How are textbooks meant to be referenced?

Question

I'm studying maths, and I've found it beneficial to write my notes as if I were writing a textbook for someone else's self study - forces me to understand the material to some extent.

It's of course incredibly unlikely these notes could actually be made into a textbook, but hypothetically, if I decided in some distant future to attempt to publish a textbook on maths, what are the rules for referencing?

Is it acceptable to source material almost solely from other textbooks, and simply place in the references at the back the names of those text books, or...?

Exercises. If I borrow exercises from other textbooks which look challenging (not every exercise) then how required am I to reference the book I found the exercise in? Even if I do reference, is there any issue that could stem from using those exercises? I've seen Wilson's theorem used as an exercise for almost every abstract algebra book I've read.

Answer 1

I strongly disagree with Dirk. You should not "always strive to keep the number of such references in a textbook as small as possible."

Also, I would say that this: "Also keep the number of different books to which you refer as small as possible." is very poor advice. It is a disservice to your readers, and wholly unnecessary.

Instead, you should have extensive references in a textbook whenever you draw on other materials. This is a matter of intellectual honesty and to provide your readers (and their teachers/advisers) links to source material. If your content or results come from other sources, including from textbooks, you should make explicit references to them.

Exercises are only in "the public domain" if they are from sources whose copyrights have expired or are from authors who have explicitly made them public domain, or variant thereof.

It may be advisable to have a section of your textbook that minimizes references -- mainly to improve readability. If so, then you'd be advised to have a parallel section titled "Sources and Further Reading" where you recapitulate the content in the main section and include all references.

Dirk says that textbooks are to be "as self-contained as possible. Hence, there are few references." This is poor advice since it confuses readability with completeness and usability. To omit references when you have copied or otherwise drawn material from other sources is both incomplete and disreputable. It harms usability because some students and many teachers will want access to the original books and papers.

Answer 2

Textbooks seldomly state original results and it is generally assumed that the author of the textbook is not the inventor of the results. So your conception that there are different rules for references for textbooks is right. Since textbooks are for students who are usually not used to look up references one aims to make textbooks as self-contained as possible. Hence, there are few references. Mostly, references point to previous textbooks (references given in the introduction, appendix or "Further reading" sections). In fact, a lot of references go into sections like "Further reading" or "Historical remarks". Sometimes you may want to give a reference for a specific result which could be contained in the book but is not for some reason. I would always strive to keep the number of such references in a textbook as small as possible. Also keep the number of different books to which you refer as small as possible. Referencing to original results is mostly omitted but you should always state names with theorems, i.e. you could write "Theorem (Taylor): ...", "Theorem (Green/Tao): ...", of course use "Banach's Fixed Point Theorem" or write "Mean Value Theorem (Cauchy): ..."

Regarding exercises: If you know a true reference for an exercise you could give it like "Exercise (Erdős): ...". Otherwise, I think that exercises are considered to be "in the public domain" (not taken as a legal claim) and can be reused without reference (but correct me, if I'm wrong).