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Course Sheet Academic Year of enrolment:
Professor and Collaborators:
Hours of classroom activity:
Objectives
Contents The aim of this course is to make students able to read and understand definitions, theorems and proofs in a mathematical text. The first part of the course is an informal introduction to mathematical logic, so that students may become familiar with the language of mathematics and deductive reasoning. In the second part of the course we apply what we have learned in the first part to basic mathematical concepts: sets, relations and functions,
Extended Syllabus Sentential Logic: deductive reasoning, logical connectives, truth tables, variables, sets, operations on sets.
Quantificational Logic: quantifiers, equivalences involving quantifiers, other operations on sets.
Proofs: proof strategies, existence and uniqueness proofs.
Relations: ordered pairs, Cartesian products, relations.
Functions: functions, injective and surjective functions, inverses of functions, images and inverse images.
Mathematical induction: proofs by mathematical induction, recursion.
Infinite sets: equinumerous sets, countable and uncountable sets.
Recommended Bibliography Daniel J. Velleman
How To Prove It: A Structured Approach (2nd edition)
Cambridge University Press
Teaching Methods
Evaluation methods Verification of learning:
Written and oral examination.