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Introduction to Logic and Discrete Mathematics

Objectives

At the end of this course the student will have acquired approaches to address discrete structures and knowledge and skills that will enable him to: work with elementary notions of propositional and quantifier logic; develop some strategies for mathematical proofs; use set theory in an informal but sufficiently rigorous style; develop counting techniques; know the main properties of integers and apply some of these techniques in the study of graphs.

General characterization

Code

12901

Credits

6.0

Responsible teacher

Manuel Messias Rocha de Jesus

Hours

Weekly - 4

Total - 48

Teaching language

Português

Prerequisites

The student must be familiar with mathematics taught at pre-university level in Portugal (12nd level - science area).

Bibliography

A. Eccles, P. J.; An Introduction to Mathematical Reasoning, Cambridge University Press, 1997.
B. Vellement, D. J.; How To Prove It, A Structured Approach, Cambridge University Press, 1994.
Discrete Mathematics: Elementary and Beyond, L. Lovász, J. Pelikán, K. Vestergombi, Springer, 2003.
H. B. Enderton. Elements of Set Theory. Academic Press, 1977.
A. J. Franco de Oliveira. Teoria de Conjuntos. Livraria Escolar Editora, 1982.
P. R. Halmos. Naive Set Theory. Springer, 1998.
Y. Moschovakis. Notes on Set Theory. 2nd ed., Springer, 2006.

Teaching method

Classes are theoretical-practical, alternating theoretical sessions and practical sessions in the most appropriate way to achieve the proposed objectives. In theoretical sessions the contents of the course are exposed and illustrated with examples. In practical sessions students will be asked to solve problems and elaborate demonstrations of some of the results presented. Any questions/doubts are clarified during classes or tutorial sessions or even in extra sessions combined directly between student and teacher.

Evaluation method

Students must attend, at least, 2/3 of problem-solving classes.

Each student will be evaluated by two tests or an exam. More details in the portuguese version.

Subject matter

1. Propositional Logic and quantifiers.
2. Proof strategies.
3. Operations, relations and functions.
4. Equipotent sets and cardinals.
5. Counting.
6. Integers, divisors and primes.
7. Graphs.