Master's degree in Mathematics

Axiomatization of geometry (seminar course)

Course code
4S001112
Name of lecturer
Enrico Gregorio
Coordinator
Enrico Gregorio
Number of ECTS credits allocated
6
Academic sector
MAT/02 - ALGEBRA
Language of instruction
English
Period
I semestre dal Oct 1, 2019 al Jan 31, 2020.

Lesson timetable

Go to lesson schedule

Learning outcomes

Introduction to the historical axiomatization of Euclidean geometry, comparing it with the modern axiomatizations, in particular Hilbert's.

Syllabus

Euclid's axioms
Implicit axioms
Axiom of parallels
Hilbert's axioms
Erlangen program and models of geometries

Assessment methods and criteria

Seminar presentation of a topic in line with the course, for instance a geometric system alternative to the Euclidean-Hilbertian or the analysis of the consequences of different axioms.

Criteri di valutazione:

• Knowledge and understanding: understanding of the axiomatic approach and knowledge of the presented theory.

• Applying knowledge and understanding: ability to apply the axiomatic method to different situations.

• Making judgements: ability to synthesize from various sources.

• Communication skills: language clarity and appropriateness.

• Learning skills: ability to read texts chosen in autonomy.





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