How to Reference a Long Breakdown of a Mathematical Model from Another Thesis?

Question

I am writing my Master's thesis, and I need to describe and break down a complex mathematical (physics-based) model. This model is absolutely central to my thesis, and all of my work essentially revolves around it. I was about 5% done the task of understanding and summarizing the model when I came across a previously written Master's thesis that used the exact same model in the exact same manner as me, and includes an incredibly detailed, yet concise step-by-step breakdown of it. It is all that author's original work.

The breakdown of the model in this previously written thesis is approximately 20 pages long, far too long for me to quote it, even in part. There's really no way for me to interpret or explain this model other than the way this author has described it. This author was pretty clearly a genius... I feel like any information I add will be superfluous; while at the same time if I were to remove or greatly modify any of the information it would be extremely detrimental to my thesis as a whole.

I feel completely stuck. This breakdown of the model is going to account for around 1/5 of the total length of my thesis, so even if I were to be able to get permission from the author/publisher to copy the information, I'd essentially be taking 20% of my thesis directly from another source. That just doesn't feel right to me.

What should I do? I'm a mere 2 months away from my defence deadline (long story short I was forced to start this new thesis topic with less than a year left in grad school, so I'm extremely far behind where I wanted to be) and this model breakdown is the only thing I have left to finish before sending in my thesis for editing.

I'm quite literally pulling my hair out over this. Any help would be appreciated.

Answer 1

It sounds to me like your thesis just got about 15% shorter.

Rather than developing the material yourself, you need to instead put a review of the key results of the prior work as they relate to the rest of your thesis. Presumably you needed to do this analysis because you were going to put its results to use elsewhere. Well, you no longer need to do the analysis. Instead, you can cite the other paper and explicitly say that you're going to review the key results that your work builds upon, e.g.,

A detailed analysis of the X algorithm has already been conducted in [cite]. Further parts of this thesis build upon some of the results of that analysis, which we summarize here for the convenience of the reader.

Then you put in your paraphrased summary of the results you will use and the important intuitions with respect to the rest of your work. You almost certainly do not need a reader to be familiar with every detail of the other proofs. Likely some of their lemmas/sub-results don't need to be stated and there may be side-results / corollaries that are irrelevant to your use of the materials as well. As such, your summary should be able to be much more terse than the original, and can be completely in your own words. Renumbering and re-organizing material is OK as well. You also don't need to put citations in everywhere continuously: as long as you write the prose in your own words and make it clear up front that everything in that collection of material is a summary of the material you are citing, the attribution should be quite clear to a reader.