Principia Mathematica to *56


Author: Alfred North Whitehead,Bertrand Russell
Publisher: Cambridge University Press
ISBN: 9780521626064
Category: Mathematics
Page: 410
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The great three-volume Principia Mathematica (CUP 1927) is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, establishing that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will of course wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part I (in which the logical properties of propositions, propositional functions, classes and relations are established); section A of Part II (dealing with unit classes and couples); and Appendices A and C (which give further developments of the argument on the theory of deduction and truth functions).

Future Sustainable Ecosystems

Complexity, Risk, and Uncertainty
Author: Nathaniel K Newlands
Publisher: CRC Press
ISBN: 131535666X
Category: Mathematics
Page: 389
View: 8276

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Future Sustainable Ecosystems: Complexity, Risk, Uncertainty provides an interdisciplinary, integrative overview of environmental problem-solving using statistics. It shows how statistics can be used to solve diverse environmental and socio-economic problems involving food, water, energy scarcity, and climate change risks. It synthesizes interdisciplinary theory, concepts, definitions, models and findings involved in complex global sustainability problem-solving, making it an essential guide and reference. It includes real-world examples and applications making the book accessible to a broader interdisciplinary readership. Discussions include a broad, integrated perspective on sustainability, integrated risk, multi-scale changes and impacts taking place within ecosystems worldwide. State-of-the-art statistical techniques, including Bayesian hierarchical, spatio-temporal, agent-based and game-theoretic approaches are explored. The author then focuses on the real-world integration of observational and experimental data and its use within statistical models. The book clarifies how complex adaptive systems theory frames sustainability as a probabilistic (i.e., stochastic) problem, highlighting the importance of adaptive policy, science and institutional arrangements, for strengthening ecosystem adaptation and resilience. The author elucidates how we must transform our thinking, illuminating the benefits and opportunities offered by the integrative risk approach to innovation and learning in the Cognitive/Risk Era. The book highlights the importance of statistics in guiding, designing and delivering real-world solutions and helping to unravel the complex array of tradeoffs, uncertainties, inter-dependencies and unforeseen risks.

The Evolution of Principia Mathematica

Bertrand Russell's Manuscripts and Notes for the Second Edition
Author: Bernard Linsky
Publisher: Cambridge University Press
ISBN: 1139497332
Category: Mathematics
Page: N.A
View: 9483

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Originally published in 1910, Principia Mathematica led to the development of mathematical logic and computers and thus to information sciences. It became a model for modern analytic philosophy and remains an important work. In the late 1960s the Bertrand Russell Archives at McMaster University in Canada obtained Russell's papers, letters and library. These archives contained the manuscripts for the new Introduction and three Appendices that Russell added to the second edition in 1925. Also included was another manuscript, 'The Hierarchy of Propositions and Functions', which was divided up and re-used to create the final changes for the second edition. These documents provide fascinating insight, including Russell's attempts to work out the theorems in the flawed Appendix B, 'On Induction'. An extensive introduction describes the stages of the manuscript material on the way to print and analyzes the proposed changes in the context of the development of symbolic logic after 1910.

Colours in the development of Wittgenstein’s Philosophy


Author: Marcos Silva
Publisher: Springer
ISBN: 3319569198
Category: Philosophy
Page: 380
View: 9892

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This book presents and discusses the varying and seminal role which colour plays in the development of Wittgenstein’s philosophy. Having once said that “Colours spur us to philosophize”, the theme of colour was one to which Wittgenstein returned constantly throughout his career. Ranging from his Notebooks, 1914-1916 and the Tractatus Logico-Philosophicus to the posthumously published Remarks on Colours and On Certainty, this book explores how both his view of philosophical problems generally and his view on colours specifically changed considerably over time. Paying particular attention to his so-called intermediary period, it takes a case-based approach to the presentation of colour in texts from this period, from Some Remarks on Logical Form and Philosophical Remarks to his Big Typescript.

Algebraic Graph Theory


Author: Norman Biggs
Publisher: Cambridge University Press
ISBN: 9780521458979
Category: Mathematics
Page: 205
View: 1003

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This is a substantial revision of a much-quoted monograph, first published in 1974. The structure is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of 'Additional Results' are included at the end of each chapter, thereby covering most of the major advances in the last twenty years. Professor Biggs' basic aim remains to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first part, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject which has strong links with the 'interaction models' studied in theoretical physics, and the theory of knots. The last part deals with symmetry and regularity properties. Here there are important connections with other branches of algebraic combinatorics and group theory. This new and enlarged edition this will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists.

A First Course in General Relativity


Author: Bernard Schutz
Publisher: Cambridge University Press
ISBN: 0521887054
Category: Science
Page: 393
View: 5478

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Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.

Adventures of Ideas


Author: Alfred North Whitehead
Publisher: Simon and Schuster
ISBN: 0029351707
Category: Philosophy
Page: 307
View: 1532

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The title of this book, Adventures of Ideas, bears two meanings, both applicable to the subject-matter. One meaning is the effect of certain ideas in promoting the slow drift of mankind towards civilization. This is the Adventure of Ideas in the history of mankind. The other meaning is the author's adventure in framing a speculative scheme of ideas which shall be explanatory of the historical adventure.

Notes on Logic and Set Theory


Author: P. T. Johnstone
Publisher: Cambridge University Press
ISBN: 9780521336925
Category: Mathematics
Page: 110
View: 3523

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A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics.

Reason, Truth and History


Author: Hilary Putnam
Publisher: Cambridge University Press
ISBN: 1139935666
Category: Philosophy
Page: N.A
View: 3811

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Hilary Putnam deals in this book with some of the most fundamental persistent problems in philosophy: the nature of truth, knowledge and rationality. His aim is to break down the fixed categories of thought which have always appeared to define and constrain the permissible solutions to these problems.

An Introduction to Harmonic Analysis


Author: Yitzhak Katznelson
Publisher: Cambridge University Press
ISBN: 9780521543590
Category: Mathematics
Page: 314
View: 1350

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First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.

Einstein's Heroes

Imagining the World Through the Language of Mathematics
Author: Robyn Arianrhod
Publisher: Oxford University Press
ISBN: 9780195308907
Category: Biography & Autobiography
Page: 336
View: 5785

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Blending science, history, and biography, this book reveals the mysteries of mathematics, focusing on the life and work of three of Albert Einstein's heroes: Isaac Newton, Michael Faraday, and James Clerk Maxwell.

Smooth Compactifications of Locally Symmetric Varieties


Author: Avner Ash,Peter Scholze
Publisher: Cambridge University Press
ISBN: 0521739551
Category: Mathematics
Page: 230
View: 4370

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The new edition of this celebrated and long-unavailable book preserves the original book's content and structure and its unrivalled presentation of a universal method for the resolution of a class of singularities in algebraic geometry.

New Theory about Light and Colour


Author: Sir Isaac Newton
Publisher: Library of Alexandria
ISBN: 1465595619
Category:
Page: N.A
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To perform my late promise to you, I shall without further ceremony acquaint you, that in the beginning of the Year 1666 (at which time I applyed my self to the grinding of Optick glasses of other figures than Spherical,) I procured me a Triangular glass-Prisme, to try therewith the celebrated Phænomena of Colours. And in order thereto having darkened my chamber, and made a small hole in my window-shuts, to let in a convenient quantity of the Suns light, I placed my Prisme at his entrance, that it might be thereby refracted to the opposite wall. It was at first a very pleasing divertisement, to view the vivid and intense colours produced thereby; but after a while applying my self to consider them more circumspectly, I became surprised to see them in an oblong form; which, according to the received laws of Refraction, I expected should have been circular. They were terminated at the sides with streight lines, but at the ends, the decay of light was so gradual, that it was difficult to determine justly, what was their figure; yet they seemed semicircular. Comparing the length of this coloured Spectrum with its breadth, I found it about five times greater; a disproportion so extravagant, that it excited me to a more then ordinary curiosity of examining, from whence it might proceed. I could scarce think, that the various Thickness of the glass, or the termination with shadow or darkness, could have any Influence on light to produce such an effect; yet I thought it not amiss, first to examine those circumstances, and so tryed, what would happen by transmitting light through parts of the glass of divers thicknesses, or through holes in the window of divers bignesses, or by setting the Prisme without so, that the light might pass through it, and be refracted before it was terminated by the hole: But I found none of those circumstances material. The fashion of the colours was in all these cases the same.

The Cambridge Companion to Newton


Author: I. Bernard Cohen,George E. Smith
Publisher: Cambridge University Press
ISBN: 9780521656962
Category: History
Page: 500
View: 9514

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In this volume a team of distinguished contributors examines all the main aspects of Newton's thought.