"Chances and Risks of Heuristic Reasoning: Some Examples using Derive"

Johann Wiesenbauer
Institut fuer Algebra und Diskrete Mathematik, Technische Universitaet Wien
Wiedner Hauptstrasse 8-10
Vienna, Austria, A-1040
Austria
E-mail:j.wiesenbauer@tuwien.ac.at


Unlike everyday life in mathematics it is not sufficient that a certain 
statement is true in many cases or is derived on the grounds of "plausible" 
assumptions, but what is needed here is an exact proof. On the other hand, 
if such a proof is either not known or too difficult for classroom 
teaching, it may be a good idea to use heuristic reasoning instead. Some 
examples of this kind are given using Derive which clearly show the chances 
but also the risks in this field.