Basic notions of Sets, Functions, Induction and Graph Theory.

The student is supposed acquire basic knowledge onGraph Theory, Set Theory and Number theory, inlearning process,logical reasoning and criticalmind are developed.

Part 1 - Sets, relations and functions

1. Sets: representations and basic operations; power set; cardinality

2. Binary relations

3. Functions: bijections; composition and inverse

Part 2 - Induction

1. Inductive definitions

2. Induction over natural numbers and structural induction

3. Complete induction and course-of-values induction

4. Recursive functions and proofs by induction

Part 3 - Graphs and applications

1. Introduction

2. Connexity

3. Trees

4. Euler graphs

5. Matrices and graphs

Bibliografia

[1] R. Johnsonbaugh, Discrete Mathematics, Prentice Hall Inter., 1997

[2] T. S. Blyth e E. F. Robertson, Sets and Mappings, Chapman and Hall, 1986

[3] N. L. Biggs, Discrete Mathematics, Oxford Science Publ., 1994

[4] K. A. Ross e C. R. B. Wright, Discrete Mathematics, Prentice Hall Inter.,1999

[5] R. J. Wilson e J. J. Watkins , Graphs an Introductory Approach, Wiley, 1990

[6] S. Lipschutz, Set Theory and Related Topics, Mc Graw-Hill, 1964

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

[8] A. J. Franco de Oliveira, Teoria de Conjuntos, Escolar Editora, 1989

[9] C. André e F. Ferreira, Matemática Finita, Universidade Aberta, 2000

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