copyright & mathematics textbooks

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  • I am working with a math faculty member who is writing a textbook for an upper level undergraduate math course, (and wants to put a CC license on it for all to use as an OER :)
    We have questions about what constitutes copyright infringement and/or plagiarism in the world of mathematics.  For example:
    • If the order in which concepts are presented is similar or identical to the way another author has done so in another textbook, is this a copyright violation?
    • What about stating theorems?  There can be subtly different ways of stating multi-line theorems; how much difference is required to avoid copyright infringement?  Or is this possibly an example of the merger doctrine, and might the expression of a theorem not be copyrightable at all?
    • What about exercises and examples?  In mathematics, there are some problems that all students should have to work through and some examples that all students should be exposed to.  Is it copyright infringement to use similar or identical exercises as another textbook?
    If you have any insight on this front or if you are aware of any guidelines we could consult, I'd love to hear from you.  I have a document of examples of the kinds of similarities of theorems, exercises and examples that we are uncertain about.  If you have experience with this sort of thing and would be willing to look at them and offer an opinion we would both be grateful.


    Christin Wixson 

    Scholarly Communication Librarian
    Plymouth State University
  • From the copyright office: Copyright law does not protect ideas, methods, or systems. Copyright protection is therefore not available for ideas or procedures for doing, making, or building things; scientific or technical methods or discoveries; business operations or procedures; mathematical principles; formulas or algorithms; or any other concept, process, or method of operation. 

    Unless the order is highly creative for some reason, I don't believe it would fall under copyright. This is not something I have a lot of experience with, but I believe that word problems may fall under copyright, but problems containing only numbers and symbols probably do not. 

  • I agree with Lori.  The copyright is thin.  I think you might be correct that this is an example of the merger doctrine in that there are only a few ways to state the theorem so they are not copyrightable.

    The order of the concepts are laid out in the book are not copyrightable.

    I would tell the faculty member to move forward based on your understanding of these copyright concepts, but you are not providing legal advice.

    Good luck!



  • Hi.  I am not a copyright expert, merely a math teacher fascinated by the copyright subject.  Nevertheless, here is my amateur opinion:

    1.  A theorem is a fact, not subject to copyright.  The proof is also a fact.

    2.  A generic example, such as find the solutions to x2 + 2x + 1 = 0 is also a fact.

    3. A more unique example may be copyrightable.  Here is an attempt at a unique example:  "A student states as a statistical hypothesis that the heights of US presidents are significantly larger than the heights of US born male adults on average.  The average height of US born male adults is x.  The heights of US Presidents since Eisenhower are {Eisenhower = h1. Kennedy = h2, ..., }.  Use this data to test this hypothesis statistically."  Do you agree this example may be copyrightable?

    4.  A textbook may state on the back of the cover page something like "Permission must be obtained from the publisher prior to any reproduction ...", suggesting that the teacher may not even write textbook example 1 on the blackboard.  My understanding is that this textbook statement is more of a request than a contract, since I never accepted it.  Do you agree?

    5.  I believe the teacher writing textbook example 1 on the blackboard easily passes Fair Use in non-profit education, and is a slightly harder fair use sell in for-profit education.  Do you agree?


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