| Code |
14759
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
Not applicable.
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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.
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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.
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Main Bibliography |
• How to Prove It, A Structured Approach, Daniel J. Velleman, Cambridge University Press, 2006
• The Elements of Advanced Mathematics, Steven G. Krantz, CRC Press, 2017
• Proofs and fundamentals. A first course in abstract mathematics, Bloch E. D., Springer, 2011
• Lógica e Aritmética, A. Franco de Oliveira, Gradiva, 1991
• An Introduction to Mathematical Reasoning: Numbers, Sets and Functions, P. J. Eccles, Cambridge, 1997
• Sets, functions and logic, Devlin Keith, Chapman and Hall/CRC, 2003.
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Teaching Methodologies and Assessment Criteria |
The classes alternate theory with practice, in order to facilitate the understanding and assimilation of the subject.
ASSESSMENT CRITERIA
1. The assessment may be carried out during the course or in a final exam.
2. Knowledge assessment throughout the teaching and learning period will consist of two periodic written tests, each lasting two hours and worth ten points. The tests will be held on 4 November and 12 December 2025.
3. Students who obtain a grade of 9.5 or higher in the assessments carried out during teaching activities will be exempt from the final exam.
4. Any attempt at fraud will result in failure of the Fundamentals of Mathematics course.
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Language |
Portuguese. Tutorial support is available in English.
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