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From a Geometrical Point of View

2008-11-20 Science
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Release : 2008-11-20
Genre : Science
Kind : eBook
Book Rating : 845/5 ( reviews)

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Book Synopsis From a Geometrical Point of View by : Jean-Pierre Marquis

Download or read book From a Geometrical Point of View written by Jean-Pierre Marquis. This book was released on 2008-11-20. Available in PDF, EPUB and Kindle. Book excerpt: From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein’s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane’s work in the early 1940’s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics. From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.

Convexity from the Geometric Point of View

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Kind : eBook
Book Rating : 077/5 ( reviews)

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Book Synopsis Convexity from the Geometric Point of View by : Vitor Balestro

Download or read book Convexity from the Geometric Point of View written by Vitor Balestro. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:

Control Theory from the Geometric Viewpoint

2013-03-14 Science
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Release : 2013-03-14
Genre : Science
Kind : eBook
Book Rating : 049/5 ( reviews)

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Book Synopsis Control Theory from the Geometric Viewpoint by : Andrei A. Agrachev

Download or read book Control Theory from the Geometric Viewpoint written by Andrei A. Agrachev. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced Studies, Trieste, Italy. Mathematical prerequisites are reduced to standard courses of Analysis and Linear Algebra plus some basic Real and Functional Analysis. No preliminary knowledge of Control Theory or Differential Geometry is required. What this book is about? The classical deterministic physical world is described by smooth dynamical systems: the future in such a system is com pletely determined by the initial conditions. Moreover, the near future changes smoothly with the initial data. If we leave room for "free will" in this fatalistic world, then we come to control systems. We do so by allowing certain param eters of the dynamical system to change freely at every instant of time. That is what we routinely do in real life with our body, car, cooker, as well as with aircraft, technological processes etc. We try to control all these dynamical systems! Smooth dynamical systems are governed by differential equations. In this book we deal only with finite dimensional systems: they are governed by ordi nary differential equations on finite dimensional smooth manifolds. A control system for us is thus a family of ordinary differential equations. The family is parametrized by control parameters.

The Geometry of an Art

2008-11-23 Mathematics
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Release : 2008-11-23
Genre : Mathematics
Kind : eBook
Book Rating : 460/5 ( reviews)

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Book Synopsis The Geometry of an Art by : Kirsti Andersen

Download or read book The Geometry of an Art written by Kirsti Andersen. This book was released on 2008-11-23. Available in PDF, EPUB and Kindle. Book excerpt: This review of literature on perspective constructions from the Renaissance through the 18th century covers 175 authors, emphasizing Peiro della Francesca, Guidobaldo del Monte, Simon Stevin, Brook Taylor, and Johann Heinrich. It treats such topics as the various methods of constructing perspective, the development of theories underlying the constructions, and the communication between mathematicians and artisans in these developments.

Advanced Calculus

2010-09-09 Mathematics
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Release : 2010-09-09
Genre : Mathematics
Kind : eBook
Book Rating : 32X/5 ( reviews)

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Book Synopsis Advanced Calculus by : James J. Callahan

Download or read book Advanced Calculus written by James J. Callahan. This book was released on 2010-09-09. Available in PDF, EPUB and Kindle. Book excerpt: With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.

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