Mathematical Writing - Vivaldi Franco 2014

Citations and Bibliography - Avoiding Plagiarism
Writing a Thesis

Scholarly writing invariably requires reference to other sources. This is carried out in two stages. First, the source is mentioned in the text in an abbreviated manner. Second, a full ordered list of all cited sources (books, journal papers, web pages, etc.) is presented at the end of the document, in a section headed ’Bibliography’ or ’References’.

There are some conventions for structuring citations and for writing the bibliography. We begin with a passage involving references to books.

We briefly review some properties of -adic numbers, introduced by Hensel in 1908 [18]. Background material may be found in Gouvea’s (2000) [14]; the arithmetical side of the theory is developed in Hasse (1980) [17, Chap. 7].

Each item enclosed in square brackets is a citation, which refers to a bibliographical entry. Citations should not intrude upon the text, and a sentence in which all citations have been removed should still read well. The citations [14] and [18] refer to books as a whole, whereas [17] refers to a specific chapter in a book. The targeted item within a book may also be a theorem [15, theorem 191], a page [15, p. 156], a range of pages ([15, pp. 156—158], [15, 156ff]²), etc. The bibliographical data corresponding to the text above are organised as follows:

[14] F.Q. Gouvêa, -adic Numbers, Springer-Verlag, Berlin (2000).

[17] H. Hasse, Number Theory, Springer-Verlag, Berlin (1980).

[18] K. Hensel, Theorie der Algebraischen Zhalen, Teubner, Leipzig and Berlin (1908).

The entries are usually ordered alphabetically by the author’s surname. Each item contains the following information: label, author(s), title, publisher, publisher’s home town, year of publication. In our case the labels are numbers (there are other possibilities, see below), and the book’s title is typeset in italic font. In [17] the publisher is ’Springer-Verlag’, located in Berlin. As the publishing industry becomes global, the publisher’s address is becoming increasingly irrelevant and publishers with multiple addresses are commonplace. The book identifier International Standard Book Number (ISBN), often given, is helpful for searches in libraries, catalogues, and databases.

There are other ways to cite books, as in the following shorter variant of our paragraph.

We briefly review some properties of -adic numbers, introduced in [18]. Background material may be found in [14]: the arithmetical side of the theory is developed in [17, Chap. 7].

To simplify the citations we have removed the author’s name and the year of publication from the text. However, reading has become more laborious because the reference number conveys no information about the source. The following labelling method offers a compromise, providing essential information in abbreviated form.

We briefly review some properties of -adic numbers, introduced in [Hen08]. Background material may be found in [Gou80]; the arithmetical side of the theory is developed in [Has80, Chap. 7].

Citations to journal papers follow the same rules given for books, although the bibliographical information is slightly different. Here is one example:

[32] P. Morton and J.H. Silverman, Periodic points, multiplicities, and dynamical units, J. Reine Angew. Math., 461 (1995) 81—122.

The data to be supplied comprises: label, author, title of paper, name of journal, volume number, year of publication, page numbers. The title is in Roman font, whereas the name of the journal appears in slanted font (a variant of italics), usually in a standard abbreviated form. Thus J. Reine Angew. Math. stands for Journal für die reine und angewandte Mathematik.³ The volume number is in boldface. Page numbers are normally given in full, but the style 361—7 (rather than 361—367) is allowed. As for books, there is an identifier for journals, called International Standard Serial Number (ISSN).

Other sources for citations are articles in electronic journals [10], articles in conference proceedings [33], books in collections [4], reprints of books [9], theses [3], etc. There are great variations in the style of a bibliography. The best thing is to look around for examples of bibliographical entries of the various types by different authors and publishers.

For unpublished documents on the web there is as yet no agreed format. The main information is the Uniform Resource Locator (URL), which identifies a web page uniquely, as in the following example:

[27] Text processing using LaTeX, Dept. of Engineering, University of Cambridge, http://www.eng.cam.ac.uk/help/tpl/textprocessing/ (January 2014).

This item is a collection of resources for electronic typesetting (see Sect. 10.5). The title is followed by the name of the institution providing the service and the URL, typeset in ’typewriter’ font. There is no reference to authors—too many to be listed here. A date is provided. Web pages don’t always carry dates (this one does), and even if they do, there is no way of deciding whether the displayed date corresponds to the last revision. The best one can do in this situation is to state when the web source was last accessed.

We present variants of bibliographical entries for web resources:

[8] P. Cvitanović, R. Artuso, R. Mainieri, G. Tanner, G. Vattay, Chaos: Classical and Quantum, chaosbook.org (Niels Bohr Institute, Copenhagen 2012).

[21] W. Jung, Core entropy and biaccessibility of quadratic polynomials, preprint (2014), arXiv:1401.4792v1, 46 pages.

Item [8] is a web-book, and the citation format adheres to the explicit instructions provided on the site. Instead of the URL there is a domain name registered in the Domain Name System (DNS), which provides a more intuitive identification of a web resource. Reference [8] has a large number of authors; to mention the authors in the text, an abbreviation is necessary: ’In Cvitanović et al. [8]...’.⁴ The web-book [8] has been available for several years, and it is gradually evolving; this document structure would impossible within the confines of traditional publishing.

The item [21] is an unpublished paper. It is stored in a large, open-access archive of preprints of scientific papers, called arXiv, supported by Cornell University Library. Each preprint in this archive has a unique 8-digit identifier, plus a version number (v1, in this example) which reflects the fact that papers may be updated. Most preprints in the arXiv will eventually become available in a more permanent form. So, when proof-reading bibliographical entries, one should check that the papers in the arXiv haven’t been published. Some editors accept only citations to permanent and accessible material.

A word of warning. When quoting from the web, be aware that there is a lot of rubbish there, and most web pages have no guarantee of correctness. Also keep in mind that anyone looking for basic information on a subject (e.g., abelian groups) can—without any assistance—type the relevant heading in a search engine and access the corresponding entry in Wikipedia. For this reason, citations to a main on-line encyclopaedia tend to be superfluous, and one should consider more substantial sources.

10.4.1 Avoiding Plagiarism

There is no copyright in mathematical ideas, the law of intellectual property being primarily commercial. But there is copyright in using other people’s words, pictures, and software. The act of publishing material produced by others as if it were your own is a serious academic offence, called plagiarism.

To respect copyright when using other people’s words one must name the author, cite the source, and make clear which are the quoted words (either by quotation marks or by display). For extensive use of someone else’s text (more than a paragraph, say), one must obtain the explicit permission of the copyright holder, and then insert a suitable remark in the acknowledgements section: ’I thank XXX for permission to quote YYY’.

The instant availability of free material on the web has increased considerably the risk of plagiarism caused by carelessness and naïvety rather than dishonesty. When cutting and pasting from other people’s text, it is essential to keep a record of the source. A text stored without a note of its source could easily be used as our own text at a later time. As articles, books, and theses are now submitted in electronic form, it is possible to detect this type of plagiarism using specialised software.