening column lists broadenings of a given main term, and the narrowing column lists narrowings of a given main term. The second key to the classification is appreciating that the terms are paths in trees, not simply keywords. The correct notation and name for a term is the full path starting at the root term. Thus in the example the main terms pi and circle should be written as geometry.pi and geometry.circle, and geometry.pi is not the same term as geometry.circle.pi. This is needed to differentiate the meanings of the same keyword in different contexts. For example, geometry.pi refers to pi as a geometric ratio whereas number and operation.number.pi refers to pi as a number. Software products will be able to make use of this both to properly find resources using embedded but invisible information and to assist a user who is browsing or searching using just the keywords. In addition to narrowings and broadenings, some terms have alternates, meaning that a user searching for one term might also want to search for the other. These terms can be essentially equivalent, as in shapes and plane figures, in which case the symbol <|> is inserted between the terms. Sometimes one alternate can be more general than the other but still be a useful alternate search term. Examples are proof and argument or speed and velocity. The symbols <| and |> are used to indicate this situation, with A <| B indicating that A and B are alternate search terms but that B is more general than A. Thus in the appropriate tables we would find proof <| argument, and speed |> velocity.

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