Sets and integration An outline of the developmentSpringer Science & Business Media, 6 de des. 2012 - 162 pàgines 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. |
Des de l'interior del llibre
Resultats 1 - 5 de 55.
Pàgina vii
... 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 ...
... 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 ...
Pàgina 4
... notion of set . Looking back in history for phenomena that we associate with set theory , we notice that mathematicians and philosophers alike have been worried by infinity at a quite early stage . It would lead us too far to pay ...
... notion of set . Looking back in history for phenomena that we associate with set theory , we notice that mathematicians and philosophers alike have been worried by infinity at a quite early stage . It would lead us too far to pay ...
Pàgina 5
... notion of the infinite was BERNARD BOLZANO , a highly original and gifted mathematician , who unfortunately was ... notions . His terminology is somewhat cumbersome , but it is not hard to identify his terms in our terminology . Bolzano ...
... notion of the infinite was BERNARD BOLZANO , a highly original and gifted mathematician , who unfortunately was ... notions . His terminology is somewhat cumbersome , but it is not hard to identify his terms in our terminology . Bolzano ...
Pàgina 6
... notion of sequence , otherwise it would also cover ordinals . Also the notion of an infinite set can be introduced now : a set A is infinite if every finite set of elements of A is a proper subset of A ( early authors did not use the ...
... notion of sequence , otherwise it would also cover ordinals . Also the notion of an infinite set can be introduced now : a set A is infinite if every finite set of elements of A is a proper subset of A ( early authors did not use the ...
Pàgina 7
... notion of number on the notion of set ( or system , as he called it ) in order to reduce arithmetic to something independent of in- tuitive observation ( Anschauung ) , essentially to the direct consequences of the pure laws of thought ...
... notion of number on the notion of set ( or system , as he called it ) in order to reduce arithmetic to something independent of in- tuitive observation ( Anschauung ) , essentially to the direct consequences of the pure laws of thought ...
Continguts
7 | |
The paradoxes | 21 |
Zermelo takes over | 34 |
Making inconsistent sets respectable | 45 |
The consistency of the axiom of choice and the continuum hypothesis | 52 |
Large cardinals | 63 |
Introduction the period before Riemann | 77 |
Riemann Lebesgue real functions | 91 |
Modern theory of the integral | 133 |
Bibliography | 149 |
Index | 155 |
List of Mathematicians | 161 |
Altres edicions - Mostra-ho tot
Sets and Integration An Outline of the Development D. van Dalen,A. F. Monna Visualització de fragments - 1972 |
Frases i termes més freqüents
algebra analysis axiom of choice axiom of foundation axiomatic set theory Baire Bolzano Borel bounded variation Burali-Forti calculable called Cantor Carathéodory cardinals Cohen concept considered constructive continuous functions continuum hypothesis countable Dedekind defined definition Denjoy denoted dérivée differential domain element ensemble equivalent example existence finite formulated Fraenkel function f geometry Georg Cantor Gödel Grundlagen Heyenoort 61 Hilbert infinity instance interval introduced König Lebesgue Lebesgue measurable Lebesgue-integral Leçons linear logic mapping Math mathematicians mathematics mathématique Measurable cardinals measure theory Mengenlehre mention method modern natural numbers Neumann nombre notation notion objects one-one ordered sets ordinals paper paradox Peano Poincaré polyhedrons principle problem proof properties proved real functions real numbers remarks Riemann Riemann-integral second number class sequence set of reals Skolem space subset Tarski theorem topology transfinite urelements valeurs variable VOLTERRA well-ordered Zermelo ZF is consistent