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Adriaen Brouwer : zo zijn leven, zo zijn werk
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ISBN: 9789082301069 Year: 2018 Publisher: Oudenaarde Uitgeverij Beatrijs

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From Sperner's Lemma to Differential Equations in Banach Spaces : An Introduction to Fixed Point Theorems and their Applications
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ISBN: 1000042944 3731502607 Year: 2014 Publisher: KIT Scientific Publishing

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Based on Sperner's lemma the fixed point theorem of Brouwer is proved. Rather than presenting also other beautiful proofs of Brouwer's fixed point theorem, many nice applications are given in some detail. Also Schauder's fixed point theorem is presented which can be viewed as a natural generalization of Brouwer's fixed point theorem to an infinite-dimensional setting. Finally, Tarski's fixed point theorem is applied to differential equations in Banach spaces.


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One hundred years of intuitionism (1907-2007) : the Cerisy conference
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ISBN: 1281876615 9786611876616 3764386533 3764386525 Year: 2008 Publisher: Basel ; Boston : Birkhauser,

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With logicism and formalism, intuitionism is one of the main foundations for mathematics proposed in the twentieth century; and since the seventies, notably its views on logic have become important also outside foundational studies, with the development of theoretical computer science. The aim of the book is threefold: to review and complete the historical account of intuitionism; to present recent philosophical work on intuitionism; and to give examples of new technical advances and applications of intuitionism. This volume brings together 21 contributions by today's leading authors on these topics, and surveys the philosophical, logical and mathematical implications of the approach initiated in 1907 in L.E.J. Brouwer's dissertation.

Brouwer meets Husserl : on the phenomenology of choice sequences
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ISBN: 1280656913 9786610656912 1402050879 Year: 2007 Publisher: Dordrecht ; [Great Britain] : Springer,

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Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? The mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. But other mathematicians and philosophers have been voicing objections to choice sequences from the start. This book aims to provide a sound philosophical basis for Brouwer's choice sequences by subjecting them to a phenomenological critique in the style of the later Husserl. "It is almost as if one could hear the two rebels arguing their case in a European café or on a terrace, and coming to a common understanding, with both men taking their hat off to the other, in admiration and gratitude. Dr. van Atten has convincingly applied Husserl's method to Brouwer's program, and has equally convincingly applied Brouwer's intuition to Husserl's program. Both programs have come out the better." Piet Hut, professor of Interdisciplinary Studies, Institute for Advanced Study, Princeton, U.S.A.


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Matt Mullican : works 1972-1992
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ISBN: 3883751839 Year: 1993 Publisher: Köln : W. König,

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