# Does the usage of mathematical symbols work differently in books than in theses?

From what I know, one cannot use a mathematical symbol for two different notations in a thesis. Is this right? The thing is that I am trying to cite a book in my thesis, but this book uses (tau) for both viscous stresses and reynolds stresses. Can I do the same in my thesis or do I have to choose another notation?

Bear in mind that I am new to academic writing, thanks!

• Are they just using tau to represent any stress? – JMac May 16 '19 at 17:27

So why not just define a tau with a subscript v and a tau with a subscript r - make it clear in your nomenclature and you're sorted.

See:

• The subscript might be confused as an index – user2768 May 16 '19 at 17:26
• @user2768 So seems to work fine for things like Cp and Cv... And if you have properly defined it in the nomenclature then there should be no confusion - perhaps for those who don't read it properly... – Solar Mike May 16 '19 at 17:28
• In principle labeling subscripts are typeset in an upright font (\mathrm or \text if you're a LeTeX user) and indexes in italics. But few readers actually pay enough attention for that to be reliable. – dmckee --- ex-moderator kitten May 16 '19 at 18:29
• @Solar That convention comes from a standards document. I think. But I can't recall which one just now, so I could be fooling myself. In any case, I don't usually both to follow it. Too much trouble and as I say, readers don't notice. But I'd never attempt serious mathematical typesetting in Word, even though the tooling has improved a bit. – dmckee --- ex-moderator kitten May 16 '19 at 18:38
• @MazenDraw You have many other possibilities. You could, for example, keep the tensor component indices as subscripts and put v/r as a superscript, use another typesetting trick like primes or tildes to tell different taus apart, or another letter altogether. – Anyon May 16 '19 at 22:56

From what I know, one cannot use a mathematical symbol for two different notations in a thesis. Is this right?

That's certainly good advice, since it avoids unnecessary confusion.

The thing is that I am trying to cite a book in my thesis, but this book uses (tau) for both viscous stresses and reynolds stresses. Can I do the same in my thesis or do I have to choose another notation?

Presumably you don't intended to use τ to mean viscous stresses and reynolds stresses in the same context, because usage of τ would then be ambigious. So, I presume you'll be using τ to mean viscous stress in one context, perhaps an entire chapter, and to mean reynolds stress in another context, perhaps a different chapter. This seems reasonable. However, you needn't use the book's notation, especially if there is a risk of ambiguity.

• Using the same symbol with two different meanings in two different chapters does seem to increase the possibilities of confusion... – Solar Mike May 16 '19 at 17:32
• "This seems reasonable." No, it's not, and academics, and indeed any one hoping to get an idea across, need to stick with a consistent method for describing different phenomena, constants and variables. It is not reasonable to basically require you to keep looking back a the beginning of a chapter in a book to determine the symbology, even given you understand what each symbol should represent normally. The book made a mistake in overloading symbols like that. – whn May 16 '19 at 18:15
• @opa : In my opinion, there's nothing wrong with using the same symbol to mean different things in different contexts, especially if they are analogous. When a student has 15 equations to solve on a test, all involving the variable x, do you think the student is confused because x appears several times in different contexts? Of course not. And if the author actually simply mentions that the symbol means this or that when it is about to be used, what's the problem? – MPW May 16 '19 at 21:51
• @opa In this case it is quite common to use tau for any kind of stress. I would certainly be confused if the stress wasn't denoted by a tau. Look into Pope's Turbulent flows what kind of symbols they had to employ to stay unique in the whole book but still I expect he uses some kind of tau for these two stresses. The book uses the same letters with many different typefaces for various variables, because the number of symbols is limited. – Vladimir F May 17 '19 at 6:34
• @opa You've quoted me out of context, the very next sentence starts "However, ..." Anyhow, I appreciate your concerns, but I'm inclined to agree with MPW and Vladimir, especially "it is quite common to use tau for any kind of stress." Of course, it really is case dependent, that is, in some cases it may be okay (because the discipline does it that way, for instance), whereas in others it might not. – user2768 May 17 '19 at 8:58

From what I know, one cannot use a mathematical symbol for two different notations in a thesis. Is this right?

Such things are not governed by hard-and-fast rules. Your institution might have specific style guidelines for a thesis, but notational choices are usually at the discretion of the author. Of course, it's ultimately your advisor and/or committee who decides whether your thesis is acceptable, though it's unlikely that notation alone would be the cause for rejection.

The thing is that I am trying to cite a book in my thesis, but this book uses (tau) for both viscous stresses and reynolds stresses. Can I do the same in my thesis or do I have to choose another notation?

It's up to you. Make your own decision as to which way will be the most clear. You can ask your advisor if you are unsure.

• Depending on field there may also being standards which are strongly adhered to, in which case it is best to follow the standard. Good luck if the thesis guidelines and the standard are in disagreement. – dmckee --- ex-moderator kitten May 16 '19 at 18:31
• I agree with this, but since OP is asking us for advice, it seems reasonable to be a bit more definitive. For my part: I would advise against overloading one symbol, and would be unconcerned about citing a book without adopting the book's notation. – cag51 May 16 '19 at 20:03
• @cag51: Feel free to write such an answer. It seemed to me like the question was mainly about what is required, not just what is best, so I addressed that. I don't know enough about the situation at hand to be able to give suggestions on what to write in this case. – Nate Eldredge May 17 '19 at 16:57

Perhaps for some perspective: the scope of a "name" can be limited, that is, "local", or it can be "global". Even fairly basic programming principles nowadays (with virtually unlimited namespace, as opposed to 1960's Fortran) recommend keeping namespaces as local as possible...

... and this advice applies to most mathematical notation, as well. That is, there are really very few symbols/notations that are understood globally and unambiguously. That's fine. I think one should be reconciled to (re-) setting the "names" in a given "scope", and not at all depend on document-dependent notation/names as though they'd be something the reader would have assimilated. (Excepting perhaps a very small number...)

Even then, if "tau" has two different and conflicting senses in the literature, there is no genuine intellectual/scientific purpose served in being mute on the point, and trying to find a way to dodge the operational ambiguity. That is, in each of your sections or subsections, tell what "tau" is. Done.

That is, do try to find a viewpoint from which this is a non-issue.

• Using the wrong "tau" in a calculation for a real engineering problem will never be a "non-issue"... – Solar Mike May 17 '19 at 6:40
• @SolarMike, presumably symbols refer to things which have a larger existence/sense/context than that single symbol. One of the points I try to make with my grad students (in math, in the U.S.) is to not get hung up in symbols, to use context to make sense of things, and so on. If someone's writing something to be checkable/readable, I'd want to also be able to check what the symbols referred to, etc. Seems like it'd be good practice. – paul garrett May 17 '19 at 16:45
• so you’re saying an answer is better than the correct answer or "some understanding" is better than a thorough grasp - bridges fall down for less... – Solar Mike May 17 '19 at 17:09
• @SolarMike, I don't see how you are interpreting my comment as "some understanding is better than thorough grasp". In any case, I meant to say, again, that I want my students to be able to explain (to me, for example) the context sufficiently to justify (to me, for example) a supposed parsing of symbols. I am intending that this be a better understanding rather than a too-glib, superficial one (that may also be "brittle" or non-robust under context-shifts). – paul garrett May 17 '19 at 17:14