Sets and integration : an outline of the development
D. Van Dalen (Author), A. F. Monna (Author)
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
1 online resource (VIII, 162 pages)
9789401027182, 9401027188
1097103075
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Set theory from Cantor to Cohen
Forebodings
The exploration of the new continent
The paradoxes
The axiom of choice
Zermelo takes over
Making inconsistent sets respectable
The consistency of the axiom of choice and the continuum hypothesis
The independence of the continuum hypothesis
Large cardinals
Games and strategies
The integral from Riemann to Bourbaki
Introduction; the period before Riemann
Riemann, Lebesgue, real functions
Modern theory of the integral
List of Mathematicians
Includes index
English