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In my background section, I have a subsection which explains ideas from research papers that my supervisor has previously published.

Basically in my thesis, I build upon these ideas and so I have a few pages in the background section which goes into the detail about the previous work.

At the start of the subsection I wrote "The following section provides a recap of the ideas that are presented in (citation)."

A lot of it I paraphrased, but some things including definitions and equations I want to copy word for word.

Is this allowed and if it what is the right way of going about it?

It is a good idea to cite the paper at the beginning of the subsection once or would I need to cite it multiple times?

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If you are paraphrasing everything then a single citation is enough, but provide a hint, at least, about where that section ends.

If you want to use direct quotes make it obvious that you are quoting using some textual hints (quote marks are only one way). It might be necessary to note that your quotes of definitions, etc, come from the original work.

It isn't hard to make sure that everything is correctly cited. What is hard is not making it look messy. If you can use foot/end notes then you can make citations less obvious, hiding the details in those notes.

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