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Hi all, I am currently in my last year of undergrad doing a dissertation relating to measure theoretic probability theory and am quite lost as to what should I include.  I have an outline and that’s fine but how does one make it an interesting read.

My supervisor has said now that I have all the maths essentially done, it is now a communications exercise.  But I do not know how to make it engaging to a reader.  I am super excited about it but there is so much theory dumping to be done before I get to the cool new stuff.  The main theorem I am proving requires several chapter of work because I am to assume that the person reading is any mathematician or computer scientist so it is a broad audience.  So I need to build up measure theory in an interesting way but also quickly and thoroughly.

Any advice?
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Write it first, think about how to make it stand out second. You just have to be very explicit about what you do, and what is required for the things you do. At the same time, even for a 'broad' audience, it is probably expected that the reader is not completely blind on the topic. You can start laying everything out as concisely as possible and expand on things as it becomes clear (either from your own reading or your supervisors) that further explanation is needed.
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Not to be cliche but... What do you find interesting about it? I've written a decent amount of abstracts and introductions but most of my math communication skills are from teaching, and being constantly reminded of how little some of my audience knows, constantly tasked with explanation and reexplanation. The exercise of simplifying language for a broader audience is one thing, but making it interesting is another. I don't know much but I know there's no way to make something interesting to an audience when I don't find it interesting myself.
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Most important parts are the intro and conclusion. In them write what is the point of the thesis and why it is important. Then in the end reinforce that that is ehat you did. Rest is pretty much up to the language used in the thesis.
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I’d suggest to write it like an intro to your past self — what would you need to get from where you were to where you are? :)

And don’t worry about writing style, that’ll come out in the editing process. Trimming explanations is easier than adding new ones, imo :D
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I would maybe think a bit more about the audience that is actually going to read your thesis. When I wrote mine, I also wanted to write my thesis for a broad audience, but only a hand few of people actually read it. My thesis ended up fairly long (a bit over 40 pages I think), and the actual interesting part was perhaps a bit too small. This made it kind of a tough read. People that don't know much about measure theoretic probability will likely have a hard time understanding your thesis, as they will not have time to get used to all the new concepts and definitions. Maybe talk to your advisor about how much you should really cover.

Of course I do not know what you actually have done, and perhaps it can be a good choice to write for a broad audience. There is also nothing wrong with attempting to write for a broad audience, but scrapping some stuff because it takes up too much space.
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Harsh reality is that most theses are never read by anyone other than the writer and hopefully the committee. Write it so that you are able to follow the concepts from start to finish so that if you ever go back to it, you can pick it up pretty easily.
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There’s no good writing, there’s only good rewriting.
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