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 6 - 10 de 67.
Pàgina 8
... mathematics and logic , exten- sively criticized the psychological undertones in contemporary contributions to the 6 ) However with different terminology and notation . 7 ) The same definition was proposed by Pierce in 1885 [ 105 ] ...
... mathematics and logic , exten- sively criticized the psychological undertones in contemporary contributions to the 6 ) However with different terminology and notation . 7 ) The same definition was proposed by Pierce in 1885 [ 105 ] ...
Pàgina 9
... mathematics an extremely elegant foundation of arithmetic based on set theory , the development of pure set theory is the work of that highly gifted and original mathematician , Georg Cantor . In the same year ( 1888 ) of the appearence ...
... mathematics an extremely elegant foundation of arithmetic based on set theory , the development of pure set theory is the work of that highly gifted and original mathematician , Georg Cantor . In the same year ( 1888 ) of the appearence ...
Pàgina 10
... mathematics . Here for the first time the uncountability of a set was established . Earlier , only the vague distinction finite - infinite was known , but here we already have two different kinds of infinity ! Probably , countability ...
... mathematics . Here for the first time the uncountability of a set was established . Earlier , only the vague distinction finite - infinite was known , but here we already have two different kinds of infinity ! Probably , countability ...
Pàgina 11
... mathematical deductions , based on the fallacy of the invariance of dimension , are inadmissable " . Dedekind , being a solid mathemati- cian , not subjected to rash conclusions , warns Cantor ( 2-7-1877 ) not to indulge in polemics ...
... mathematical deductions , based on the fallacy of the invariance of dimension , are inadmissable " . Dedekind , being a solid mathemati- cian , not subjected to rash conclusions , warns Cantor ( 2-7-1877 ) not to indulge in polemics ...
Pàgina 12
... of a general theory of manifolds . 11 ) On various viewpoints concerning the actual infinite . 12 ) Communications on the theory of the Transfinite . In the mathematical world , opposition against Cantor was lead 127 D. van Dalen.
... of a general theory of manifolds . 11 ) On various viewpoints concerning the actual infinite . 12 ) Communications on the theory of the Transfinite . In the mathematical world , opposition against Cantor was lead 127 D. van Dalen.
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