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If I take a math textbook and transcribe some of its text to obtain a pdf copy, is this copyright infringement? Would I be able to show my transcribed pdf copy to other people or post it online?

Actually when I read a book I create a pdf document that has notes on what I read. The first step is usually to transcribe the text. Afterwards I will modify the text to aid my understanding of the content. I will then use the pdf document as a reference so that I don't have to rely on the book itself. It is easier to recall and remember what I read by reading the notes than reading the original book. I'm essentially replacing the book with my new version. I was wondering if sharing the notes with someone would be problematic.

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Such transcription is making a copy without permission. It could, therefore, constitute copyright infringement. If you had simply saved your own notes on the content to a PDF, and those notes did not contain any of the original content there would not be any infringement.

However, such a copy, made purely for personal study, would probably fall under fair use (in the US) or fair dealing (in the UK and other commonwealth countries). It might fall under one of the exceptions similar to fair dealing that the Berne Convention allows countries to include in their laws, and that many countries have included.

But once a person starts distributing such a copy to others, the fair use or fair dealing claim becomes weaker. Publishing it, including via the internet, would make such claims weaker yet. Whether they would be upheld in such a situation depends on the detailed facts of the case, and the view of the particular court.

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It is actually illegal to copy any portion of a copyrighted work without the express permission of the copyright holder. It is even illegal if you are not being paid for the copy(ies). Under no circumstances are you to copy it - unless you contact the holder of the rights and receive written permission. Then, keep that written permission so that when you are accused of plagiarism or copyright infringement, you will be able to provide proof of your permission to use that print. As with most rules, there are exceptions: The Fair Use Act, a legal doctrine which provides a limited use of copyrighted material without permission from the rights holders. For example, for commentary, criticism, news reporting, research, teaching, or scholarship. During my years in universities, I used parts of copyrighted materials as quotes in essays and other written documents written by me - and they were cited properly. To use that information and not cite it properly will lead to expulsion from school, or a huge accusation of plagiarism. Please take note, however - Fair Use is NOT a blanket exemption to copyright law, the rules must be followed. For more information and details on which details apply to your situation, see the resources below. Resource(s): Section 107, Copyright Act, 37 C.F.R. 201.2 (a)(3) (2010). What faculty need to know about copyright for teaching. American University, Library. . Retrieved May 15, 2021, from https://www.american.edu/library/documents/upload/copyright_for_teaching.pdf

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    This has several minor but significant errors. Copyright infringement is not "illegal" (except in cases of bulk commercial infringement), rather it is a tort, which gives the holder grounds for a lawsui if the holder chooses to sue. Copyright transfers must be in writing, and signed, but licenses can be oral. Writing is usually a good idea. Plagiarism isnot a legal concept, but is vital in an academic or journalistic context. I don't know of any "fair use act"; fair use is covered by 17 USC 107, which was part of the Copyright ACT OF 1976. This answer better if divided into paragraphs.
    – David Siegel
    May 15, 2021 at 20:31

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