As a math undergrad, your experience with math literature has been largely limited to textbooks, math websites, and perhaps some scholarly sources searched and selected for you by professors. Working more independently on your own research projects, the following responsibilities and decisions rest with you.
One of the challenges you face is doing research in light of the fact that most of the research literature out there is not written for undergraduates. So in addition to evaluating the credibility of sources, you also need to evaluate the degree to which you are prepared or can prepare yourself to understand and use a source.
When searching and selecting information sources, consider the following in your evaluations.
|Considerations||Questions to Ask||Answer Examples|
|Prerequisites||Who is the intended audience?||Researchers? General public? Graduate students?|
|What do readers need to know, learn, or review to make use of this work?||Advanced algebra? Recursion theory? Fluid mechanics?|
|Rigor||How rigorous is this work intended to be?||Extremely? Not rigorous at all?|
|How was this work reviewed and published?||Self-reviewed and self-published? Society publication?|
|Who was likely involved in the writing, review, and publishing of this work?||Author only? Author and editor? Author, editor, and peer-reviewers?|
|What are the credentials of those involved?||PhD in mathematics? High school math teacher?|
|Objectives||What is the intended purpose of this work?||Entertain? Teach? Explain complex concepts to non-experts? Share the findings of a research study?|
|How might this work's intended purpose affect (1) how you use this work in your research and (2) your search for information?|
f(x) = y
How does this work relate to the other information sources you've selected for your research?
NOTE: Information sources (variables) that you plug into your research (function) must change and adapt to complement other information sources used in your research.
|How does your research relate to, or build upon, the information sources you've selected (bibliography)?|
Just as mathematical proofs argue mathematical statements, researchers must be ready to argue and defend their use of particular information sources.
To evaluate sources, it helps to know what kind of information source you're looking at. Talk with your advisor about the types of sources you should seek and avoid.
Scholarly articles -- sometimes called research articles, primary research articles, original research articles, peer-reviewed articles, and refereed articles -- are written by and for experts to publish the latest original research. Scholarly articles undergo a peer-review editorial process and are published in scholarly journals. To conduct, understand, and build off research rigorous enough to undergo peer-review, these experts have years of education (Ph.D.s) and experience under their belts. One way to gauge the "readability" of a scholarly article to to learn more about the journal itself. For example, the AMS journal overview for Representation Theory states that it aims for high quality exposition. Bear in mind that you may also come across scholarly books.
Popular news publications like Time magazine and the New York Times publish short articles typically written by journalists for the general public. Popular books, like Abbott's Flatland, are written for readers interested in math, and could be written by math professors (e.g., Ian Stewart's Cows in the Maze). These accessible texts may help you comprehend the more scholarly texts.
Trade magazines, sometimes called trade journals, serve as a kind of middle ground between popular publications and scholarly journals. Articles are written to inform and address issues facing trade professionals such as math teachers and professors, math researchers and statisticians. They do not include original research, lack the rigor associated with scholarly articles, and are written in a more accessible to its readers.
Since books take a long time to get made they are not the best places to find breaking developments in a field. Yet their ability to examine a topic within the context of related topics can benefit you as a researcher. A book's preface will sometimes outline the background necessary to read and understand the book or chapters within it. Book reviews mentioned in this guide also offer help in this area. Science encyclopedias, dictionaries, and textbooks, all written for non-experts, can be great complements to understanding more rigorous texts.
Conference proceedings are the written versions of research shared at conferences. Experts present their research, and learn from each other at these conferences. Presentation proposals and their proceedings may undergo the peer-review process.
Dissertations and theses are extensive research projects undertaken while working toward a master's or Ph.D. Although thorough reviews are done by an advisory committee, dissertations and theses do not undergo a formal peer-review process. Although dissertatons and theses may be excellent sources of information, only a few print copies exist and libraries are unlikely to lend them out. They are best obtained through online repositories or directly from the researchers themselves.