Generally, problems and equations are considered fact, and would not be protected, although related text can be. Also, mathematicians have been correcting and nitpicking each other's work for centuries.
Altering a copyrighted painting to teach a technique is still copyright infringement as that falls under derivative works.
The reproduction or use of someone else's copyright material without permission or license.Copyright infringement is the unauthorized or prohibited use of works under copyright, infringing the copyright holder's exclusive rights, such as the right to reproduce or perform the copyrighted work, or to make derivative works.
From the US Copyright Office FAQ...."As a general matter, copyright infringement occurs when a copyrighted work is reproduced, distributed, performed, publicly displayed, or made into a derivative work without the permission of the copyright owner."
Yes; it would be considered creating a derivative work, which is one of the exclusive rights of the copyright holder.
You are guilty of copyright infringement and in most cases it is considered a felony if you use it improperly. And they determine whether or not you used it improperly.
Infringement is the use, without permission, of copyrighted material that does not fall under a "fair use" or other exception to copyright law,
The Digital Theft Deterrence and Copyright Damages Act
Since it is copyrighted, you would need to obtain written permission.
Copyright infringement, a civil offense.
No. Unless a "fair use" exception applies use of someone elses copyrighted property without permisson is the definition of copyright infringement.
Using Bittorrent is considered illegal by the US Government because of copyright infringement. It is seen as a hyperlink. For this reason some Bittorrent files are considered illegal by the US Government.
Yes, although if your song follows the storyline of the book too closely, it might be considered a derivative work, which would require a license.