Banca de DEFESA: JORGE BELÉM E SILVA

COMBINATORY ANALYSIS IN THE CONTEXT OF COMPETITIONS AND APPLICATIONS

Combinatorial Analysis. Application of Theory to Practice. Contests and
entrance exams.

In this work we present a contextualized approach to Combinatorial Analysis, with the

objective of explaining this matter in a practical and objective way, through the explora-
tion of problems. For that, we resort to the detailed resolution of problems extracted from

competitions, entrance exams and books, and through them, we cover the most important
topics of the combinatorics taught to us at school. The text is structured in three chapters.
In the rst one, we introduce the most basic topics, such as the Fundamental Principle
of Counting, Permutations, Arrangements, Combinations and others. In the second, we
deal with more technical topics, such as the Pigeonhole Principle, Newton's Binomial,
Pascal's Triangle, Principle of Inclusion and Exclusion and Other Forms of Counting.
In the third and nal chapter, we provide the reader a list, with answer key, containing
ninety problems extracted from competitions carried out by several exemination boards.
Throughout the rst two chapters, we have thoroughly resolved several questions extrac-
ted from competitions, entrance exams and books. As the reader evolves in the text, the
problems become more interesting and demand more and more of him/her; however, the
structure remains independent of each problem, exempting the reader from the need to
return to previous pages to review another problem that serves as a basis for what is
being analyzed. Everything to be useful as study material for students of competitions
and entrance exams or as a supporting text for teachers of the high school students use
in their classes. In full, the work leads to the conclusion that combinatorics learning is
only attainable through involvement and hard work, that is, putting into practice what
is being studied.