| Code |
14759
|
| Year |
1
|
| Semester |
S1
|
| ECTS Credits |
6
|
| Workload |
TP(60H)
|
| Scientific area |
Mathematics
|
|
Entry requirements |
Not applicable.
|
|
Learning outcomes |
On completion of this unit successful students will be able:
1. to understand the meaning of mathematical statements involving quantifiers and logical connectives.
2. to construct and interpret truth tables for logical propositions.
3. to recognize incorrect and sloppy mathematical reasoning.
4. to construct and write elementary proofs of mathematical statements using a range of fundamental and standard proof techniques (direct argumentation, induction, contradiction, contraposition).
5. to use basic set-theoretic language and constructions to prove results about finite, denumerable and uncountable sets.
|
|
Syllabus |
1. Basic Logic: propositions and predicates, the elementary connectives, truth tables, quantifiers; arguments, premises, conclusions, truth and validity, natural deduction.
2. Methods of Proof: Direct proof, proof by contradiction, contrapositives; the induction principle and proof by induction; proof by cases.
3. Elements of Set Theory: operations on sets, relations, and functions.
|
|
Main Bibliography |
1. S. G. Krantz, The Elements of Advanced Mathematics, 4th edition, CRC Press, 2017
2. A. Franco de Oliveira, Lógica e Aritmética, Gradiva, 1991
3. P.J. Eccles, An Introduction to Mathematical Reasoning: Numbers, Sets and Functions, Cambridge University Press,1997
4. Devlin Keith, Sets, functions, and logic, Chapman and Hall/CRC, 3rd edition, 2003
5. Daniel J. Velleman, How To Prove It. A Structured Approach, 2nd edition, Cambridge University Press, 2006
6. Elon Lages Lima, Curso de Análise - Volume 1, 14.ª Edição, Projeto Euclides, IMPA, 2014
|
|
Teaching Methodologies and Assessment Criteria |
The classes intersperse theory with practice, in order to facilitate the understanding and assimilation of the subject.
Assessment criteria:
1. The assessment can be done during the classes or at the final examination.
2. The assessment of knowledge throughout the teaching-learning period will be periodic and will consist of two written tests, each lasting two hours and rated at ten (10) points, to be held on 14th November 2022 and 9th January 2023.
3. Students who obtain a mark of 9.5 or higher in the assessment carried out throughout the teaching activities shall be exempted from sitting the final examination.
4. Any attempt of fraud will result in failure in the curricular unit Fundamentals of Mathematics.
|
|
Language |
Portuguese. Tutorial support is available in English.
|