The University of Hawaii Student Conduct Code defines plagiarism this way:
Being found guilty of plagiarism can result in your dismissal from the university. Get into the habit of citing your sources. It is a good ethical practice, and provides you with a way of collecting resources that you can consult in the future.
You are probably familiar with APA, MLA, and Chicago styles of citations for research papers. For mathematics papers there is no standard citation style, but a good one to learn is the one used by the American Mathematical Society.
Ask your advisor or professor about the citation style they prefer. Regardless of the style, apply it consistently throughout your paper and make sure to proofread it the same way you would proofread the rest of your paper.
Citing the work that supports your research is both an ethical issue and a legal issue.
The ethics of citing is based on the scholarly tradition of giving credit for information and ideas that are not one's own. Science has a long tradition of acknowledging priority through citations. You have the ethical responsibility to cite all works that were used to support your research, to give credit to the earlier work and to provide a clear path for those who follow in your footsteps.
As so eloquently expressed by Isaac Newton in a letter to Robert Hooke in 1675 (Merton 1965):
If I have seen further it is by standing on ye sholders of Giants.
The legal issues of citing one's sources are codified in Copyrights, Title 17 of the U.S. Code, which describes the legal protections of authors' and creators' intellectual property rights.
[Merton, RK. 2006. On the shoulders of giants: a Shandean postscript. New York: The Free Press. p. 31]
American Society for Horticultural Science (ASHS) Style Manual
PDF file of the Manual
Examples from the Manual:
Hartmann, H.T., D.E. Kester, and F.T. Davies, Jr. 1990. Plant propagation principles
and practices. 5th ed. Prentice Hall, Englewood Cliffs, N.J.
Brown, A.G. 1995. Apples, p. 3–37. In: J. Janick and J.N. Moore (eds.). Advances
in fruit breeding. Purdue Univ. Press, West Lafayette, Ind.
Goldberg, D., B. Cornat, and Y. Bar. 1991. The distribution of roots, water, and
minerals as a result of trickle irrigation. J. Amer. Soc. Hort. Sci. 96:645–648.
Locascio, S.J., J.G.A. Fiskell, and P.E. Everett. 2000. Advances in watermelon
fertility. Proc. Trop. Reg. Amer. Soc. Hort. Sci. 14:223–231.
Endnote is an application that imports citations from your searches in web databases and helps you organize your references. It works with Microsoft Word helping you create in-text citations, footnotes, and bibliographies.
EndNote Basic (formerly EndNote Web) is an online program that helps you organize references and create properly formatted bibliographies. This is a separate program from the desktop version of EndNote. It is a free version of EndNote available for institutions which subscribe to ISI Databases, like Web of Science.
Mendeley allows you to share references with others or to maintain a private library. Mendeley collections can be exported to Endnote, CiteULike, or Zotero libraries. Mendeley works with Word 2008 and OpenOffice to insert citations into your documents. It enables you to extract citation information from downloaded pdfs.
Zotero is a plug-in from Mozilla that you use with the Firefox browser. Simply download the plug-in, activate the Zotero application by clicking on the Zotero icon in your browser. You can now capture citations into a library held on your hard drive or on a flash drive. Zotero works with Word and OpenOffice after you have downloaded the plug-ins.