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What's the Meaning of...?

As a language involving both words and symbols, mathematics depends on clear and common meaning of its terms. For over fifty years, the "standard" was the dictionary by James and James. New versions of it are still available today, but several other dictionaries are proving useful as well.

Over thirty years plus of teaching and playing with mathematics, James and James Mathematics Dictionary (548 pp) has proven to be one of my most useful references. The new Fifth Edition incorporates updated terms and concepts in its coverage of more than 8,000 topics. In addition to the expected definitions, it includes extensive descriptions of mathematical theories, practices and principles....plus a multilingual index.

A competitor that I also use and find less complex is Clapham and Nicholson's Oxford Concise Dictionary of Mathematics (528 pp), now in its Third Edition. Expanded with 500 new entries that cover ideas such as fractals, game theory, and chaos theory, this dictionary includes brief entries on famous mathematicians as well.

A third option is Nelson's Penguin Dictionary of Mathematics (150 pp), also in its Third Edition. Though it has 3,200 entries supported by explanatory diagrams, this dictionary is a little less substantial or broad in its coverage of mathematical ideas, yet it does have biographies of more than 200 significant mathematicians.

So how does one decide on which dictionary to purchase? One way is to focus on price (as it will separate the three choices rapidly). A second way is to find all three and compare how each defines common terms (e.g. trapezoid, matrix, game, dimension, etc.). A third way is to buy the one found in your local bookstore. I should add that it is quite common to find copies of earlier editions of the James/James dictionary in used bookstores.