Discrete Thoughts

ESSAYS ON MATHEMATICS, Science, and Philosophy

Author: KAC,ROTA,SCHWARTZ

Publisher: Springer Science & Business Media

ISBN: 1489966676

Category: Mathematics

Page: 264

View: 4250

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Gaither's Dictionary of Scientific Quotations

A Collection of Approximately 27,000 Quotations Pertaining to Archaeology, Architecture, Astronomy, Biology, Botany, Chemistry, Cosmology, Darwinism, Engineering, Geology, Mathematics, Medicine, Nature, Nursing, Paleontology, Philosophy, Physics, Probability, Science, Statistics, Technology, Theory, Universe, and Zoology

Author: Carl C. Gaither,Alma E. Cavazos-Gaither

Publisher: Springer Science & Business Media

ISBN: 1461411130

Category: Science

Page: 2770

View: 4297

This unprecedented collection of 27,000 quotations is the most comprehensive and carefully researched of its kind, covering all fields of science and mathematics. With this vast compendium you can readily conceptualize and embrace the written images of scientists, laymen, politicians, novelists, playwrights, and poets about humankind's scientific achievements. Approximately 9000 high-quality entries have been added to this new edition to provide a rich selection of quotations for the student, the educator, and the scientist who would like to introduce a presentation with a relevant quotation that provides perspective and historical background on his subject. Gaither's Dictionary of Scientific Quotations, Second Edition, provides the finest reference source of science quotations for all audiences. The new edition adds greater depth to the number of quotations in the various thematic arrangements and also provides new thematic categories.
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Bernhard Riemann 1826–1866

Wendepunkte in der Auffassung der Mathematik

Author: Detlef Laugwitz

Publisher: Springer-Verlag

ISBN: 3034889836

Category: Mathematics

Page: 348

View: 7368

Das Riemannsche Integral lernen schon die Schüler kennen, die Theorien der reellen und der komplexen Funktionen bauen auf wichtigen Begriffsbildungen und Sätzen Riemanns auf, die Riemannsche Geometrie ist für Einsteins Gravitationstheorie und ihre Erweiterungen unentbehrlich, und in der Zahlentheorie ist die berühmte Riemannsche Vermutung noch immer offen. Riemann und sein um fünf Jahre jüngerer Freund Richard Dedekind sahen sich als Schüler von Gauss und Dirichlet. Um die Mitte des 19. Jahrhunderts leiteten sie den Übergang zur "modernen Mathematik" ein, der eine in Analysis und Geometrie, der andere in der Algebra mit der Hinwendung zu Mengen und Strukturen. Dieses Buch ist der erste Versuch, Riemanns wissenschaftliches Werk unter einem einheitlichen Gesichtspunkt zusammenzufassend darzustellen. Riemann gilt als einer der Philosophen unter den Mathematikern. Er stellte das Denken in Begriffen neben die zuvor vorherrschende algorithmische Auffassung von der Mathematik, welche die Gegenstände der Untersuchung, in Formeln und Figuren, in Termumformungen und regelhaften Konstruktionen als die allein legitimen Methoden sah. David Hilbert hat als Riemanns Grundsatz herausgestellt, die Beweise nicht durch Rechnung, sondern lediglich durch Gedanken zu zwingen. Hermann Weyl sah als das Prinzip Riemanns in Mathematik und Physik, "die Welt als das erkenntnistheoretische Motiv..., die Welt aus ihrem Verhalten im un- endlich kleinen zu verstehen."
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Classics of Mathematics

Author: Ronald Calinger

Publisher: Pearson College Division

ISBN: 9780023183423

Category: Mathematics

Page: 793

View: 5004

Appropriate for undergraduate and select graduate courses in the history of mathematics, and in the history of science. This edited volume of readings contains more than 130 selections from eminent mathematicians from A `h-mose' to Hilbert and Noether. The chapter introductions comprise a concise history of mathematics based on critical textual analysis and the latest scholarship. Each reading is preceded by a substantial biography of its author.
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Perspectives on Science

Historical, Philosophical, Social

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Science

Page: N.A

View: 3449

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Choice

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Best books

Page: N.A

View: 8040

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Information-gap Decision Theory

Decisions Under Severe Uncertainty

Author: Yakov Ben-Haim

Publisher: N.A

ISBN: 9780120882519

Category: Technology & Engineering

Page: 330

View: 9095

Information-Gap Decision Theory presents a distinctive new theory of decision-making under severe uncertainty. Applications in engineering design and analysis, project management, economics, strategic planning, social decision making, environmental management, medical decisions, search and evasion problems, risk assessment, and other areas are discussed. Info-gap theory deals with many of the problems and questions of classical decision analysis such as risk assessment, gambling, value of information, trade-off analysis, and preference reversal, but the distinctive character of info-gap uncertainty repeatedly gives rise to new insights and unique decision algorithms. Furthermore, this book deals with many of the difficult interface issues facing the responsible decision maker such as value judgments concerning risk and immunity to failure, as well as philosophical implications of decision under uncertainty. This book is a fresh approach to the age-old problem of deciding responsibly with deficient information. An info-gap is the disparity between what is known and what needs to be known in order to make a well-founded decision. The book begins with a discussion of info-gap models of uncertainty, which provides an innovative approach to the quantification of severe lack of information. This book can be used in advanced undergraduate and graduate courses on decision theory and risk analysis. It is also of interest to practicing decision analysts and to researchers in decision theory and in human decision-making.
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History of Science

Author: Alistair Cameron Crombie,Michael A. Hoskin

Publisher: N.A

ISBN: N.A

Category: Science

Page: N.A

View: 381

A review of literature and research in the history of science, medicine and technology in its intellectual and social context.
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New Dictionary of Scientific Biography

Author: Noretta Koertge

Publisher: Scribner

ISBN: N.A

Category: Science

Page: 7

View: 5704

Also available online as part of the Gale Virtual Reference Library under the title Complete dictionary of scientific biography.
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Experience and Theory

An Essay in the Philosophy of Science

Author: Stephan Korner

Publisher: Routledge

ISBN: 1135028370

Category: Reference

Page: 272

View: 1841

Originally published in 1966. This volume analyzes the general structure of scientific theories, their relation to experience and to non-scientific thought. Part One is concerned with the logic underlying empirical discourse before its subjection to the various constraints, imposed by the logico-mathematical framework of scientific theories upon their content. Part Two is devoted to an examination of this framework and, in particular, to showing that the deductive organization of a field of experience is by that very act a modification of empirical discourse and an idealization of its subject matter. Part Three analyzes the concordance between theories and experience and the relevance of science to moral and religious beliefs.
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Thinking about Godel and Turing

Essays on Complexity, 1970-2007L

Author: Gregory J. Chaitin

Publisher: World Scientific

ISBN: 9812708979

Category: Computational complexity

Page: 368

View: 9734

Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as GAdel and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of GAdel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity."
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