I am writing my STEM thesis, 90% percent of which is about mathematical modeling. However, I am unsure at what level I should write for the introduction.
Should I write it so it is accessible for everyone? Or should I assume a high level of technical expertise?
Does anyone have experience in this matter?
Target anyone with an undergraduate degree in your field. Any more advanced and it becomes difficult for others to follow unless they are already specialists in your field. It does cost more space, which could be undesirable for research papers, but yours is a thesis - space is less important, and you could easily have readers who aren't specialists (I believe in many institutions one of the PhD examiners is intentionally chosen to be from another field).
My answer to this question is always:
What I mean is that you should write the thesis (especially the intro) in a way that if you would have read it when you started to work on the topic you would able to understand everything without additional sources.
This advice is close to "write it for a generic undergraduate" but I have the feeling that it helps to have a specific person in mind.
I think it is an opinion-based question.
In my school (community), we follow a top-down writing approach. We first, start with an outline which should be understandable by any reader and then, we break it into pieces. We follow the same approach with every piece and so on.
This writing approach makes readability easier for all readers. Some of them will understand up the deepest level in the structure and some of them a bit earlier.
I am currently (procrastinating about) writing my thesis. As I am almost finished, I speak only from the recent experience of a student on this question.
Should I write it so it is accessible for everyone?
Definitely do not try to do that. Humans have far too diverse of interests to try to get everyone into it. Even if you covered your subject from absolutely elementary principles, your thesis may also become far too long for even your committee members to read it. Try to remember to respect their time.
And I just hinted to you who the primary target audience is: your supervisor, the external examiner, and the other committee members. While you can aim to write with a little more breadth than this small group of people as your target audience, remember that they are the gatekeepers to completing your thesis. I recommend attempting to get early feedback from your committee members since they can, and in my experience do, share valuable information about what they are looking for.
Writing for your committee members does not mean taking the argument maximum of technical level at every part of the thesis. Among others, I have a mathematician and a biologist on my committee. They do not speak the same language, so where their interests meet (e.g. mathematical modelling of something in biology) I have made the language accessible to both of them. But someone who studies something very different, say 17th century poetry, might not follow the jargon or train of thought if they happened to pick up my thesis.
This advice should hold for most of the thesis, although it may be fine to make a particular point that perhaps only a single committee member will understand if it is going to be important to them. Beyond that, show your models and the story they have to tell.
When I want to learn something new, I often turn to PhD theses. Not all theses are equal, but some are very good to start with.
Very often, the introduction is quite naïve, in comparison to what a professor would write. Yet, I don't skip it. Every good thesis has the canonical references in the field cited there.
But, the most important part are the tools (experimental, and theoretical) that the student used for their work. In some theses, I can find a lot of details on how the results were obtained, and those details are often unavailable from other sources. There are also worked out examples, and results I could reproduce, that are described in detail in a PhD thesis.
As others mentioned, the best thing about a good thesis is that is accessible to people from somewhat different background than the author. In other words, a postdoc in Experimental Condensed Matter should be able to kick start his research in a field of Condensed Matter Theory, using a good thesis as a guide. With some more serious additional work and sources, a persistent postdoc should be able to learn a lot from a thesis in Quantum Optics.
In other words, the thesis should be aimed, in my opinion, at active researchers who want a quick and painless introduction to the author's field. The other category a thesis should be aimed at would be researchers who want to learn the methods and techniques used to obtained the results presented in it.
It really depends on the culture.
The introduction to my PhD thesis was
It was 1/3 of a page long.
My advisor was not thrilled (but we had a fantastic relationship, he knew that I was a bit "special" and finally was actually curious how this whole circus would unwind), and the reviewers were 50% "great" and 50% not thrilled. But they all conceded that it is a matter of taste and should not influence my thesis which was not about the history of physics either.
Reference: https://www.youtube.com/watch?v=hPUjtzS_zwY
Ask your advisor/supervisor.
It's a good question, but it should be answered really by your advisor/supervisor.
Every other answer here in my humble opinion is in effect speculating as to what the advisor/supervisor would say. Ultimately, mathematics doesn't exist in a vacuum. See Is a proof still valid if only the writer understands it? Any particular mathematical text always has a specific audience in mind. For example textbooks usually say at the start eg 'This is to introduce geometry for maths majors who have 1 course in point set topology but at the same time be not so highfalutin to be accessible to physics majors. This is not meant to be comprehensive or encyclopedic. This textbook introduces mainly only the minimum necessary in order to understand [big theorem X] and [big concept Y].'
