Logic and Foundations

Code:

M3009

Acronym:

M3009

Level:

300

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - 2S

Active?	Yes
Web Page:	http://moodle.up.pt/course/view.php?id=2989
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:F	0	Official Study Plan	2	-	6	56	162
			3
L:G	0	study plan from 2017/18	3	-	6	56	162
L:M	49	Official Study Plan	2	-	6	56	162
			3
L:Q	0	study plan from 2016/17	3	-	6	56	162

Teaching language

Portuguese

Objectives

To learn the basic notions and techniques of First-order Logic, of Set Theory and of its axiomatics. In particular, to clarify the notion of proof, to master proof methods and to know some more operational aspects of Set Theory, namely cardinal arithmetic. 

Learning outcomes and competences

To develop competence at the level of formal language and communication of Mathematics, as well as of mathematical reasoning and the mastering of the mathematical method. To enlarge and develop mathematical culture and maturity and to promote thought about this science, recognizing the importance of these theories in foundation and evolution of Mathematics, as well as in the development of Computer Science.

Working method

Presencial

Program

MATHEMATICAL LOGIC

Propositional calculus, first-order languages and their syntax, semantics, deductive system and completeness.

FOUNDATIONS OF MATHEMATICS

Zermelo-fraenkel axiomatics for set theory (with the Axiom of Choice). Natural numbers, ordinal and cardinals.

 

Mandatory literature

J. Almeida, H. Ribeiro; Introdução à Lógica, 2002
R. Cori, D. Lascar; Mathematica Logic: A Course with Exercises, Part I, Oxford University Press, 1993
K. Hrbacek, T. Jech; Introduction to Set Theory, New York: Marcel Dekker, 1978
Putnam, Hilary; , Lógica. Enciclopédia Einaudi nº 13 - Lógica/Combinatória, pág. 11-71, Imprensa Nacional-Casa da Moeda, 1998
Robbin, J. W.; Mathematical Logic, W. A. Benjamin, Inc., 1969

Teaching methods and learning activities

Exposition of the theory by the teacher. Notes for study and support of the classes are available as well as exercise sheets. The webpage of the course contains other materials, e.g. tests and resolutions from previous years. Regular tutorial time to provide individual support to the students. The students have access to the evaluation tests and exams, and are entitled to receive all the explanations and corrections they require.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	50,00
Teste	50,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

Every student can attend the exam.

Calculation formula of final grade

Regular examination season:

- Weekly resolution of exercises, after the wednesday class (about 15 minutes), chosen among the exercises that are in the notes on the subjects studied until the previous week. These exercises will be quoted for a total of 2 values in the Logic part and 2 other values in the Foundations part.

- Two tests, one on the part of Logic to be carried out during the semester, and another on the part of Fundations to be carried out during the normal period of examinations.

- The final classification in the normal season, except for the cases mentioned in the next point, will be the sum of the classifications obtained in the part of Logic and in the part of Foundations, each of these being calculated as the best between:

- the classification of the corresponding test quoted for 10 values

- the classification of the test converted to 8 values added to the classification obtained in the corresponding exercises.

- In order to obtain final classifications of more than 18, a complementary proof will be required.



Second examination season:

- Final exam divided into two parts quoted for 10 values, one on Logic and one on Foundations.

- The student can choose to solve in the examination each one of the parts or to use the classification already obtained in the normal time. In case of choosing to settle in the exam, it will be the classification obtained there used to calculate the final classification.


- In order to obtain final classifications of more than 18, a complementary proof of valuation will be required.

- For students who achieve a final grade between 8 and 9.4 points, there may be a complementary test to decide on 9 or 10-pass or fail-over.

 

Special assessment (TE, DA, ...)

The exams required under the special cases previewed in the law will be written, but may be preceded by na oral exam to establish if the student should be admitted or not to the written exam.

Classification improvement

It is not possible to improve the distributed evaluation component (weekly exercises).