Non-standard Analysis

Author: Abraham Robinson

Publisher: Princeton University Press

ISBN: 1400884225

Category: Mathematics

Page: 308

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Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.

Hypermodels in Mathematical Finance

Modelling Via Infinitesimal Analysis

Author: Siu-Ah Ng

Publisher: World Scientific

ISBN: 9810244282

Category: Business & Economics

Page: 298

View: 6851

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At the beginning of the new millennium, two unstoppable processes are taking place in the world: (1) globalization of the economy; (2) information revolution. As a consequence, there is greater participation of the world population in capital market investment, such as bonds and stocks and their derivatives. Hence there is a need for risk management and analytic theory explaining the market. This leads to quantitative tools based on mathematical methods, i.e. the theory of mathematical finance.Ever since the pioneer work of Black, Scholes and Merton in the 70's, there has been rapid growth in the study of mathematical finance, involving ever more sophisticated mathematics. However, from the practitioner's point of view, it is desirable to have simpler and more useful mathematical tools.This book introduces research students and practitioners to the intuitive but rigorous hypermodel techniques in finance. It is based on Robinson's infinitesimal analysis, which is easily grasped by anyone with as little background as first-year calculus. It covers topics such as pricing derivative securities (including the Black-Scholes formula), hedging, term structure models of interest rates, consumption and equilibrium. The reader is introduced to mathematical tools needed for the aforementioned topics. Mathematical proofs and details are given in an appendix. Some programs in MATHEMATICA are also included.

Philosophical Lectures on Probability

collected, edited, and annotated by Alberto Mura

Author: Bruno de Finetti

Publisher: Springer Science & Business Media

ISBN: 1402082010

Category: Science

Page: 216

View: 6661

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Bruno de Finetti (1906–1985) is the founder of the subjective interpretation of probability, together with the British philosopher Frank Plumpton Ramsey. His related notion of “exchangeability” revolutionized the statistical methodology. This book (based on a course held in 1979) explains in a language accessible also to non-mathematicians the fundamental tenets and implications of subjectivism, according to which the probability of any well specified fact F refers to the degree of belief actually held by someone, on the ground of her whole knowledge, on the truth of the assertion that F obtains.

Topology from the Differentiable Viewpoint

Author: John Willard Milnor

Publisher: Princeton University Press

ISBN: 9780691048338

Category: Mathematics

Page: 64

View: 8440

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This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.

General Theory of Relativity

Author: Paul Adrien Maurice Dirac

Publisher: Princeton University Press

ISBN: 9780691011462

Category: Science

Page: 69

View: 3935

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Einstein's general theory of relativity requires a curved space for the description of the physical world. If one wishes to go beyond superficial discussions of the physical relations involved, one needs to set up precise equations for handling curved space. The well-established mathematical technique that accomplishes this is clearly described in this classic book by Nobel Laureate P.A.M. Dirac. Based on a series of lectures given by Dirac at Florida State University, and intended for the advanced undergraduate, General Theory of Relativity comprises thirty-five compact chapters that take the reader point-by-point through the necessary steps for understanding general relativity.

Homological Algebra

Author: Henri Cartan,Samuel Eilenberg

Publisher: Princeton University Press

ISBN: 9780691049915

Category: Mathematics

Page: 390

View: 3211

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When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.

Intelligent systems

architecture, design, and control

Author: Alexander M. Meystel,Alex Meystel,James Sacra Albus

Publisher: Wiley-Interscience

ISBN: 9780471193746

Category: Computers

Page: 696

View: 8976

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This comprehensive treatment of the field of intelligent systems is written by two of the foremost authorities in the field. The authors clearly examine the theoretical and practical aspects of these systems. The book focuses on the NIST-RCS (Real-time Control System) model that has been used recently in the Mars Rover.

Deleuze and the Fold: A Critical Reader

Author: Sjoerd van Tuinen,Niamh McDonnell

Publisher: Palgrave MacMillan

ISBN: N.A

Category: Philosophy

Page: 263

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This collection of essays presents a thorough explication of one of Deleuze's most difficult works, 'The Fold.'

Mathematical Foundations of Quantum Mechanics

Author: John Von Neumann

Publisher: N.A

ISBN: 9780691028934

Category: Mathematics

Page: 445

View: 8088

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Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.

Über die Hypothesen, welche der Geometrie zu Grunde liegen

Author: Bernhard Riemann,Hermann Weyl

Publisher: Springer-Verlag

ISBN: 3662248611

Category: Mathematics

Page: 50

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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Convex Analysis

Author: R. Tyrrell Rockafellar

Publisher: Princeton University Press

ISBN: 9780691015866

Category: Mathematics

Page: 451

View: 5046

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Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle- functions.This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading."This book should remain for some years as the standard reference for anyone interested in convex analysis." J. D. Pryce, Edinburgh Mathematical Society

Books in Print

Author: R.R. Bowker Company

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 5057

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Das kleine Buch der Stringtheorie

Author: Steven S. Gubser

Publisher: Spektrum Akademischer Verlag

ISBN: 9783827428486

Category: Science

Page: 174

View: 8676

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Das kleine Buch der Stringtheorie bietet eine knappe und unterhaltsame Einführung in eines der meistdiskutierten Gebiete der modernen Physik. Die Stringtheorie gilt als eine „Theorie für Alles“, mit der sich sämtliche Grundkräfte der Natur beschreiben lassen. Bisher allerdings konnte sie experimentell nicht bestätigt werden, und unter Physikern wird sie sehr kontrovers diskutiert. Dieses Buch gibt Ihnen die Gelegenheit, sich ein eigenes Bild zu machen!