Discrete Mathematics

Objectives

1. Analyze problems using mathematical methodologies, abstract thinking, logical inference from premises, and rigorous, concise solutions.
2. Convert between number systems and perform arithmetic operations in these systems.
3. Solve problems using set theory.
4. Solve problems using graph theory.
5. Solve problems using elementary number theory.
6. Apply modular arithmetic in cryptographic systems and identification systems.

Program

1. Number systems.
2. Propositional logic and predicate logic.
3. Sets and binary relations. Equivalence and order relations.
4. Introduction to graph theory.
5. Introduction to number theory.
6. Congruences. Cryptography. Identification systems.

Teaching Methodologies

Theoretical classes are lecture-based, where topics are presented with the use of examples.
Theoretical-practical classes are integrated with theoretical ones and focus on problem-solving exercises and the exposition and resolution of problems.
The UAc e-Learning platform Moodle (at http://moodle.uac.pt) is used as a repository for pedagogical and didactic materials supporting learning, as well as for scheduling, disseminating, and promoting complementary activities and managing assessment elements.

Bibliography

D. M. Cardoso, J. Szymanski e M. Rostami, Matemática Discreta, Escolar Editora, 2009.

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 Mathematics, Prentice-Hall, 1996.

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