## What is “Modeling” ?

Tony Hürlimann

info@matmod.ch

November 12, 2023

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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.