Introduction to Calculation

With this free course of 94 video lessons you will learn about the most important concepts of Calculus

In general the term calculus (from the Latin calculus, pebble, used to count or as an aid in calculating)1 refers to the result corresponding to the action of calculating. Calculate, on the other hand, consists of carrying out the necessary operations to predict the result of a previously conceived action, or to know the consequences that may arise from previously known data.

However, the most common use of the term "calculus" is the logical-mathematical. From this perspective, the calculation consists of a mechanical procedure or algorithm, by means of which we can know the consequences that derive from previously known data duly formalized and symbolized.

The two meanings of calculus (the general and the restricted) defined above are intimately linked. Calculus is a natural and primordial activity in man, which begins at the very moment he begins to relate some things to others in a thought or discourse. Natural logical calculus as reasoning is the first elementary calculation of the human being. Calculus in the logical-mathematical sense appears when one becomes aware of this capacity to reason and tries to formalize.

Therefore, we can distinguish two types of operations:

Operations oriented towards the achievement of an end, such as foreseeing, programming, guessing, estimating, precavering, preventing, projecting, configuring, etc. that include in each case a series of complex activities and skills of both thinking and conduct. Taken together, these activities take the form of an argument or reasons justifying a practical or cognitive purpose.
Formal operations as an algorithm that applies either directly to known data or to the symbolic schemes of the logical-mathematical interpretation of such data; the possible conclusions, inferences or deductions of such an algorithm are the result of the application of strictly established rules in advance.
Result which is:
Conclusion of a reasoning process.
Result directly applicable to initial data (troubleshooting).
Model of relationships previously established as a scientific and significant theory with respect to certain realities (Creation of scientific models).
Mere symbolic formal game of substantiation, creation and application of the rules that constitute the formal system of the algorithm (Logical-mathematical calculation, proper).
Given the importance that logical-mathematical activity has historically acquired in human culture, this article refers to the latter sense. In fact the word, in its usual usage, is almost restricted to this scope; for some, it is even reduced to a single type of mathematical calculation, since in some universities it was called "Calculus" to a specific subject of mathematical calculation (such as infinitesimal calculus, mathematical analysis, differential and integral calculus, etc.).
In a general article on the subject, the content of what logical-mathematical calculation entails at present cannot be developed. Here only the basis of its simplest elements is exposed, taking into account that on these simple structures the most complex calculations are built both in the logical and mathematical aspects.