|SCIENTIFIC DISCIPLINARY SECTOR||MAT/01|
|MODULES||This unit is a module of:|
The lecture course presents intuitions and mathematical results which relate to the developments in mathematical logic of the last 80 years. This allows to perform a deep analysis of the mathematical practice. The explicit study of mathematical logic lets the expert increase the understanding of the mathematical sciences and produces a fundamental basis for the presentation of mathematical themes and for the accretion of one's own mathematical intuition.
Study of first-order theories and their models, to analyze semantic issues, such as completeness and compact theorems, and syntactic questions such as the incompleteness theorems.
At the end of the lecture course, a student has improved one's awareness of the mathematical facts and one's own understanding abilities of themes in mathematics in order to
The course considers logic as useful means in the practice, the didactics, and the research in mathematics, and presents the main tool for the mathematical study of logic: category theory. By this, the course develops the mathematics of deductive calculi and of formal logical theories, also by means of examples from the students' previous experience.
None. Fluency with mathematical notations is useful.
During lectures, the instructor explains the theory and its applications to several examples and for the resolution of the exercises. In his personal work, the student needs to acquire the knowledge and the concepts of mathematical logic, and be able to solve the exercises that will be assigned and discussed in class.
The lecture course will present and discuss the following subjects:
Course notes and slides presented during the lectures will be available on aula@web, complemented by other material. Notes taken at the lectures and the material on aul@web are enough in preparation for the exam. The books listed below are good references.
Ebbinghaus, H.-D.; Flum, J.; Thomas, W. Mathematical logic. Springer.
Mac Lane, S. Categories for the working mathematician. Springer.
Office hours: By appointment.
Office hours: by appointment
ALESSANDRO DE STEFANI (President)
RICCARDO CAMERLO (President Substitute)
ALDO CONCA (President Substitute)
EMANUELA DE NEGRI (President Substitute)
STEFANO VIGNI (President Substitute)
ANNA MARIA BIGATTI (Substitute)
GIUSEPPE ROSOLINI (Substitute)
FRANCESCO VENEZIANO (Substitute)
The class will start according to the academic calendar.
All class schedules are posted on the EasyAcademy portal.
The exam consists of a written examination. The exams is on the topics of the lecture course and asks for the presentation of particular subjects taught in the course an the solution of exercises. The oral examination is a presentation and an open discussion fo subjects in the syllabus. The solution of the exercises assigned during the lessons can contribute to the final evaluation.
Students with DSA certification (specific learning disabilities), disability or other special educational needs are advised to contact the teachers at the beginning of the course to establish teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.
The exam verifies the actual acquisition of the mathematical knowledge of the basic notions of mathematical logic and evaluates the skills developed to use such knowledge in the analysis of mathematical theories by means of problems and open questions. It aims at evaluating that the student has acquired an appropriate level of knowledge and analytical skills. The evaluation takes into account the correctedness of the solutions, the clarity of the exposition, and the rigour of the arguments developed.