What is “Modeling” ?

Tony Hürlimann
info@matmod.ch

November 12, 2023

Abstract

Whereas mathematical solution and visualization techniques are omnipresent, modeling techniques – translating a problem into formal notation – received only little attention, although modeling is one of the most creative and mostly quite challenging task. Is is an art and a discipline on its own right, and deserves a outstanding place when learning how to solve problems.

This paper is the first of several papers on modeling and it gives an informal and a formal introduction to the concepts of modeling and model. It explains the importance and functions of models. Certainly, “model” is a very general term, an its meaning varies throughout various branches of science (Science is modeling). Since we are interested basically in mathematical models, a precise definition is given. An intuitive notion is given in this paper of some basic concepts, such as Boolean and arithmetic operators, sets, vectors, tuples, vector spaces. However, to understand fully the mathematical examples, the reader should be familiar with these concepts. More is not needed at this point. Many more mathematical models can be found in my books, especially my puzzle book: See My Modeling Books.