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Fundamentals of Mathematics

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, cardinality.
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 1. The assessment may be made during the period of classes or in a final examination.
2. The evaluation of knowledge throughout the teaching-learning period shall be periodic and shall consist of two written tests, each lasting two hours and rated at ten (10) points, to be held on 25 November 2021 and 20 January 2022.
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.
Last updated on: 2021-10-21

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