Discrete Mathematics
Objectives
The student is supposed acquire basic knowledge on Graph Theory, Set Theory and Number theory, in learning process, logical reasoning and critical mind are developed.
General characterization
Code
3629
Credits
6.0
Responsible teacher
Isabel Maria Oitavem Fonseca da Rocha Kahle
Hours
Weekly - 5
Total - Available soon
Teaching language
Português
Prerequisites
Available soon
Bibliography
Main reference:
Jean Gallier, Discrete Mathematics, Springer, 2011
Other references:
[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, OxfordScience 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
Teaching method
Basic concepts will be introduced in lectures ("aulas teóricas") and problems will be solved in problem solving classes ("Aulas práticas").
Evaluation method
There will be two test during the term and a final exam.
The students are required to subscribe to each test/exam, at the CLIP.
Pre-registration: electronically at CLIP, during the period indicated for each test. Take exam sheets on the day of the test to the room where you will take the test, which you must hand over to the professor.
Frequency: there is no frequency.
The tests are graded on a scale of 0 to 20. The final grade will be the average of the two tests.
If the tests do not lead to approval, the student can take the final exam.
During tests or exams, any type of consultation or the use of any type of machine is not permitted: calculator, cell phone, computer, etc.
Tests may have multiple choice questions. In case any of these questions are cancelled, students will be given the same mark on these questions.
Subject matter
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