How closely can I follow a cited mathematical derivation in my PhD dissertation?

Question

There is a well known result from 60 years ago that only ever has its result quoted these days. I found a 20+ year old MS thesis that had a very clear mathematical derivation of the result from first principles, although it doesn't have any (meaningful) citations.

The derivation is so clear I would like to include a detailed outline of it in my dissertation because I think it really illuminates why we do what we do in our lab, which is what the dissertation is centered around.

It it ok to put something like "Following the derivation of [MS source], first performed by [original source], we start with..." and walking through the 4-5 page derivation to get to the result? It's obviously not plagiarism, since it's well known and I am citing the source, but it isn't original work. On the other hand, something that was done decades ago would never be mistaken for original work in 2016, and I think it would really add to my motivation/background chapter.

Answer 1

The short answer is that you can indeed put properly cited, sourced, attributed background material in a background section. Because what is the background section for other than for you to present what people have done before you?

You obviously need to include enough of your own work in this document. However if a relevant derivation has been done before you cite it, possibly review it for the ease of the reader or completeness of your own expository structure and get on to the stuff you have done.

Answer 2

The appropriate wording for something like what you envision -- making clear that you are closely paraphrasing another publication -- would look like this:

Since the derivation of the result by [ABC, 1956] is not widely available in common textbooks, the remainder of this section closely follows the excellent outline provided previously in the MSc thesis by DEF, see [DEF, 1987]. In this thesis, the author shows that ...