IPLUSO 1656

Discrete Mathematics

• ApresentaçãoPresentation

  Discrete Mathematics is an area of ¿¿mathematics of growing interest to computer sciences, life sciences, telecommunications, electronics, processor industry, integrated circuit design, cryptography and security in communications transmission, automobile traffic systems. The reciprocal influence of discrete mathematics with other areas of mathematics is increasingly visible, as in the case of operational research, algebra, number theory, geometry and topology. Discrete mathematics is divided into two major areas: combinatorics and graph theory. It deals with processes that consist of sequences of separate states, or numerable sets of objects, including, of course, finite sets, with common patterns, in many cases difficult to identify without resorting to its powerful analysis techniques.
• ProgramaProgramme

  CP1. Propositional Calculus: Logical Operations. Tautologies and contradictions, correct arguments. Normal shapes. Natural formal system. CP2. Calculation of predicates: Predicates. Logical equivalences. Rules of inference for the existential and universal quantifiers. Formal demonstrations. CP3. Sets, relations and functions: Basics, binary relations, boolean matrices and properties. Equivalence relations and partially ordered sets. CP4. Binary trees, sequences, lists and strings. CP5. Graphs: Directed and undirected graphs. Matrix of paths with graphs. trees. Graphs with weights and Dijkstra's algorithm. CP6. Python/Octave: Basic notions and application to program themes.
• ObjectivosObjectives

  OA1. Acquire appropriate mathematical foundations and techniques for a better understanding and mastery of the tools to be used by a computer engineer. OA2. Understand and formulate mathematical content with clarity and rigor, applying the knowledge acquired in different scenarios. OA3. Develop logical reasoning expressed by propositional and predicate calculations. OA4. Acquire basic notions about relations, equivalence relations, partially ordered sets, functions and partial functions. OA5. Use and formulate recursive definitions, apply ordinary and structural recursive proof. Apply basic concepts of graph and tree theory.
• BibliografiaBibliography

  W. K. Grassmann e J.-P. Tremblay, Logic and Discrete Mathematics - A Computer Science Perspective, Prentice Hall, 1996. K. Rosen, Discrete Mathematics and its Applications, MacGraw-Hill, 1999  
• MetodologiaMethodology

  The teaching methodologies are based on two aspects, namely: Theoretical classes: Expository method, using a board and projector, interspersed with situations of dialogue with students aimed at developing mathematical intuition, critical thinking and the ability to formulate concepts. Theoretical-practical classes: Complementing the subjects studied in the theoretical classes and solving exercises including discussion of the statement, time interval in which students try to solve the exercise on their own, discussion of possible solutions, presentation of a final answer. Some classes are in a computer lab. Use of the e-learning platform. The assessment comprises: two tests or an exam, and a supplementary test for grades above 16 points.
• LínguaLanguage

  Português
• TipoType

  Semestral
• ECTS

  6
• NaturezaNature

  Mandatory
• EstágioInternship

  Não