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Author: Luitzen Egbertus Jan Brouwer
Publisher: North Holland
ISBN: 9780444106438
Category : Mathematics
Languages : en
Pages : 706
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Book Description
L.E.J. Brouwer Collected Works ...
Author: Luitzen Egbertus Jan Brouwer
Publisher: North Holland
ISBN: 9780444106438
Category : Mathematics
Languages : en
Pages : 706
Get Book
Book Description
L.E.J. Brouwer Collected Works ...
Author: A. Heyting
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages :
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Book Description
Author: A. Heyting
Publisher: Elsevier
ISBN: 1483278158
Category : Mathematics
Languages : de
Pages : 644
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Book Description
L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examines mathematics and experience and mathematics and logic. Topics include denumerably unfinished sets, continuum problem, logic of relations, consistency proofs for formal systems independent of their interpretation, infinite numbers, and problems of space and time. The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.
Author: Hans Freudenthal
Publisher: Elsevier
ISBN: 1483257541
Category : Mathematics
Languages : en
Pages : 734
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Book Description
L. E. J. Brouwer Collected Works, Volume 2: Geometry, Analysis, Topology, and Mechanics focuses on the contributions and principles of Brouwer on geometry, topology, analysis, and mechanics, including non-Euclidean spaces, integrals, and surfaces. The publication first ponders on non-Euclidean spaces and integral theorems, lie groups, and plane transition theorem. Discussions focus on remarks on multiple integrals, force field of the non-Euclidean spaces with negative curvature, difference quotients and differential quotients, characterization of the Euclidean and non-Euclidean motion groups, and continuous one-one transformations of surfaces in themselves. The book also takes a look at vector fields on surfaces and new methods in topology, including continuous vector distributions on surfaces and orthogonal trajectories of the orbits of a one parameter plane projective group. The book then ponders on mechanics and topology of surfaces, as well as the motion of a particle on the bottom of a rotating vessel under the influence of gravitational force. The publication is a valuable reference for researchers interested in geometry, topology, analysis, and mechanics.
Author: Martin H Krieger
Publisher: World Scientific
ISBN: 9814571865
Category : Mathematics
Languages : en
Pages : 492
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Book Description
Doing Mathematics discusses some ways mathematicians and mathematical physicists do their work and the subject matters they uncover and fashion. The conventions they adopt, the subject areas they delimit, what they can prove and calculate about the physical world, and the analogies they discover and employ, all depend on the mathematics — what will work out and what won't. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connections between algebra and topology, and the series of rigorous proofs of the stability of matter. The many and varied solutions to the two-dimensional Ising model of ferromagnetism make sense as a whole when they are seen in an analogy developed by Richard Dedekind in the 1880s to algebraicize Riemann's function theory; by Robert Langlands' program in number theory and representation theory; and, by the analogy between one-dimensional quantum mechanics and two-dimensional classical statistical mechanics. In effect, we begin to see "an identity in a manifold presentation of profiles," as the phenomenologists would say. This second edition deepens the particular examples; it describe the practical role of mathematical rigor; it suggests what might be a mathematician's philosophy of mathematics; and, it shows how an "ugly" first proof or derivation embodies essential features, only to be appreciated after many subsequent proofs. Natural scientists and mathematicians trade physical models and abstract objects, remaking them to suit their needs, discovering new roles for them as in the recent case of the Painlevé transcendents, the Tracy-Widom distribution, and Toeplitz determinants. And mathematics has provided the models and analogies, the ordinary language, for describing the everyday world, the structure of cities, or God's infinitude. Contents:IntroductionConvention: How Means and Variances are Entrenched as StatisticsSubject: The Fields of TopologyAppendix: The Two-Dimensional Ising Model of a FerromagnetCalculation: Strategy, Structure, and Tactics in Applying Classical AnalysisAnalogy: A Syzygy Between a Research Program in Mathematics and a Research Program in PhysicsIn Concreto: The City of MathematicsAppendices:The Spontaneous Magnetization of a Two-Dimensional Ising Model (C N Yang)On the Dirac and Schwinger Corrections to the Ground-State Energy of an Atom (C Fefferman and L A Seco)Sur la Forme des Espaces Topologiques et sur les Points Fixes des Représentations (J Leray)Une Lettre à Simone Weil (A Weil) Readership: Mathematicians, physicists, philosophers and historians of science. Keywords:Means and Variances;Topology;SyzygyReviews: Reviews of the First Edition: "The book Doing Mathematics, by Martin Krieger is truly a masterpiece. He has not only explained ways of doing mathematical work to aspiring mathematicians and the intelligent laymen, but has also shown how various pieces of research work are related to each other. Even experts may not have realized such inter-relations. The cases studied include, especially, the stability of matter and the Ising model, two topics of great depth. Such clear explanations cannot be found anywhere else. Furthermore, his style of writing makes the book exceptionally enjoyable to read." T T Wu Gordon McKay Professor of Applied Physics Professor of Physics, Harvard University, USA "This is the first time I have seen a mathematician deal substantively with the issue of mathematics as culturally based, and he does it superbly and mathematically … Although this book is no easy read, it is well worth the effort, and I am sure it will stimulate and inform, perhaps even surprise, the most sophisticated of mathematical readers. It is refreshing to find such a book being published." Mathematical Reviews "Both challenging and provocative reading, Doing Mathematics sheds bright light on some of the main characteristics of the mathematical quest." Library of Science "Krieger has made some effort to accommodate different levels of readers; for example, structuring his text so that lay readers are alerted to sections that can be safely skipped and paragraphs that provide nontechnical summaries." Mathematical Association of America
Author: Luitzen Egbertus Jan Brouwer
Publisher:
ISBN:
Category :
Languages : en
Pages : 706
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Book Description
Author: Luitzen Egbertus Jan Brouwer
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Teun Koetsier
Publisher: Elsevier
ISBN: 9780080457352
Category : Mathematics
Languages : en
Pages : 716
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Book Description
Mathematics and the Divine seem to correspond to diametrically opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn’t the Divine that which is immeasurable ? The present book shows that the domains of mathematics and the Divine, which may seem so radically separated, have throughout history and across cultures, proved to be intimately related. Religious activities such as the building of temples, the telling of ritual stories or the drawing of enigmatic figures all display distinct mathematical features. Major philosophical systems dealing with the Absolute and theological speculations focussing on our knowledge of the Ultimate have been based on or inspired by mathematics. A series of chapters by an international team of experts highlighting key figures, schools and trains of thought is presented here. Chinese number mysticism, the views of Pythagoras and Plato and their followers, Nicholas of Cusa's theological geometry, Spinozism and intuitionism as a philosophy of mathematics are treated side by side among many other themes in an attempt at creating a global view on the relation of mathematics and Man’s quest for the Absolute in the course of history. · Mathematics and man's quest for the Absolute · A selective history highlighting key figures, schools and trains of thought · An international team of historians presenting specific new findings as well as general overviews · Confronting and uniting otherwise compartmentalized information
Author: Michael Detlefsen
Publisher: Routledge
ISBN: 1134916760
Category : Education
Languages : en
Pages : 170
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Book Description
Distinguished contributors tackle the main problem that arizes when considering an epistemology for mathematics, the nature and sources of mathematical justification.
Author: Dirk von Dalen
Publisher: Springer Science & Business Media
ISBN: 0857295373
Category : Mathematics
Languages : en
Pages : 532
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Book Description
L.E.J. Brouwer (1881-1966) is best known for his revolutionary ideas on topology and foundations of mathematics (intuitionism). The present collection contains a mixture of letters; university and faculty correspondence has been included, some of which shed light on the student years, and in particular on the exchange of letters with his PhD adviser, Korteweg. Acting as the natural sequel to the publication of Brouwer’s biography, this book provides instrumental reading for those wishing to gain a deeper understanding of Brouwer and his role in the twentieth century. Striking a good balance of biographical and scientific information, the latter deals with innovations in topology (Cantor-Schoenflies style and the new topology) and foundations. The topological period in his research is well represented in correspondence with Hilbert, Schoenflies, Poincaré, Blumenthal, Lebesgue, Baire, Koebe, and foundational topics are discussed in letters exchanged with Weyl, Fraenkel, Heyting, van Dantzig and others. There is also a large part of correspondence on matters related to the interbellum scientific politics. This book will appeal to both graduate students and researchers with an interest in topology, the history of mathematics, the foundations of mathematics, philosophy and general science.
