1. For use in an editable electronic book having hyperlinks and a table of contents with hyperlinks to corresponding sections of the electronic book, the electronic book including a first expression symbolically defining a first variable and a second expression including at least a symbolic evaluation operator and the first variable, a computer-based method for modifying symbolic expressions in real-time in the electronic book, the method comprising the steps of: displaying the electronic book on a screen of a computer such that the first expression is displayed in the electronic book and the second expression is displayed at a position in the electronic book below or to the right of the first expression; maintaining a data structure representing mathematical dependencies between expressions explicit in the expressions of the electronic book, the data structure including an acyclic directed graph including a first node representing the first expression and a second node representing the second expression; performing a predetermined symbolic function on the second expression to produce a first resultant expression, the first resultant expression being mathematically equivalent to the second expression in combination with the first expression; displaying the first resultant expression in the electronic book; accepting as input from the user an instruction to modify the first expression in the electronic book; displaying the modified first expression in the electronic book; examining the data structure to determine all expressions that reference the first variable; automatically and without further user intervention, passing the second expression as symbolic data and the modified first expression as symbolic data to the symbolic algebra engine; at the symbolic algebra engine, automatically and without further user intervention, performing the predetermined symbolic function on the second expression to produce a modified resultant expression, the modified resultant expression being mathematically equivalent to the second expression in combination with the modified first expression; adding the modified resultant expression to the data structure; and displaying the modified resultant expression in the electronic book in place of the resultant expression.