Mathematics

General aims: to acquire basic knowledge and skills in mathematical logic and to be able to apply them in various contexts, including teaching. Specific aims: Knowledge and understanding: The successful student will have acquired basic notions and results in mathematical logic: propositional calculus, predicates calculus, Peano arithmetic and incompleteness results. Applying knowledge and understanding: The successful student will be able to solve exercises and problems of mathematical logic; exercises and problems refer to the topics covered, to other mathematical areas, to teaching and learning mathematics, to natural language. S/he will recognize various kinds of formulas in the simplest cases (tautologies, valid formulas, ...). S/he will be able to recognize and apply inference rules. Critical and judgmental skills: The successful student will be familiar with mathematical rigor and formalism. S/he will have reflected on known mathematical contents and on the translation of concepts in axiomatic theories with appropriate languages. S/he will be able to discuss the role of intuition and rigor in teaching mathematics in different situations. Communication skills: The successful student will be able to present subjects and arguments in the oral test, and to explain what s/he learned. Learning skills: The acquired knowledge will allow to study more specialized subjects. The student will be motivated to extend the acquired knowledge.