| 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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Language |
Portuguese. Tutorial support is available in English.
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