Philosophy and the New Physics
Philosophy and the New Physics

Author: Jonathan H Powers

Publisher: Taylor & Francis

Published: 2023-07-14

Total Pages: 171

ISBN-13: 1000964116

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First Published in 1982 Philosophy and the New Physics is a compact and yet remarkably rich excursion through the history of physics from Newtonian mechanics to quantum physics. The theory of relativity, quantum mechanics and ideas about the ‘fundamental constituents’ of matter have attracted a great deal of philosophical comment. Indeed, the originators of some of these theories thought they were solving philosophical problems as well as scientific ones. Classical physics is often portrayed as epitomizing ‘mechanistic materialism’, and the revolution in modern physics is variously claimed to vindicate ‘logical positivism’, ‘operationalism’, ‘organicism’, ‘dialectical materialism’ and ‘Buddhist metaphysics’. In this book Jonathan Powers criticizes all of these claims and argues that such varied and conflicting interpretations are possible because of ineradicable elements of conventionality in scientific theories. This is a must read for scholars and researchers of philosophy of science and philosophy in general.

Naming Infinity
Naming Infinity

Author: Loren Graham

Publisher: Harvard University Press

Published: 2009-03-31

Total Pages: 252

ISBN-13: 0674032934

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In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.

Algorithms for Computer Algebra
Algorithms for Computer Algebra

Author: Keith O. Geddes

Publisher: Springer Science & Business Media

Published: 2007-06-30

Total Pages: 594

ISBN-13: 0585332479

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Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.

Software Pioneers
Software Pioneers

Author: Manfred Broy

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 714

ISBN-13: 3642594123

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A lucid statement of the philosophy of modular programming can be found in a 1970 textbook on the design of system programs by Gouthier and Pont [1, l Cfl0. 23], which we quote below: A well-defined segmentation of the project effort ensures system modularity. Each task fonos a separate, distinct program module. At implementation time each module and its inputs and outputs are well-defined, there is no confusion in the intended interface with other system modules. At checkout time the in tegrity of the module is tested independently; there are few sche duling problems in synchronizing the completion of several tasks before checkout can begin. Finally, the system is maintained in modular fashion; system errors and deficiencies can be traced to specific system modules, thus limiting the scope of detailed error searching. Usually nothing is said about the criteria to be used in dividing the system into modules. This paper will discuss that issue and, by means of examples, suggest some criteria which can be used in decomposing a system into modules. A Brief Status Report The major advancement in the area of modular programming has been the development of coding techniques and assemblers which (1) allow one modu1e to be written with little knowledge of the code in another module, and (2) alJow modules to be reas sembled and replaced without reassembly of the whole system.

Knowing the Odds
Knowing the Odds

Author: John B. Walsh

Publisher: American Mathematical Society

Published: 2023-08-16

Total Pages: 439

ISBN-13: 1470473879

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John Walsh, one of the great masters of the subject, has written a superb book on probability. It covers at a leisurely pace all the important topics that students need to know, and provides excellent examples. I regret his book was not available when I taught such a course myself, a few years ago. —Ioannis Karatzas, Columbia University In this wonderful book, John Walsh presents a panoramic view of Probability Theory, starting from basic facts on mean, median and mode, continuing with an excellent account of Markov chains and martingales, and culminating with Brownian motion. Throughout, the author's personal style is apparent; he manages to combine rigor with an emphasis on the key ideas so the reader never loses sight of the forest by being surrounded by too many trees. As noted in the preface, “To teach a course with pleasure, one should learn at the same time.” Indeed, almost all instructors will learn something new from the book (e.g. the potential-theoretic proof of Skorokhod embedding) and at the same time, it is attractive and approachable for students. —Yuval Peres, Microsoft With many examples in each section that enhance the presentation, this book is a welcome addition to the collection of books that serve the needs of advanced undergraduate as well as first year graduate students. The pace is leisurely which makes it more attractive as a text. —Srinivasa Varadhan, Courant Institute, New York This book covers in a leisurely manner all the standard material that one would want in a full year probability course with a slant towards applications in financial analysis at the graduate or senior undergraduate honors level. It contains a fair amount of measure theory and real analysis built in but it introduces sigma-fields, measure theory, and expectation in an especially elementary and intuitive way. A large variety of examples and exercises in each chapter enrich the presentation in the text.