Following my experimentation with educational mathematic computer software products and virtually surrendering, I encountered Algebrator. During the second half of the 19th century, various important mathematical advances led to the study of sets in which any two elements can be added or multiplied together to give a third element of the same set. It's misleading, because any particular example will have a number of special properties that will not be true of groups in general. (Addition of integers is commutative, for example, and the integers form a cyclic group.) And so if one needs to have concrete things to think about (and I think that almost all of us do), one needs to think not just in terms of one example, but in terms of a number of very dissimilar examples.

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