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I am considering including a glossary and a list of notations in my PhD thesis on mathematics. Is it a good idea to write them separately or combine them?

For example, a typical entry of the list of notation is:

[a,b] The commutator of a and b, defined by [a,b]=a^{-1}b^{-1}ab.

An entry of the glossary is:

Commutator The commutator of a and b is defined to be the product a^{-1}b^{-1}ab.

(Note: the definition of commutator is well-known to mathematicians, but since another definition aba^{-1}b^{-1} is also possible, I would like to add the definition to avoid any possible ambiguity.)

I have a strong feeling of combining these two entries together, maybe even combining the glossary and the list of notations together.

Is it a good idea to combine the glossary and the list of notations in a mathematical PhD thesis?

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    Mathematicians rarely use glossaries, but sometimes include an index and/or index of notation. On the other hand, there is often a section on notation at the beginning. Is there a reason you specifically want a glossary? – Kimball Feb 9 '15 at 13:00
  • @Kimball, in this link, the commentator mentions that I can create a "cheat list", which I believe is a very good idea: academia.stackexchange.com/questions/32355/… – Zuriel Feb 9 '15 at 13:27
  • @Kimball, basically I want to make my thesis more organized and reader-friendly. – Zuriel Feb 9 '15 at 13:28
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    If you mean jakebeal's answer to that question and the comments therein, it seems what they are talking about is what I call an "index of notation," not a glossary. I currently don't see any reason why an index of notation and/or a preliminary notation section is not sufficient. BTW, despite the comments saying it doesn't happen in for (shortish) papers in math, I have included an index of notation in this joint paper, and was told it was very helpful. – Kimball Feb 9 '15 at 14:44
  • what does your supervisor say? – henning -- reinstate Monica Jun 25 '15 at 8:20
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Have your definitions in line rather than in a glossary, it improves the readability of the entire manuscript (whether or not those definitions are actually necessary). People rarely go through glossaries anyway, since it would involve spending twice the amount of time just to switch pages back and forth. Inline definitions, instead, help the reader to flow on without dismissing the attention on the context.

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    How does that improve things? If I encounter something on page 10 and I wonder how it is defined, is it not easier to flip to the Glossary (which is in a fixed place) than having to search through the paper to see where it was defined? – Tobias Kildetoft Jun 25 '15 at 8:55
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    What flipping back and forth? Just tear out the glossary pages. (Or print an extra copy of the glossary. Or open a second window.) – JeffE Jun 25 '15 at 19:01
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    To answer @Jeff: I strongly doubt that tearing out the glossary pages is an intelligent solution to the question. Likewise printing an extra copy does not seem to be much smarter than having to read the above line to find the definitions. Along the same lines also to Tobias: having definitions inline does not mean searching through the entire paper, rather it means providing one more line of explanation whenever suitable for the reader. Even more direct: take any 100 random books in mathematics and count how many of them have inline definitions and how many have glossaries. – gented Jun 26 '15 at 0:50
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Typically, a glossary defines words while a list of notations defines symbols. To my mind, at least, these tend to serve fundamentally different purposes in a document:

  • A glossary is a refresher on standard vocabulary, to support reading by people with a broader set of backgrounds.
  • A list of notations collects all of your special definitions in one place

To take the example in your question: most mathematicians will know what a commutator is, and thus won't need to re-read its definition, but it's nice to have it in a glossary for anybody who's feeling hazy on it. There are several conventions for how to notate commutators, though, and lots of meanings for square brackets, though, so pretty much every reader will appreciate a symbol table entry that says:

[a,b] The commutator of a and b

The reason is that words tend to be much more stable from document to document than symbols. Words have some differences in definition (and you should be clear which you're using), but symbols are expected to be variables that often change radically from paper to paper because there are simply too few symbols and symbol-structures relative to the number of distinct objects that need to be labelled by them.

The important thing here is not the names of the sections, or even the distinction between single and multiple-character objects, it is the difference of purposes. Most readers should use a glossary rarely but a list of notations often: as such, if you create something that mixes the two purposes, then you're making it harder for the reader by swelling a critical section with things they usually won't be looking to read.

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In my extensive experience reading all sorts of books, "reader friendly" in terms of definitions and notation is to place that into an early chapter, or introduce it as you go. A complete index is very useful, a glossary much less so. A short overview of notation (sometimes found at the back of the title page) can be useful, but no more than one or two pages. Footnotes are a distraction, endnotes just get ignored.

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I would say keep them separate, because you should:

  • Inline the bodies of definitions in the ``natural'' narrative progress of your thesis (interspersing them with comments, observations etc.)
  • Have entries of the list of notations be very short and (always, or almost always) refer to terms in your glossary
  • Have terms in your glossary either defined very briefly or undefined at all, but always make a reference to the full inline definition.

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