20. The method of claim 19 wherein the step of symbolically evaluating each mathematical expression comprises the step of utilizing the dependency graph to ascertain all mathematical expressions on which each mathematical expression directly and indirectly depends.
19. For use with an electronic book, a computer-based method for performing live symbolic mathematical operations and for editing and processing mathematical expressions, the method comprising the steps of: displaying the electronic book on an output device of a computer, the electronic book including a table of contents with hyperlinks to sections of the electronic book; providing a symbolic evaluation operator signifying that a mathematical expression is to be evaluated symbolically; displaying mathematical expressions in standard mathematical form in the electronic book, a subset of the mathematical expressions comprising the symbolic evaluation operator; maintaining a dependency graph so that the dependency graph continuously represents mathematical dependencies between the mathematical expressions in the electronic book; symbolically evaluating each mathematical expression in the electronic book that includes the symbolic evaluation operator; displaying in the electronic book results of the symbolic evaluation of each mathematical expression evaluated at the previous step; editing one or more mathematical expressions in the electronic book; and automatically updating the electronic book whenever a mathematical expression is edited, said automatically updating step including the substeps of: automatically updating the dependency graph to include the edited one or more mathematical expressions, automatically ascertaining a subset of mathematical expressions that include the symbolic evaluation operator that need to be updated, and automatically symbolically evaluating each mathematical expression in the subset of mathematical expressions ascertained at the previous substep.