I need to include some basic definitions, and simple proofs from a standard text book to my thesis. Those definitions and proofs are very basic, e.g. probability, entropy etc. Everybody knows they should be in some text books.

Consider, for example, this proof from wiki. My questions are:

  • Is this plagiarism if I bring this whole proof word by word into my thesis?
  • If this is plagiarism, what is the method to "paraphrase" a proof? Since the derivation is straightforward, and it is very difficult to write it in a different way?

Thank you.

  • 2
    If your thesis is about information theory or statistics, the proof you show can be omitted. I would recommend simply citing some "bible of your field" which contains all these basic stuff. That's the way most people do it. Or they don't cite anything at all.
    – yo'
    Commented Feb 9, 2015 at 0:13
  • @yo' my thesis is in Software Security, and many great researchers I met forgot those definitions long long time ago.
    – sean
    Commented Feb 9, 2015 at 0:23
  • 1
    Cannot just cite formally or informally the source?
    – Greg
    Commented Feb 9, 2015 at 7:28

2 Answers 2


It is very common for theses in the mathematical sciences to spend a significant amount of time and space repeating known or even standard definitions and results. (In fact, up through the master's level, at least in many places one can write a perfectly acceptable thesis that only does this.) In fact this is generally viewed as a positive feature of the thesis: the candidate has taken the time and effort to synthesize a presentation which is complete and self-contained up to a certain point. It is also generally very helpful to do so in terms of readability: a math paper that repeated nothing that was already known would be well-nigh impenetrable except (perhaps) by a select coterie of insiders.

Also the virtue of rewording is not as strong in this area. If you are going to give the definition of, say, entropy, in a thesis, then I would say the best thing to do is to close all your textbooks and write down what you think is a good wording of the definition. Once you've done that you check back with the sources to see that you've actually gotten the definition right, i.e., that it is mathematically equivalent to the one from the textbooks. But if your language is similar or identical to what you found in the textbooks: okay, fine. You don't need to change it for that purpose. There are a lot of ways to list the axioms for a group, and if you wanted to you could pull out fifty textbooks and make sure that your wording is different from all fifty of them. But this would be a big waste of time: it is not necessary to do so, and what do you bet that these fifty wordings capture most of those that are best in terms of efficiency, readability, and so forth?

When it comes to copying entire proofs word for word, I would pay close attention to how often you are doing this. If you are simply copying multiple pages of proofs verbatim out of a single standard source, then you should start wondering about the value added in doing so (and, after a certain point, issues of copyright do emerge). There is a key word that I used in the first paragraph: synthesis. When you revisit old results, ideally you are synthesizing them: i.e., no one source has everything that you want, so you are combining multiple sources in a novel way. Too much copying and too little synthesizing does not necessarily put you at risk for plagiarism and copyright violation -- it would have to be quite extreme for that to be an issue -- but it does not sound like the path to a strong thesis.

I hope that everyone who is writing an academic thesis has a thesis advisor. You should talk to her about this issue. To a certain degree, the right answer is what she thinks is best.

  • 5
    And don't forget to cite and say you are copying verbatim! Otherwise it is most certainly plagiarism!
    – jakebeal
    Commented Feb 9, 2015 at 1:21
  • 1
    @jakebeal: Indeed. Commented Feb 9, 2015 at 1:30

In questions of potential plagiarism, you can think about whether a reader will get the impression some work is yours. If they will, and it's not, you've got a problem.

To apply this: I found I could "follow" the approach in a major text, abbreviating some sections of a derivation and expanding on others (mainly due to where in the text concepts were introduced). Partly as I was using a numeric citation style, a simple citation wasn't enough. If you put the derivation/proof in its own subsection and say "following the approach given by Smith in reference 42 it is clear that..." or something like that. A verbatim copy will often be unhelpful to the reader anyway - imagine reading "using the result given on page 393" in a 3-page paper (absurd, but you need to integrate the cross-referenced material, not just paste it in).

(This was going to be a comment as I can't add much to Pete L. Clark's answer, but I did want to make a couple of points that wouldn't fit.)

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