: Handling Dependencies in Essays Suppose I'm writing an essay on topic A. My view on A, however, requires the reader to be familiar with certain aspects of other, perhaps seemingly unrelated,

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If those topics are necessary a-priori knowledge to understand your reasoning then you should expect your readers to know the basics.

If you can't expect them to know what you are talking about the following question arises: "Where do I start with the required pre-requisites?" You would have to ask yourself whether you can start with Graph Theory. But do your readers know what pairwise relationship are in a mathematical context? And for that matter, do your readers even know what numbers are? Or how to read?

Obviously this example is a hyperbole, but the reasoning is still valid. If you don't trust your reader to have the knowledge to understand your topic in the depth you are planning to use, how do you trust them to have the knowledge to have understand the basics of those basics? And the basics of those?

Answer: you can't. You have to define some amount of previous knowledge that is necessary for understanding your text.

You can include the most relevant parts as a kind of "refresher". Even if someone studied those topics there might be a few details they don't remember anymore and as long as you focus on the things that are absolutely necessary and expect your reader to have heard about it or to look it up on their own this is fine.

In regards to where and how you can introduce these bits of knowledge: you should do that whenever they become necessary. For example at the start of each section you are briefly talking about "stuff you need to know to understand the following paragraphs: a graph consists of vertices that are connected by edges. In this case the edges are undirected."

In any case: you should make sure that the prerequisites you are describing are:

absolutely necessary to understanding your following paragraph
common enough for your target audience to have heard about the topic at some point
uncommon enough that it's reasonable that your audience may have forgotten a lot of it or hasn't had a deep dive into the topic

It depends a lot on your target audience.

Are you writing for your peers that have a similar educational background, interests and probably knowledge of state-of-the-art techniques? In that case you may simply expect them to know the prerequisites. If they don't know them already they will probably not be interested enough in the topic to even read your essay.
Or are you combining different topics where people may know a lot about one half and next to nothing about the other? Then you need to explain the basics of each half, because you know that most people won't have all the knowledge and your goal is to give them some insights into how the other topic can help them with their work.
Or are you writing for an audience that hasn't heard anything about the topic at all, like someone writing a pop-science book for Joe Average that should give him just a basic idea of what you are doing? In that case you shouldn't care about details and explain everything in simple analogies.

Your description sounds like the second case, where you are writing about a technique that uses a mix of different topics from a wide range of fields. I would therefore recommend to start each section/chapter/... with a little description of the basics. Whenever you can you should try to make it an analogy that is suitable for the specific case you are talking about - your goal is not to teach anyone Graph Theory after all, your goal is to give them an idea of what Graph Theory is about so that they may understand what you are doing.

If your essay is good your readers will then go ahead and research the topics you mentioned briefly on their own. And as long as you point out that you are only trying to convey the rough concept nobody will say that you should have written longer about those tangential topics.

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