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Do you think it's appropriate to introduce notational aspects right after presenting the main topic in the introductory section of your thesis? Personally, I prefer not to include notations in an appendix.

Specifically, what are your thoughts on including very basic information such as notation for real numbers in the introduction? Additionally, do you think it's advisable to introduce the necessary notation for more complex objects in the advanced chapters, at the beginning of each chapter?

Furthermore, would you consider it redundant to explain the organization of each chapter again at the beginning, especially if it was already covered, to some extent, in the introductory part?

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    Have a look at other dissertations, long papers, short books, and so forth to figure out what you see as effective, courteous to the intended audience, and aesthetically acceptable to you. Mar 30 at 20:17
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    Which kind of thesis? Bachelor's? Master's? PhD? And most importantly: What does your advisor say regarding those topics? Mar 30 at 21:30
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    Yes, repeating yourself is redundant, but you should do it nonetheless, because it makes the reader's life easier. You are not writing for a robot with perfect memory who reads in a strictly linear fashion, who still remembers on p. 97 the remark you made on p. 13, and who does not understand normal human language and ordinary notational conventions but is a native speaker of first-order logic. You are writing for humans who will typically not read your thesis in a linear fashion and who do not have perfect memory, but who do not need to be explicitly told that e.g. R denotes the reals. Mar 30 at 23:20
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    In my experience from reading theses and other long documents, I don't think a list of notation at the start is helpful at all. I'm not going to read the list, and if I don't know what something means I'm more likely to skim upwards looking for a definition than scroll all the way to the top to look at the list. Including things like ℝ on the list makes it even less helpful, because it just makes it harder to find the things that aren't obvious. Instead, just introduce notation at the point where it's used, and make sure the definitions are clearly marked and easy to find.
    – N. Virgo
    Mar 31 at 14:32

2 Answers 2

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Advice

  1. Talk to your advisor. At the end of the day, your goal is to complete a degree. The primary obstacle[1] to completion is your advisor, followed by your committee. If your advisor has a strong preference, do what they tell you to do.[2]

  2. Read other theses in your area. Particularly from your institution. See what other people in your department have done in the past, and what other people writing on similar topics have done in the past. Your institutional library should have a collection of past theses by people at the institution—have a look at what other people from your department (and even advisor) have done, and emulate their structure.

  3. Refer to your institution's guides. Your institution will have a guide for theses. It will (perhaps) tell you about which fonts you can and cannot use, how wide your margins should be, how sections should be numbered, what pages are necessary, and so on. It is possible[3] that this guide has some guidance about how to organize your thesis. If it does,[4] do what it tells you to do.

  4. Read texts in your area. See what other people in your field are doing. If appendices of notation are common, go that way. If introductory sections of notation are common, do that.

  5. Do what you like. Ultimately, at the end of the day, your thesis is your document. You get to decide about style. You have expressed a dislike for appendices, so don't include one! The reality is that none of the above points are likely to apply. Most advisors aren't going to care about the structure of your thesis, your institution's style guide is likely silent on the issue, and I would imagine that there is no consensus in your field.

Anecdote

For what it is worth, my own solution was to include an index of new, idiosyncratic, or otherwise non-standard[5] notation just after the table of contents and the list of figures. I then introduced notation in the basic flow of the text, and had LaTeX build the index of notation automatically. A lot of notation was introduced in my first two chapters (background and introduction), but I continued to introduce notation throughout the document. I think that this worked pretty well.

Notes

[1] My use of "obstacle" here is a bit tongue-in-cheek. Hopefully, your relationship with your advisor is good, and they are an active help, rather than hinderance.

[2] For example, my masters advisor very strongly disliked the Oxford comma. I very strongly disagreed with him. There are no Oxford commas in my masters thesis.

[3] Possible, but I think highly unlikely.

[4] And it probably doesn't.

[5] There is absolutely no need to define standard notation in your field. Don't waste your readers' time with that.

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    Upvoted. Two small remarks: Regarding 1., depending on the location it could also be an undergraduate degree, i.e. the thesis could be a Bachelor's thesis. In 2. I think the sentence "Your institution will have a style guide for theses" is a bit of an overgeneralization. E.g., none of the math departments where I've worked so far had a style guide for theses. Mar 31 at 7:45
  • @jochen By "institution", I meant college or university. I've never heard of a departmental style guide, though I am sure that one exists, somewhere. Mar 31 at 11:41
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    "See what other people in your field are doing." I would add – see what other people are doing and reflect on whether it works and if so / if not, why. Mar 31 at 16:01
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    @JochenGlueck Honestly, I would be kind of surprised to learn that any institution which requires one to submit a theses does not have guidelines for the submission of that document. For example, this is what my phd institution has to say: live-ucr-graduate.pantheonsite.io/document/format-guide-2324 . Note that the guide is mostly about the technical structure of the document (e.g. margins, spacing, etc), hence I would imagine that it is silent on things like organizational structure, but such a guide could be more specific, I suppose. Apr 1 at 14:20
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    @JochenGlueck That is just one example. My father, at the University of Arizona, had a remove a page from his dissertation because the numbering didn't match the institutional style guide. My masters institution had its own style guide. Perhaps it is a European vs American thing, but I am willing to be that if you google "[American university] dissertation guide", you are going to find a similar document. Apr 1 at 21:08
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The placement isn't all that important in theory. It is even acceptable to introduce specialized notations at first use rather than collecting it. If you collect it as an appendix, make an early note that it exists at the end. If you put it early, make sure it doesn't interfere with the flow. But a stand-alone section early on is fine.

Standard notations in the subfield probably don't need to be stated if you use them in the standard way. That might even get in the way.

Your university may have a style guide. Your advisor may have preferences. Don't neglect those.

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    Yes, emphatically, standard notation should not really be introduced, assuming your audience is mathematicians of some sort. And you should hesitate to introduce toooo much non-standard notation, because it'd be an obstruction. Don't think that math is fundamentally "formal" :) It is by far best to explain new ideas in terms of old/standard, rather than accidentally pretending to be operating in a vacuum. Mar 30 at 20:47
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    @paulgarrett: "you should hesitate to introduce toooo much non-standard notation" I wish one could find a way to force all math book authors in the world to follow this advice. My favourite example is a book where the author introduced a separate notation for the imaginary line (something like $\mathfrak{J}$ if I remember correctly) instead of just writing $i \mathbb{R}$. My short term memory is really too small to hold a couple of unnecessary variables and similar quirks when I read a book (or a paper). Mar 31 at 9:33
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    @JochenGlueck, I am confident that you are all-too-well-aware of the conceit that mathematics is just a formal thing, that we can make any definitions that we want, prove theorems about them, ... and use whatever fonts we want to name them... "Hilarious"... if the goal is just to leave indecipherable standing stones in the desert... :) Apr 1 at 21:59

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