Sets and Integration An Outline of the Development
The present text resulted from lectures given by the authors at the Rijks Universiteit at Utrecht. These lectures were part of a series on 'History of Contemporary Mathematics'. The need for such an enterprise was generally felt, since the curriculum at many universities is designed to suit an efficient treatment of advanced subjects rather than to reflect the development of notions and techniques. As it is very likely that this trend will continue, we decided to offer lectures of a less technical nature to provide students and interested listeners with a survey of the history of topics in our present-day mathematics. We consider it very useful for a mathematician to have an acquaintance with the history of the development of his subject, especially in the nineteenth century where the germs of many of modern disciplines can be found. Our attention has therefore been mainly directed to relatively young developments. In the lectures we tried to stay clear of both oversimplification and extreme technicality. The result is a text, that should not cause difficulties to a reader with a working knowledge of mathematics. The developments sketched in this book are fundamental for many areas in mathematics and the notions considered are crucial almost everywhere. The book may be most useful, in particular, for those teaching mathematics.
Què en diuen els usuaris - Escriviu una ressenya
No hem trobat cap ressenya als llocs habituals.
The exploration of the new continent
Zermelo takes over
No s’hi han mostrat 9 seccions
Altres edicions - Mostra-ho tot
algebra already analysis appeared application axiom of choice axiomatic Borel bounded calculable called Cantor cardinals collection concept concerning considered consistent constructive contains continuous functions continuum countable Dedekind defined definition denoted derivative determined differential domain element equal equivalent example existence fact finite formulated Foundation Fraenkel function f functions gave geometry give given Gödel important independence infinite instance integral interesting interval introduced known later leading Lebesgue letter limit linear logic mapping Math mathematicians mathematics means measure mention method notion objects obtained operations ordinals paradox points possible principle problem proof properties proved published question reader refer relation remarks respect Riemann sense sequence set theory showed space studied subset surface theorem topology universe variable well-ordered Zermelo