Modelling Theory and Practice/Motivation and Summary
From Wikibooks, open books for an open world
- structural: the nice thing about mathematics is that "1 + 1 = 2" can stand for one cow plus another one makes two cows as well as ???. In the same way this book cares about structures first, such as orders, trees, etc, that then can become 'alive' in various domains.
- relational: in a mathematical language there are two kinds of ??? symbols: functions like "+" and relations like "=" or ">". Here we focus on the relations.
- discrete/ finite: ???
- bottom-up (simple to complex): the book starts with very simple structures, like unary relations (all they can express is: does sth have a certain property - yes/ no). It is like with the periodic table: the simpler atoms occur more often in nature, just because of their simplicity. However this does not mean that they are the most interesting ones to study, this is why one of the important assumptions (inspired by practical experience) is that a lot of the relevant structures in 'real life' are simpler than we think (or than things like UML may suggest)
- case based: in order to connect such solely structural thing to the 'real world', the book provides emperical cases of applications, s.t. a modeller can use them as a kind of experience base in its everyday modelling. This corresponds to the way humans approach problems and is known as Case-based reasoning. Notice that thus we do not model the modelling process itself. Instead the book leaves it to the modeller to extract the models from the empirical cases, in a way it is best suited to its domain and experience.