A remarkable and independent thinker, Luitzen Egbertus Jan Brouwer was a leader in twentieth century mathematics and in Dutch cultural life, where he was the key figure in a number of controversial issues, including a campaign to reverse the boycott of German scientists. In mathematics, he was a founder of modern topology and the creator of intuitionism, one of the most important schools of thought on the philosophy of mathematics. This biography discusses his fascinating life and provides a detailed analysis of his work.

Mystic, Geometer, and Intuitionist: The Life of L. E. J. BrouwerVolume 1: The Dawning Revolution

Biographies & Memoirs

van Dalen, Dirk.

Professionals & Academics

Oxford University Press

Luitzen Egbertus Jan Brouwer is a remarkable figure, both in the development of mathematics and in wider Dutch history. A mathematical genius with strong mystical and philosophical leanings, he advocated the intuitionist view of mathematics and science as a constructive mental activity. This drew him into a discussion with David Hilbert, the leading advocate of the formalist school, about the nature of mathematics, a debate which made Brouwer a legend during his lifetime. He also contributed significantly to research in topology, and was a member of the socio-linguistic Signific Circle. As well as his diverse mathematical interests he had a great impact in wider Dutch society. His keen sense of justice made him a party in many conflicts, both scientific and political. He would often be involved in controversial issues, such as the campaign to undo the boycott of German scientists, and this made him a figure both of admiration and embarrassment in his native Holland. Although his abilities won him offers from prestigious universities such as Berlin and Gottingen, he preferred to stay in Amsterdam, so that he could pursue a life of quiet unconventionality in the artist community at Laren. This book, the second in a two-volume set, provides a sophisticated analysis of this crucial era of mathematical research, but also gives an important insight into the wider life of one of the most fascinating characters involved.

Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer

A book which efficiently presents the basics of propositional and predicate logic, van Dalen's popular textbook contains a complete treatment classical logic on the basis of Gentzen's Natural Deduction and the traditional two-valued semantics, culminating in the completeness theorems. The first chapter, containing a leisured treatment of propostional logic, is followed by an equally elaborate chapter on predicate logic. On the basis of the material of the first of two chapters the completeness theorem is established and an excursion is made into model theory. The main facts of model theory, e.g. compactness, Skolem-Loewenheim, elementary equivalence, non-standard models, quantified elimination and Skolem functions are covered in chapter Three. The exposition of classical logic is rounded off with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, one chapter is devoted to intuitionistic logic. This chapter contains a completeness proof for Kripke's semantics and a number of specific constructive features have been incorporated, e.g. a study of equality and apartness the disjunction and existence property, the Goedel translation. A new chapter has been added at the end of this edition, with the basics of the proof theory of natural deduction; derivations are studued for their own sake and weak normalisation is proved. A choise of exercises is added ranging from simple applications of the definitions to more sophisticated problems.

Logic and Structure (Universitext)

Politics & Social Sciences

Philosophy

Springer, Verlag

Dirk van Dalen’s popular textbook, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel’s famous incompleteness theorem. Includes a new section on ultra-products.

Science & Math

Mathematics

Springer

Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.

L.E.J. Brouwer – Topologist, Intuitionist, Philosopher: How Mathematics Is Rooted in Life

Reference

Dirk van Dalen's biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer.Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics.Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer's main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name 'intuitionism'. This made him one of the main protagonists in the 'foundation crisis' of mathematics.As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role.The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.

Inverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms for solving inverse scattering problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques. The limitations of these methods have led in recent years to an alternative approach to the inverse scattering problem which avoids the incorrect model assumptions inherent in the use of weak scattering approximations as well as the strong a priori information needed in order to implement nonlinear optimization techniques. These new methods come under the general title of qualitative methods in inverse scattering theory and seek to determine an approximation to the shape of the scattering object as well as estimates on its material properties without making any weak scattering assumption and using essentially no a priori information on the nature of the scattering object. This book is designed to be an introduction to this new approach in inverse scattering theory focusing on the use of sampling methods and transmission eigenvalues. In order to aid the reader coming from a discipline outside of mathematics we have included background material on functional analysis, Sobolev spaces, the theory of ill posed problems and certain topics in in the theory of entire functions of a complex variable. This book is an updated and expanded version of an earlier book by the authors published by Springer titled Qualitative Methods in Inverse Scattering Theory Review of Qualitative Methods in Inverse Scattering Theory All in all, the authors do exceptionally well in combining such a wide variety of mathematical material and in presenting it in a well-organized and easy-to-follow fashion. This text certainly complements the growing body of work in inverse scattering and should well suit both new researchers to the field as well as those who could benefit from such a nice codified collection of profitable results combined in one bound volume. SIAM Review, 2006

O livro-texto popular de Dirk van Dalen, Lógica e Estrutura, agora em sua quinta edição, oferece uma introdução abrangente aos fundamentos da lógica clássica e da lógica intuicionística, da teoria dos modelos e do famoso teorema da incompletude de Gödel. A lógica proposicional e a lógica de predicados são apresentadas num estilo fácil de ler usando a dedução natural de Gentzen. O livro prossegue com alguns conceitos e fatos básicos da teoria dos modelos: uma discussão sobre compaccidade, Skolem-Löwenheim, modelos não-padrão e eliminação de quantificadores. A discussão da lógica clássica é encerrada com uma exposição concisa da lógica de segunda ordem. Em vista do crescente reconhecimento de métodos e princípios construtivos, a lógica intuicionística e a semântica de Kripke são cuidadosamente exploradas. Uma série de características construtivas específicas, como a separação e a igualdade, a tradução de Gödel, as propriedades da disjunção e da existência também foram incluídas. O último capítulo sobre o primeiro teorema da incompletude de Gödel é autocontido e fornece uma exposição sistemática da teoria da recursão necessária. Esta nova edição foi devidamente revisada e contém uma nova seção sobre ultraprodutos.

Logica e Estrutura (Portuguese Edition)

College Publications

Logic and structure (Universitext)

See the best price to sell, buy, or rent books by van Dalen, Dirk.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by van Dalen, Dirk.

See the best price to sell, buy, or rent books by van Dalen, Dirk.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Mystic, Geometer, and Intuitionist: The Life of L. E. J. BrouwerVolume 1: The Dawning Revolution

Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer

Logic and Structure (Universitext)

Logic and Structure (Universitext)

L.E.J. Brouwer – Topologist, Intuitionist, Philosopher: How Mathematics Is Rooted in Life

L.E.J. Brouwer – Topologist, Intuitionist, Philosopher: How Mathematics Is Rooted in Life

Logic and Structure (Universitext)

Logica e Estrutura (Portuguese Edition)

Logic and Structure (Universitext)