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There is an at-times dizzying array of symbols used in math and CS papers. Yet many assume basic familiarity that seems rarely taught in one place. I am looking for a dictionary something like the following, especially from a CS perspective.

  • It would list all the basic mathematical symbols and give their meanings and examples. It would talk about symbols that are sometimes used in equivalent ways. It would note common beginner mistakes.
  • It would talk about the subtleties surrounding different meanings of a single symbol (much like multiple definitions of the same word in a dictionary).
  • It would not merely be a very terse description of each symbol, such as one word descriptions like "subset".
  • It would show how symbols are sometimes "overloaded". For example, $\binom{x}{y}$ could have $z$ as an integer, but sometimes $z$ can be a set with this notation and it means to choose elements from this set. $[n]$ sometimes means a set of integers $1 \ldots n$, or other times its a one-element array.
  • It might talk about how to describe all kinds of different "objects" in terms of different symbols or equivalent ways of referring to them (but which are more clear) and the operations possible on those objects. In other words, kind of like an API for math objects.

I.e. it would be also at times a "style manual" for different nuances in how to present mathematical writing. This would be a very helpful resource for anyone writing questions in mathematical stackexchanges, where many questions fail to make sense based on not fitting into tricky mathematical conventions.

Some book introductions have many of these features. however ideally it would be a separate treatment. Also, ideally of course it would be online. There are tables of latex symbols, but they don't really fulfill many of the above criteria.

Has anyone seen a "dictionary of symbols" that matches these features?

(Alternatively, it seems like an excellent wiki or FAQ project if good references like this don't exist.)

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    $\begingroup$ Wikipedia's list of mathematical symbols is a good start but still quite a ways from the comprehensive resource you describe. Still, it's been enough to get me through most of the theoretical CS papers I've read. $\endgroup$
    – Kyle Jones
    Dec 13, 2012 at 4:45
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    $\begingroup$ Notation is not always standard. There is "common practice" notation, but it varies geographically and throughout time. When using non-standard or less-common notation, sources would indicate the meaning of the notation. $\endgroup$
    – Yuval Filmus
    Dec 13, 2012 at 12:16
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    $\begingroup$ see also good examples of how to write well in cs, tcs.se, although this is more general style and not so much focused on notation $\endgroup$
    – vzn
    Dec 13, 2012 at 15:49

4 Answers 4

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You can use this sheet. It has a lot of handy formulas and some definitions.

You can also use Wikipedia's list of mathematical symbols propsed by Kyle Jones in comments.

There is also Worfram MathWorld which is a great resource, but you need to know what are you looking for.

When it comes to printed resources, each volume of The Art of Computer Programming has a great reference of mathematical notations, especially volume 1.

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To know something's secret name is to steal its power. - Dr. Daniel Jackson

For the times when we can only draw the symbol and want a name.

See: shapecatcher

You draw the symbol and if there is a unicode char for it, it will find it and give you a name. If there are many such as =, it will list many results.

Then it is just a matter of Googling.

Enjoy!

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    $\begingroup$ Good idea, but did not work well for me. $\endgroup$
    – The Unfun Cat
    Dec 13, 2012 at 19:16
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To the other answers' references for mathematical notation and symbols, I would like to add a reference for mathematical use of English words.

The book, A Handbook of Mathematical Discourse is a dictionary of words and phrases used in semi-formal mathematical writing—especially words like "where" and "all" that are used quite differently from non-mathematical writing.

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You won't find all of your requirements in one place. As to:

it would be also at times a "style manual" for different nuances in how to present mathematical writing.

Check out:

Mathematical Writing, Issue 14 of MAA notes, Donald Ervin Knuth, Tracy Larrabee, Paul M. Roberts

Publisher Mathematical Association of America, 1989 ISBN 161444322X, 9781614443223

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