Banca de DEFESA: LINDBERG BARBOSA LIRA DE ALMEIDA

LOGIC, AXIOMATIC THEORIES AND DEMONSTRATION METHODS IN BASIC EDUCATION

Logic-Axiomatic Theories -Sets -Demonstrations -Basic Education

This work presents an introduction to the Logic used in the development of Axiomatic Theories associated with the Basic Education Mathematics Curriculum according to the Common National Curriculum Base. Emphasis is given to the discussion regarding the most used demonstration methods to justify the main mathematical results presented at this level. It highlights, among others, the Methods of Demonstration by Direct Proof, Reduction to Absurdity and Mathematical Induction, being that, unlike most of the literature, it presents the whole relation of these methods with Logic its principles, operations and rules of inference fundamental prerequisites justification for their use. In particular, it makes a more comprehensive discussion of the Mathematical Induction Method associating it both to the Induction Principle or Axiom and to the Induction Theorem, demonstrating it and presenting its various applications whether in the rigorous definition of mathematical objects or as a powerful instrument to demonstrate the most varied results involving natural numbers in basic education. In addition, it brings examples of Axiomatic Theories developed at this level and enunciates several Theorems making their respective demonstrations using one or more of the demonstration methods presented including the demonstration in standard argument notation thus explaining its direct relationship with logic and its algebra. The work can be used as a reference material for the teacher of basic education or graduating from a Bachelor's Degree in Mathematics who wants to deepen with respect to Theorem Demonstration Techniques and all the Logic behind this process.