How to write Master's thesis summary for PhD application

Question

I am currently applying for several PhD programs (in mathematics) and for many of them, it is required to write a short (approx. 2 pages; no more than 10.000 characters) summary of my Master's thesis. It should contain the motivations of the thesis and research, the methods used as well as the results obtained in my research.

Now, the application commitee is probably less interested in the precise topic of my research or in the project itself, but I guess that the aim of this writing in my application is more for them to examine my ability of writing and explaining my research to others, as the latter is one of the key abilities a scientist should probably have, in my opinion.

My questions are now the following:

(1) How detailed should such a writing be? In my specific case, I am appliying for a math PhD and many things which I did in my thesis, which lied in the border of math and physics, are very abstract, so it not always easy to explain them in simple, non-technical, terms (and I guess, this applies for most of the projects done in pure mathematics). So, should I aim in writing this text in a more "popular" science way, or should I "confront" them with full technical details (the middle way is, as written above, hardly possible, as the things are kind of abstract).

(2) Should I aim in writing this stuff more formally, or more from a personal point of view? So, should I, for example, write about my personal reasons for chosing this particular problem, or should I more concentrate on the scientific reasons of why this type of questions are interesting?

Answer 1

Note that your essay will be read by other mathematicians, but most of them won't be in your specialty. An overly detailed presentation, such as you might present to your advisor won't be the best.

You are probably correct that they are looking for a writing sample, so focus on the writing at least as much as the math.

A personal view of "why" you chose this path is probably not the right focus, though a sentence might be fine.

First, though, what is the most important result in your thesis? It might be a theorem, but it might also be an interesting (thought provoking) proof technique. Talk about that result primarily, and situate it within the mathematical literature. Talk about why it is an important result. If possible, talk about what it might lead to, though you may not yet be sophisticated enough to understand that.

If the work gave you any special "insights" into the wider world of your specialty (or math in general) include a few words about that. Is there follow up research that is indicated?

As to the level, think about how you would explain the thesis to a good upper level undergraduate class. I'm guessing that such a level might be the best, of course, but all of your readers (various mathematicians) would be able to understand it.

The details are in the thesis, of course, and the committee will probably have access to that as well, so a higher level (or lower level, if you like) presentation is probably enough.

Answer 2

Make it in 3 parts

1. Synopsis: This is what you have written at the start of your Master's thesis.
2. Brief description of your work: Describe what (and how) you did in your Master's project.
3. Results: What new goals you achieved in your work.

The whole language is slightly technical, without many complex formulas and equations.