Choquet G. What Is Modern Mathematics

Transl. from the French: C. Gattegno. — Educational Solutions, 1963. — 53 p.In spite of the subtitle I do not intend in this short text to embark upon the rash project of trying to read the mind of that many-headed genius Bourbaki.
However, since I am concerned with the whole of analysis, and since Bourbaki has such clear-cut concepts and is so intimately associated with the development of mathematics in our time, we can hope that a study of 'his' philosophical and mathematical work may lead us to the essence of modern trends in analysis.
Such a study may serve to develop for all levels of education a teaching of mathematics better adapted to the needs of our time and to the level of awareness of our generation.Presentation
Foreword
The Axiomatic Method
Structures
Characteristics of the Axiomatic method
Dangers of the axiomatic method
Some of the tools of axiomatics
Morphisms
Universal Applications
Categories and Functors
Discovery methods linked with axiomatic method
The loosening of axioms
The tightening of the axioms
Study of structures not too different
Generation of structures answering given requirements
Some characteristics of Bourbaki's contribution to analysis
Axiomatics and multivalency
Bourbaki is essentially an algebraist
The constant renewal of the Opus
Choice of definitions
Choice of contents and theorems
Modern analysis in the world today
The impact upon modern mathematics educationФайл: отскан. стр. (b/w 600 dpi) + OCR