Discrete Mathematics

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Objectives

1. To develop the rigorous mathematical reasoning.

2. To formalize the reasoning in propositional logic and predicate logic.

3. To develop the ability to analyze problems using mathematical methodologies, abstract thinking, logical inference and rigorous and concise solutions.

4. To familiarize the student with problems of elementary number theory and graph theory.

Program

1. Propositional logic and predicate logic.
2. Mathematical reasoning.
3. Mathematical induction and recursion
4. Elementary set theory.
5. Boolean algebras.
6. Binary relations Equivalence and order relations.
7. An introduction to number theory. Congruences. Cryptography.
8. Introduction to graph theory.

Teaching Methodologies

The topics are presented, discussed and developed in theorical and practical classes, through problem-solving, exercises-solving and online activities developed in the moodle platform.

The texts and documents are made available to the students in advance or simply projected in class, depending on the difficulty of its contents.

Documents that target the autonomous work by students are also available.

Bibliography

R. Graham, D. Knuth e O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, (2nd Edition), Eddison-Wesley, 1994.

P. Mateus e C. Sernadas. Matemática Discreta, DMIST, 2004.

Winfried Karl Grassman e Jean-Paul Tremblay, Logic and Discrete Matehematics, Prentice-Hall, 1996.

Edgar de Alencar Filho, Teoria Elementar dos Números, Livraria Nobel, 1981.

Code

01060923

ECTS Credits

6

Classes

  • Teóricas - 30 hours
  • Teórico-Práticas - 30 hours

Evaluation Methodology

  • 1st Frequency: 45%
  • 2nd Frequency: 45%
  • Attendance and Participation: 10%