Books about Invariance from Amazon.com

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Price: $52.01 [Notify me when price goes down.]

One of the newest and most controversial approaches to financial pricing. In Physics of Finance the author applies the methods of theoretical physics to financial economics to develop an altogether original method for pricing financial assets that steps outside the equilibrium paradigm in finance.
In Physics of Finance, basic assumptions underlying equilibrium pricing are re-examined, the risk factors hidden in the implications of equilibrium theory and the potential profit in unstable markets are discussed and gauge modelling is introduced..
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In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems.

But between 1916 and 1950, the theorem was poorly understood and Noether’s name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the various popular or historical accounts they wrote. Worse, earlier attempts which had been eclipsed by Noether’s achievements were remembered, and sometimes figure in quick ‘historical’ accounts of the time.

This book carries a translation of Noether’s original paper into English, and then describes the strange history of its reception and the responses to her work. Ultimately the theorems became decisive in a shift from basing fundamental physics on conservations laws to basing it on symmetries, or at the very least, in thoroughly explaining the connection between these two families of ideas. The real significance of this book is that it shows very clearly how long it took before mathematicians and physicists began to recognize the seminal importance of Noether’s results. This book is thoroughly researched and provides careful documentation of the textbook literature. Kosmann-Schwarzbach has thus thrown considerable light on this slow dance in which the mathematical tools necessary to study symmetry properties and conservation laws were apparently provided long before the orchestra arrives and the party begins.

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Price: $43.42 [Notify me when price goes down.]

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.

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Price: $60.78 [Notify me when price goes down.]

Recent scientific advances have placed many traditional philosophical concepts under great stress. In this pathbreaking book, the eminent philosopher Robert Nozick rethinks and transforms the concepts of truth, objectivity, necessity, contingency, consciousness, and ethics. Using an original method, he presents bold new philosophical theories that take account of scientific advances in physics, evolutionary biology, economics, and cognitive neuroscience, and casts current cultural controversies (such as whether all truth is relative and whether ethics is objective) in a wholly new light. Throughout, the book is open to, and engages in, the bold exploration of new philosophical possibilities.

Philosophy will never look the same. Truth is embedded in space-time and is relative to it. However, truth is not socially relative among human beings (extraterrestrials are another matter). Objective facts are invariant under specified transformations; objective beliefs are arrived at by a process in which biasing factors do not play a significant role. Necessity's domain is contracted (there are no important metaphysical necessities; water is not necessarily H2O) while the important and useful notion of degrees of contingency is elaborated. Gradations of consciousness (based upon "common registering") yield increasing capacity to fit actions to the world. The originating function of ethics is cooperation to mutual benefit, and evolution has instilled within humans a "normative module": the capacities to learn, internalize, follow norms, and make evaluations. Ethics has normative force because of the connection between ethics and conscious self-awareness. Nozick brings together the book's novel theories to show the extent to which there are objective ethical truths.

(20010806).
Price: $30.00 [Notify me when price goes down.]

Whether processes in the natural world are dependent or independent of the scale at which they operate is one of the major issues in hydrologic science. In this volume, leading hydrologists present their views on the role of scale effects in hydrologic phenomena occurring in a range of field settings, from the land surface to deep fractured rock. Self-contained and thought-provoking chapters cover both theoretical and applied hydrology. They provide critical insights into important topics such as general circulation models, floods, river networks, vadose zone processes, groundwater transport, and fluid flow through fractured media. This book is intended as an accessible introduction for graduate students and researchers to some of the most significant questions and challenges that will face hydrologic science in the twenty-first century..
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This is the first comprehensive treatment of the three basic symmetries of probability theory - contractability, exchangeability, and rotatability - defined as invariance in distribution under contractions, permutations, and rotations. Originating with the pioneering work of de Finetti from the 1930's, the theory has evolved into a unique body of deep, beautiful, and often surprising results, comprising the basic representations and invariance properties in one and several dimensions, and exhibiting some unexpected links between the various symmetries as well as to many other areas of modern probability. Most chapters require only some basic, graduate level probability theory, and should be accessible to any serious researchers and graduate students in probability and statistics. Parts of the book may also be of interest to pure and applied mathematicians in other areas. The exposition is formally self-contained, with detailed references provided for any deeper facts from real analysis or probability used in the book.

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Price: $55.97 [Notify me when price goes down.]

Most observers agree that modern physical theory attempts to provide objective representations of reality. However, the claim that these representations are based on conventional choices is viewed by many as a denial of their objectivity. As a result, objectivity and conventionality in representation are often framed as polar opposites.

Offering a new appraisal of symmetry in modern physics, employing detailed case studies from relativity theory and quantum mechanics, Objectivity, Invariance, and Convention contends that the physical sciences, though dependent on convention, may produce objective representations of reality. Talal Debs and Michael Redhead show that both realists and constructivists have recognized important elements of an understanding of science that may not be contradictory.

The position--"perspectival invariantism"-- introduced in this book highlights the shortcomings of existing approaches to symmetry in physics, and, for the constructivist, demonstrates that a dependence on conventions in representation reaches into the domain of the most technical sciences. For the realist, it stands as evidence against the claim that conventionality must undermine objectivity. We can be committed to the existence of a single real ontology while maintaining a cultural view of science.

(20070901).
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