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State of the art computer algebra packages allow treatment of mathematical concepts beyond those which are traditionally offered or predefined. This is important for mathematics education since such concepts are precisely those which were scarcely understood by students both in secondary and tertiary education. Implementation of these mathematical concepts will greatly improve the possibilities for mathematics education at these levels. Examples of such concepts are: * handling of inequalities; * limits, continuity, Lipschitz conditions and smoothness; * growth of functions and the speed with which limit values are approached; * quotients of structures; * spatial geometry and visualization of objects in up to four dimensions. Examples of this methodology are given using Mathematica. Quotients are handled in detail and this part includes examples of the Mathematica code used. These can be made active by pasting in Mathematica notebook format.
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