Logic and Foundations

Code:

M3009

Acronym:

M3009

Level:

300

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2016/2017 - 1S

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	1	Official Study Plan	3	-	6	56	162
L:M	33	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
Van Dalen, D. & Monna, A. F; Sets and integration, Wolters-Noordhoff Publishing, Groningen, Netherlands . ISBN: ISBN 9001597750

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	100,00
Total:	100,00

Eligibility for exams

Every student can attend the exam.

Calculation formula of final grade

- There will be two tests, each one marked with a maximum of 10 values.

- The final exam will consist in two correspondent parts, marked with the same value.

- A student that gets a minimum of 4,7 values in one test does not have to do the correspondent part of the exam. In this case, the mark obtained in the test will be used to determine the final mark.

- If a student gets a minimum of 4,7 values in one part of an exam he(she) can use that classification in the correspondent part of a posterior exam.

- A student that gets a minimum of 2 values in each test and a sum of at least 9,5 values, will not be required to do the final exam. In case he(she) chooses not to do the exam, the final mark will be the sum of the mark obtained in the two tests, except eventually if it is greater than 17 (see below).

- In any case, if the student chooses to do either part of an exam, the correspondent classification will be entirely determined by the result obtained in this exam. - Every student can attend the final exam.

- Only in the second period of exams, there may be a complementary test to the students that get a final classification greater or equal to 8,5 values but less than 9,5 values, to decide if the student will pass.

- Eventually, there will be a complementary excellence exam to the students that obtain classification greater than 17 values.

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 grade. The rules for improvement of the final grade are the ones determines by the faculty.