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I am starting to design my personal website and I would like to devote part of the site to sharing knowledge in the fields of Mathematics and Computer Science.

My main concern is determining what is ethical to share and what isn't.

I don't plan on publishing solutions to homework exercises or questions from my previous exams, as this seems obvious to me.

What I would like to share is the content of the individual subjects such as:

  • Definitions
  • Theorems
  • Examples (Those of which I create myself)
  • References
  • My personal interpretation of the subject matter

My concern is in regards to sharing definitions and theorems is ensuring I am not plagiarizing works from textbooks and professor's lectures.

Since there is only but so many ways to rephrase a definition before it loses its meaning, how much should I change the representation of a definition (or Theorem) so I am not plagiarizing how it appears in particular text?

My final concern is in regard to reference other sources of knowledge. Throughout my college experience, I am constantly looking for multiple resources to supplement my learning. For example, YouTube video series X does a really good job with an introduction to Linear Algebra. Would it be ethical to reference or add links on my personal website to YouTube video series X?

  • "I don't plan on publishing solutions to homework exercises or questions from my previous exams, as this seems obvious to me." - I'm curious, can you clarify? This is not obvious to me. – Pedro A Mar 10 '18 at 11:36
  • @Hamsterrific I am guessing this is for courses the OP has taken as a student rather than is teaching. Most faculty I know don't want their old exams/homework solutions posted online. – Kimball Mar 10 '18 at 12:03
  • @Kimball Ohhh OP is the student, not the teacher, it's amazing how that didn't even cross my mind. Makes sense, thanks! – Pedro A Mar 10 '18 at 12:06
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You can avoid plagiarism the same way you would in a research paper: by citing your sources! So long as you’re not just quoting the same sources over and over again, you can quote a short excerpt from a relevant source and cite it. It’s also worth noting that definitions of common terms, as well as equations, are not normally subject to copyright, because of the exact reason you mention: there are only so many legitimate ways to define a term or write an equation, which places a constraint on expressing them without using someone else’s definition.

As far as links go, there’s no reason you can’t cite what you want.

  • You can avoid plagiarism the same way you would in a research paper: - I agree with this words, but for me the next natural ones would be: "write things in your own words." – Kimball Mar 10 '18 at 12:06
  • That works if it’s something other than stating definitions. There are only so many scientifically or mathematically accurate ways to define a term. At some point, every definition is a paraphrase of somebody else’s. – aeismail Mar 10 '18 at 16:39
  • My point is, even for definitions, there's a difference between copying and writing something on your own. There are lots of ways to phrase things, and I agree that two independent write-ups may have many phrases in common because of the issue you point out, but it's very unlikely that they will have long paragraphs in common if they are written independently. Anyway, I agree that depending on what exactly the OP is doing, it might be good to say something like, "these notes are based on course X by prof Y in spring 2018." – Kimball Mar 10 '18 at 18:21

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