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 vi
... Perron 126 Further developments 129 Modern theory of the integral 133 Integrals as linear functions 133 Generalizations 141 Carathéodory 144 Haar - measure 146 Bibliography 149 Index 155 List of Mathematicians 161 VI.
... Perron 126 Further developments 129 Modern theory of the integral 133 Integrals as linear functions 133 Generalizations 141 Carathéodory 144 Haar - measure 146 Bibliography 149 Index 155 List of Mathematicians 161 VI.
Pàgina vii
... 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 ...
... 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 ...
Pàgina viii
... mathematicians of sundry back- grounds and that it may pass on some of the fascination that mathematics had for our predecessors . Several people read our manuscripts and helped us with suggestions and comments for which we are grateful ...
... mathematicians of sundry back- grounds and that it may pass on some of the fascination that mathematics had for our predecessors . Several people read our manuscripts and helped us with suggestions and comments for which we are grateful ...
Pàgina 4
... mathematicians into transfinitists ( who gladly swallow the axiom of choice and more ) and constructivists ( some of whom deny sense to the second number class ) . One could say that no branch of mathematics did more to send the ...
... mathematicians into transfinitists ( who gladly swallow the axiom of choice and more ) and constructivists ( some of whom deny sense to the second number class ) . One could say that no branch of mathematics did more to send the ...
Pàgina 5
... mathematicians carried over procedures and facts from the domain of the finite to the domain of the infinite with a ... mathematician , who unfortunately was somewhat isolated as a scholar . Bolzano wrote a monograph : " Paradoxien des ...
... mathematicians carried over procedures and facts from the domain of the finite to the domain of the infinite with a ... mathematician , who unfortunately was somewhat isolated as a scholar . Bolzano wrote a monograph : " Paradoxien des ...
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