Goedel’s Way: Exploits into an undecidable world

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Author : Gregory Chaitin
Genre : Mathematics

Summary : Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

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Author : Kiat Shi Tan
Genre : Computers

Summary : Symbolic C++: An Introduction to Computer Algebra Using Object-Oriented Programming provides a concise introduction to C++ and object-oriented programming, using a step-by-step construction of a new object-oriented designed computer algebra system - Symbolic C++. It shows how object-oriented programming can be used to implement a symbolic algebra system and how this can then be applied to different areas in mathematics and physics. This second revised edition:- * Explains the new powerful classes that have been added to Symbolic C++. * Includes the Standard Template Library. * Extends the Java section. * Contains useful classes in scientific computation. * Contains extended coverage of Maple, Mathematica, Reduce and MuPAD.

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Author : James R. Newman
Genre : History

Summary :

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Author : J. Loeckx
Genre : Computers

Summary : The Second Colloquium on Automata, Languages and Programming is the successor of a similar Colloquium organized by IRIA in Paris, July 3-7, 1972. The present Colloquium which takes place at the Unl- versity of Saarbrucken from July 29th to August 2nd, 1974, is spon sored by the Gesellschaft fur. Informatik and organized in cooperation wlth the Special Interest Group on Automata and Computability Theory (SIGACT) and with the European Association for Theoretical Computer Science (EATCS). As its predecessor the present Colloquium is devoted to the theo retical bases of computer science. This volume contains the text of the different lectures of the Colloquium whlch have been selected by the Program Committee out of about 130 submitted papers. About one third of the papers of this volume is concerned with formal language theory, one other third with the theory of computation and the rest with complexity theory, automata theory, programming languages, etc.

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Author : James Roy Newman
Genre : Mathematics

Summary : Presents 33 essays on such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the mathematical way of thinking, the unreasonableness of mathematics, and mathematics as an art. A reprint of volume 3 of the four-volume edition originally published by Simon and Schuster in 1956. Annotation c. Book News, Inc., Portland, OR (booknews.com).

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Author : Matthias Baaz
Genre : Mathematics

Summary : This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.

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Author : New York (State). Court of Appeals.
Genre : Law

Summary : Volume contains: 51 NY 253 (Alexander v. Sun Mut. Ins. Co.) 54 NY 334 (Anderson v. Rome, W. & O. R.R Co.) 54 NY 392 (Meyer v. Cullen) 54 NY 398 (Hammond v. Varian) 54 NY 599 (Trimm v. Marsh) 54 NY 660 (Holland v. Hayman) 54 NY 663 (Bain v. Matteson) 54 NY 668 (Noyes v. Hartford F. Ins. Co.) Unreported Case (Baker v. Drake) Unreported Case (Beard v. Jackson) Unreported Case (Marvin v. Marvin)

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Author : Raymond M. Smullyan
Genre : Mathematics

Summary : Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.

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Author : John Dawson
Genre : Logicians

Summary : This authoritative biography of Kurt Goedel relates the life of this most important logician of our time to the development of the field. Goedel's seminal achievements that changed the perception and foundations of mathematics are explained in the context of his life from the turn of the century Austria to the Institute for Advanced Study in Princeton.

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Author : Petr Hajek
Genre : Computers

Summary : This is a proceedings volume of the conference celebrating the 90th anniversary of the birth of Kurt Goedel. The conference has been recognized as an ASL sponsored meeting. Invited papers and contributed papers concern mainly mathematical logic but also philosophy of mathematics, computer science and physics and are devoted to topics related to Goedel's work and reflect the present state of knowledge domains deeply influenced by Goedel.