Provas de identidades via argumentos combinatórios

Abstract

The Combinatorial analysis is the branch of mathematics that analyzes structures and discrete relationships. From their study it is possible to solve many problems, especially those that lead us to determine cardinality, that is, list or count the subsets of a given finite set and satisfying certain given conditions. For this, we have various counting techniques such as, combinations, arrangements and permutations, which are considered among many others the best known and the most practically used in primary education and even in undergraduate degrees in mathematics. This work comes not show the algebraic formulas that are used to solve counting problems. Is presenting a very interesting technique and of great relevance for those who wish to enhance and / or reshape the vision of how to use this branch to solve counting problems without necessarily is linked to ready-made formulas. In this sense, we present some combinatorial identities will be demonstrated algebraically and applied problem solving, from arguments guided by the basic principles underlying this study. Thus, you can see how the Combinatorial Analysis sharpens thinking mathematics, especially when it comes to contextualized problem situations, which provides more precise and concrete learning on the topic, expanding the field of view and the possibilities for use without resorting to mere formulas ready.