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Mathematics

This guide will help you navigate information sources in mathematics.

Sources of Information

Information comes from many sources including:

  • Journal articles
  • Magazine articles
  • Newspaper articles
  • Monographs (books)
  • Reference tools like dictionaries and encyclopedias
  • Technical reports
  • Conference proceedings
  • Conference posters
  • Preprints
  • Dissertations
  • Websites
  • Personal communication

These information sources differ in utility, content, intended audience, and authority -- among other things. However, there are only a couple of distinctions that are important to understand about information sources in science: scholarly vs. popular and primary vs. secondary.

What is Peer Review?

Depending on the policies of a particular scholarly journal, before an article is accepted for publication in that journal, it must undergo peer review. The editor of the journal will identify a few other scholars (peers) who have expertise on the subject that the article is about and send a copy of the article to those individuals. The peers will review the article for quality and rigor and give the editor their comments and recommendations. Depending on what the peers say, the editor may reject the article (if the peers found it to be substandard), or ask the author to revise and improve the article based on recommendations the peers provided. If the article needs revision then the author will make the necessary alterations and then resubmit the article. The article will usually be accepted for publication if the author makes all the required revisions.

What are Review Articles?

Review articles are a particular type of scholarly article that provide a systematic overview and analysis of the primary literature in a particular field. Review articles sum up the current state of research including the major advances and discoveries, ongoing debates, and where there are gaps in our knowledge that require more research. Because review articles discuss and cite the research articles that are advancing the field, you can quickly get an idea of who the major researchers are in that field.

Scholarly Sources vs. Popular Sources

CHARACTERISTICS OF SCHOLARLY SOURCES

  • The authors of scholarly books and journals usually have academic credentials and it is common for their academic affiliation to be provided on the publications they author.
  • Many scholarly articles are organized into formal categories such as: abstract, introduction, materials and methods, results, conclusion.
  • The writing style for both scholarly books and articles tends to be neutral and factual.
  • The audience is other researchers or students in the discipline, not the general reader; so, the writing is technical and uses specialized vocabulary.
  • The author will reference other scholarly sources to support his/her analysis and conclusions, and these citations will be provided in a bibliography at the end of the article or book.
  • Scholarly articles often report on findings that will advance that field of research -- that is, they are primary sources (see box below for more information).
  • To assure quality and accuracy, scholarly articles are usually peer-reviewed before being accepted for publication.
  • Scholarly books and journals are usually published by reputable and respected publishers.

In general, you can feel very confident about the quality and accuracy of information that you find in scholarly sources. However, scholarly sources can be challenging to use because the vocabulary and concepts are technical and specialized.

CHARACTERISTICS OF POPULAR SOURCES

  • The intent of popular writing is to impart information to general readers in a way that will be understandable.
  • The writing style is informal and uses vocabulary that is easily understood.
  • The credentials and qualifications of the author are usually not provided (the author may be a journalist or professional writer, but not have any particular academic expertise or affiliation).
  • Popular articles and books rarely reference other sources.
  • There is no peer review process, but there may be fact-checking.
  • Popular writing may be neutral, but may also be exaggerated and sensationalized (to sell copies or advertising space).
  • Popular writing may also be one-sided (to appeal to a particular audience).

It is not as easy to judge the quality and accuracy of information you find in popular sources (compared to scholarly sources). Your best bet is to stick with reputable, mainstream publications. Watch out for information that has been hyped or sensationalized.

Primary Sources vs. Secondary Sources

PRIMARY SOURCES

In science, primary sources are those documents that report on new scientific findings. When researchers discover something new, they usually write up their findings and publish them in the form of an article in a scholarly journal. The objective of such an article is to share the new findings with others and advance that field of research. Scientific articles that report on new findings contain a section on the materials and methods used in the research project so that others can replicate and/or verify the results. Most journals that publish articles like this have policies in place to send the article out to be peer-reviewed before it is formally accepted for publication. The way peer-review works is that the journal editor will identify a few experts (peers) in the field, send them the article, and ask them to review the article to ensure the research is rigorous.

Primary sources are not always journal articles. New scientific findings might also be presented in conference papers or posters, technical reports, or dissertations. These types of sources are often called gray literature because they fall outside the formal scholarly publication process. However, they may still describe original research (which makes them primary sources). Quality standards for gray literature may be less stringent (or non-existent) so you should exercise more caution when using these materials.

SECONDARY SOURCES

Secondary sources provide a simplification, summary, or analysis of information that was originally derived from primary sources. Most scholarly books do not report on new scientific findings, but instead provide context, analysis, and theory -- so they are secondary sources. Some other examples of secondary sources are student textbooks, encyclopedia entries, and articles in popular science books or magazines.

A very important secondary source to know about is the review article. (See box to the left for details.)