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I am an incoming math PhD student in the US. I am thinking of starting a math blog. The intended audience is myself plus maybe other math graduate students.

I am a little concerned about citations to avoid plagiarism. Of course if a theorem or proof comes from a paper, I need to cite it. What about theorems and proofs coming from textbooks. For example, say I give a definition of a group, which appears in virtually all standard textbooks in introductory algebra.

I guess the latter case will happen more frequently since my blog is mostly entry level graduate material math that you can find in many textbooks.

Questions:

  1. If a theorem or proof comes from a textbook, can I assume that it is considered common knowledge, with respect to the targeted audience, and just state and prove the theorem?

  2. At what point does a theorem or proof stop becoming common knowledge, maybe it only appears in some very advanced textbooks?

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    Book, like a journal article, is in general a publication. Haven't you seen books cited in papers? If you take an exposition from a particular book, you just cite it. – user68958 Apr 17 '18 at 14:16
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    A proof could be common knowledge, but there are still better and worse ways to explain it, and the textbook author put work into that exposition. Even if it's a theorem known to high schoolers, it's still best practice to say "this proof appears in, for example, [citation]." – user37208 Apr 17 '18 at 14:41
  • Some textbooks avoid citations on the basis that they get in the way. Some of those textbooks include endnotes. Others avoid references completely. (Presumably references do appear in the author's notes.) Pick the style that suits you, make the style clear to the reader. (If you write your blog in html, then you can use html comments to include citations and other notes, you can advertise them to the reader, if you like.) – user2768 Apr 17 '18 at 15:19
  • Can you clarify the purpose of the blog? – aparente001 Apr 19 '18 at 2:39
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Blog posts don't need to have a formal bibliography, but you should always provide attribution to others work, whether it is an original piece of research, or just a textbook whose presentation you are following. In a blog post, you can do this in a conversational style: point out results you enjoyed (with links!) and textbooks you find helpful. Not only will the folks you mention appreciate this, it will be helpful to your readers who want to follow up and learn more.

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The citations may not have to be quite as formal, either. If you know you have favorite textbooks you cite all the time, you could have as part of the footer:

Common References:

JKL: Jennings, Klondike, and Lawrence. (2018). Best Textbook Ever. Unicorn Press. ...

Then you can say at the top of a post: Most of the definitions in this post are based on JLK and XYZ.

If formally dealing with citations is going to hold you back from getting the blog posts written, then doing something like this can help you properly attribute.

(There may be a different kind of copyright problem if you basically reproduce all of the useful parts of the textbook on your blog, even if the content is paraphrased and attributed.)

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