Discrete Mathematics

Presentation

The major goal of this  discilpine is that the  student develops a logical reasoning and critical mind and also acquires the basic knowledge on theory of mathematical logic, numerical sets, recursion and graph theory, as well as its most appealing applications, namely construction. of paths and circuits, coloring of maps and others during the learning process

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Programme

IT Engineering

Level of Qualification|Semesters|ECTS

| Semestral | 4

Year | Type of course unit | Language

1 |Mandatory |Português

Code

ULP452-1656

Recommended complementary curricular units

Not applicable.

Professional Internship

Não

Syllabus

• ELEMENTS OF MATHEMATICAL LOGIC. Algebra of propositions: conjunction, inclusive and exclusive disjunction, negation, its truth tables. Principle of non-contradiction and principle of the excluded third.Tautology, contradiction and contingency. De Morgan's formulas. Mathematical demonstrations.
• ELEMENTS OF SET THEORY. Definition of the different numeric sets. Set operations. Cardinal of a finite set. Partition of a set. Generating fraction. Principle of inclusion and exclusion.
• INDUCTION AND RESOURCE. Principles of mathematical induction, recursion.
• THEORY OF GRAPHS. Graph Definition and Terminology. Matrix representation. Euler and Hamilton graph Minimum cost generating trees. Graph coloring. Maximum flow and minimum path networks

Objectives

One of the main objectives of this course is to learn new tools and techniques to facilitate problem solving analysis in various areas. Students should be able to analyze problems using mathematical methodologies, abstract thinking, logical inference from logic principles, and rigorous and concise solutions. In this way, developing the students' logical-deductive reasoning is achieved through the contents, seen as a means to achieve this end. It is intended that students have acquired skills that allow them to advance both in subjects throughout the course and in more advanced content.

Teaching methodologies and assessment

The theoretical classes are of fundamental importance in the assimilation of the discipline, and allow the student to apply the acquired knowledge. The practical classes are a component that will allow students to acquire the ability to solve theoretical -practical exercises. In the classes the presentation must be made by the teacher of the global objectives that are intended and the planning of the practical sheets should be done at the same time as the theoretical material was given. It is intended to perform exercises to the interpretation and application of given matter. This phase is very useful from the point of view of student training. In any case one must try to achieve the fundamental objective, which is to develop in students the ability to work in a practical context with the knowledge acquired in the discipline.

References

• Apontamentos fornecidos pelas docentes das aulas teóricas e práticas.

• S. Lipschutz, M. Lipson, Matematica Discreta, Coleccao Schaum, 1997.

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