I have a question about publication copyright rules. Is it rightful to write a new book that contains some parts of another book but with different notation and different examples? I mean the content is same but it's briefed and notation and questions are changed, and this book is rewritten for a special exam. Thank you so much.
You don't provide enough information to give a complete answer. However, generally, it is not permitted to copy any portion of a previously published work without the copyright owner's express permission.
No - "pure" copying is not allowed. Quoting someone, with attribution, is okay. Making new examples is okay if they are truly new - otherwise, merely changing minor details from another is not.
That is a tough question because how you characterize what you have done and what i may characterize it - could be drastically different. But that aside, let me say that you need only copy a few paragraphs from a 500 page book to infringe its copyright.
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