Class Discrete Mathematics

Discrete mathematics, as a course intended to first-year students, contains a preliminary chapter where informally, some aspects of mathematical logic are addressed. The preliminary chapter will allow students do detect errors or reasoning that arise, with some frequency, in our daily lives. This chapter also has the merit of linking mathematics and the Portuguese language.   The student will have the opportunity to be confronted with some aspects of the syntax of the Portuguese language. Discrete mathematics will familiarize the student with the language of the intuitive theory of the sets. The student will have the opportunity to acquire the ability to operate with formal languages and identify regular languages, in addition to acquiring skills that allow using formal grammars and finite automata as language generator mechanisms.

Not applicable

Elements of Mathematical Logic. Elements of Set theory:  Generalities. Operations with sets. Power set. Generalities about functions. Finite sets. Cardinal of a finite set. Binary relations. Operations with binary relations. Equivalence relations. Set partition. Digraphs. Morphisms of digraphs. Formal Language: Generalities. Operations with languages. Free monoide of words over a finite alphabet. Universal property. Closure of a language. Formal grammars. Generalities. Derivation. Language generated by a grammar. Regular grammars. Finite Automata: Generalities. Deterministic and nondeterministic automata. Language recognized by a automata Recognizable languages.

Short supporting texts are available. These texts make it possible to elaborate questions to be asked during the lessons. The concepts to be studied arise naturally from the analysis of a problem. The theoretical-practical classes are supported by worksheets that address the main topics presented in the theoretical ones. These forms and supporting texts present illustrative examples that alert to frequent errors and promote the creativity of the student in the construction of  strategies for solving the problems. Evaluation comprises a continuous component which includes the level of attendance, actives participation in classes and 4 homework assignments weighting 40% of the final classification. A final written test takes place at the end of de semester weighting 60%. Students having more than 16, may have to perform and extra test. The non-appearance of which yield a final mark of 16.

Almada, T.; Matemática Discreta; Sebenta Universitária; Edições Lusófonas; 2004. Howie, J. M,; Automata and Languages; Oxford Science Publications; 1991. McEliece, R. J.; Ash, R.B. and Ash, C,; Introduction do Discrete Mathematics; McGraw-Hill 1989.