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Heyall, just asking a question out of curiousity.

I'm a mathematics undergraduate, who likes to write quite detailed notes from textbooks as a method of revising. These notes tend to follow roughly the structure of the textbook chapters - with the same definitions, theorems, etc - but often with differing proofs and exposition. I've been told by classmates that these notes are quite useful for them for revision.

Now, I have no intention of ever turning these notes into anything other than notes - I wasn't even sure about keeping them after the exams ended - but thinking about doing so raised questions for me.

When writing a textbook, what precisely constitutes plagiarism?

For example, in an Abstract Algebra textbook, there are only so many ways to cover group theory - as far as I can tell, the only major differences between how several books I've seen cover group theory is in the exposition and superficially in the proofs and definitions.

If a mathematician was annoyed that the only textbook in his/her subfield was notoriously low on detail, and wrote a book that was very similar - with the exception that it were an easier read - would that constitute plagiarism? (If so, that seems a bit restrictive to me.)

It cannot be that textbooks only contain original research, else few textbooks on undergraduate maths could've been written in the last one hundred years.

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    This is an interesting question and I hope it will get thoughtful answers. Just a quick note: building on someone else's work isn't plagiarism if you attribute the work that is not yours! – ff524 Aug 3 '16 at 17:08
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    @ff524 On what level? Specifically citing every theorem, or perhaps stating before a section 'This development of the predicate calculus largely stems from that in [1]'? – Nethesis Aug 3 '16 at 17:10
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    I'm not writing a full answer - just pointing out that you wrote "It cannot be that textbooks only contain original research". To avoid plagiarism, you don't have to only write original research - you can write about other people's work too, as long as you attribute. – ff524 Aug 3 '16 at 17:11
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It's the words. Speaking as a mathematician the formulas and calculations are all common knowledge, even if it's new to undergraduates. But the words you use to explain it need to be your own. The style you use will uniquely identify you. For examples check out Carl sagan's cosmos and Stephen Hawkins a brief history of time. Beautifully worded explanations of complex mathematics.

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When writing something which is aimed at becoming public, free or not, the rule is extremely simple: everything you have not created/discovered/written all by yourself has to be accompanied by a reference to the original work.

If you copied & pasted full sentences to your notes (which you could do at that time because your notes were private), you will have to either attribute them to their author(s) or rewrite them with your own words.

It is clear that the most difficult part will be to identify the sentences you have copied & pasted. IMHO, it would be easier to completely rewrite your notes while keeping the overall structure.

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    Except for well-known facts, written in the new author's own words. If I wrote a book on computer architecture, I could write an entire section on Karnaugh maps without a single attribution, provided all the words were completely my own. If I quote or paraphrase, say, Alan Clements, then citation is needed. – Bob Brown Aug 3 '16 at 20:22
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    But, again, on what level? Specifically citing every theorem, or perhaps stating before a section 'This development of the predicate calculus largely stems from that in [1]'? – Nethesis Aug 3 '16 at 20:34
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    Even well known facts have an origin. I reckon that you do not have to justify that earth is not flat or give a reference for Pythagore's theorem, but for anything which is not common knowledge, citation should be provided. – SteffX Aug 3 '16 at 21:14
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    @SteffX But what sorts of thing would constitute 'common knowledge' in an undergraduate text? – Nethesis Aug 4 '16 at 8:13
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    @Nethesis It is difficult to give a clear cut frame so let's say it is better to be overcautious. As it is intended for undergraduate students, everything learned before should be considered common knowledge because it is the base to understand your work. Also, many methods would be considered common knowledge. I am a chemist, so I am useless at maths but let's say that diagonalizing a matrix is common knowledge unless someone created a brand new method for that. To summarize, if you feel like 1 (or 2, or 3) person would need to be thanked, then you must cite the original paper. – SteffX Aug 5 '16 at 18:18

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