Advanced course in Foundations of Mathematics (2009/2010)

Course code
4S02854
Name of lecturer
Ruggero Ferro
Coordinator
Ruggero Ferro
Number of ECTS credits allocated
6
Academic sector
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
Language of instruction
Italian
Location
VERONA
Period
2nd Semester dal Mar 1, 2010 al Jun 15, 2010.

Lesson timetable

Learning outcomes

To develop a critical and conscious attitude towards different views of mathematics. Reasons for, analysis, and relevance of the mathematical notions.

Syllabus

Greek viewpoint of mathematics. Mathematics as a prototype of deductive science. The problem of infinity. First crisis of the foundations of mathematics. The problem of the consistency of theories. Reduction of a theory to another. Different viewpoints of mathematics: neo-platonic, logicist, formalist, constructivist. Second crisis of the foundations of mathematics. Effective computability. The problem of communicating mathematical concepts through the language. Beyond the language. How to capture and communicate concepts which are non definable through the language. The problems of objectivity, certainty and relevance of the mathematical knowledge.

Assessment methods and criteria

Open questions written test and possible oral integration.