From A Geometrical Point Of View
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Author | : Jean-Pierre Marquis |
Publisher | : Springer Science & Business Media |
Total Pages | : 316 |
Release | : 2008-11-20 |
Genre | : Science |
ISBN | : 1402093845 |
Download From a Geometrical Point of View Book in PDF, Epub and Kindle
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.
Author | : Andrei A. Agrachev |
Publisher | : Springer Science & Business Media |
Total Pages | : 415 |
Release | : 2013-03-14 |
Genre | : Science |
ISBN | : 3662064049 |
Download Control Theory from the Geometric Viewpoint Book in PDF, Epub and Kindle
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.
Author | : Kirsti Andersen |
Publisher | : Springer Science & Business Media |
Total Pages | : 837 |
Release | : 2008-11-23 |
Genre | : Mathematics |
ISBN | : 0387489460 |
Download The Geometry of an Art Book in PDF, Epub and Kindle
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.
Author | : James J. Callahan |
Publisher | : Springer Science & Business Media |
Total Pages | : 542 |
Release | : 2010-09-09 |
Genre | : Mathematics |
ISBN | : 144197332X |
Download Advanced Calculus Book in PDF, Epub and Kindle
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.
Author | : Ernst Mach |
Publisher | : |
Total Pages | : 164 |
Release | : 1906 |
Genre | : Geometry |
ISBN | : |
Download Space and Geometry in the Light of Physiological, Psychological and Physical Inquiry Book in PDF, Epub and Kindle
Author | : Alberto Verjovski |
Publisher | : #N/A |
Total Pages | : 744 |
Release | : 1991-08-12 |
Genre | : |
ISBN | : 981456964X |
Download Group Theory From A Geometrical Viewpoint Book in PDF, Epub and Kindle
This proceedings presents the latest research materials done on group theory from geometrical viewpoint in particular Gromov's theory of hyperbolic groups, Coxeter groups, Tits buildings and actions on real trees. All these are very active subjects.
Author | : Tim Maudlin |
Publisher | : |
Total Pages | : 374 |
Release | : 2014-02 |
Genre | : Mathematics |
ISBN | : 0198701306 |
Download New Foundations for Physical Geometry Book in PDF, Epub and Kindle
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Author | : Tevian Dray |
Publisher | : CRC Press |
Total Pages | : 151 |
Release | : 2012-07-02 |
Genre | : Mathematics |
ISBN | : 1466510471 |
Download The Geometry of Special Relativity Book in PDF, Epub and Kindle
The Geometry of Special Relativity provides an introduction to special relativity that encourages readers to see beyond the formulas to the deeper geometric structure. The text treats the geometry of hyperbolas as the key to understanding special relativity. This approach replaces the ubiquitous γ symbol of most standard treatments with the appropriate hyperbolic trigonometric functions. In most cases, this not only simplifies the appearance of the formulas, but also emphasizes their geometric content in such a way as to make them almost obvious. Furthermore, many important relations, including the famous relativistic addition formula for velocities, follow directly from the appropriate trigonometric addition formulas. The book first describes the basic physics of special relativity to set the stage for the geometric treatment that follows. It then reviews properties of ordinary two-dimensional Euclidean space, expressed in terms of the usual circular trigonometric functions, before presenting a similar treatment of two-dimensional Minkowski space, expressed in terms of hyperbolic trigonometric functions. After covering special relativity again from the geometric point of view, the text discusses standard paradoxes, applications to relativistic mechanics, the relativistic unification of electricity and magnetism, and further steps leading to Einstein’s general theory of relativity. The book also briefly describes the further steps leading to Einstein’s general theory of relativity and then explores applications of hyperbola geometry to non-Euclidean geometry and calculus, including a geometric construction of the derivatives of trigonometric functions and the exponential function.
Author | : John Stillwell |
Publisher | : Springer Science & Business Media |
Total Pages | : 240 |
Release | : 2005-08-09 |
Genre | : Mathematics |
ISBN | : 0387255303 |
Download The Four Pillars of Geometry Book in PDF, Epub and Kindle
This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises
Author | : R. J. Adler |
Publisher | : Springer Science & Business Media |
Total Pages | : 455 |
Release | : 2009-01-29 |
Genre | : Mathematics |
ISBN | : 0387481168 |
Download Random Fields and Geometry Book in PDF, Epub and Kindle
This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.