From A Geometrical Point Of View

Author : Jean-Pierre Marquis
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 48,6 Mb
Release : 2008-11-20
Category : Science
ISBN : 9781402093845

Get Book

From a Geometrical Point of View by Jean-Pierre Marquis Pdf

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 : Kirsti Andersen
Publisher : Springer Science & Business Media
Page : 837 pages
File Size : 40,8 Mb
Release : 2008-11-23
Category : Mathematics
ISBN : 9780387489469

Get Book

The Geometry of an Art by Kirsti Andersen Pdf

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 : A.T. Fomenko
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400930698

Get Book

Integrability and Nonintegrability in Geometry and Mechanics by A.T. Fomenko Pdf

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. 1hen one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin' . • 1111 Oulik'. n. . Chi" •. • ~ Mm~ Mu,d. ", Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Author : Shun-ichi Amari
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461250562

Get Book

Differential-Geometrical Methods in Statistics by Shun-ichi Amari Pdf

From the reviews: "In this Lecture Note volume the author describes his differential-geometric approach to parametrical statistical problems summarizing the results he had published in a series of papers in the last five years. The author provides a geometric framework for a special class of test and estimation procedures for curved exponential families. ... ... The material and ideas presented in this volume are important and it is recommended to everybody interested in the connection between statistics and geometry ..." #Metrika#1 "More than hundred references are given showing the growing interest in differential geometry with respect to statistics. The book can only strongly be recommended to a geodesist since it offers many new insights into statistics on a familiar ground." #Manuscripta Geodaetica#2

Author : Georgios E. Stavroulakis
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 48,9 Mb
Release : 2012-10-19
Category : Technology & Engineering
ISBN : 9783642339677

Get Book

Recent Advances in Contact Mechanics by Georgios E. Stavroulakis Pdf

Contact mechanics is an active research area with deep theoretical and numerical roots. The links between nonsmooth analysis and optimization with mechanics have been investigated intensively during the last decades, especially in Europe. The study of complementarity problems, variational -, quasivariational- and hemivariational inequalities arising in contact mechanics and beyond is a hot topic for interdisciplinary research and cooperation. The needs of industry for robust solution algorithms suitable for large scale applications and the regular updates of the respective elements in major commercial computational mechanics codes, demonstrate that this interaction is not restricted to the academic environment. The contributions of this book have been selected from the participants of the CMIS 2009 international conference which took place in Crete and continued a successful series of specialized contact mechanics conferences.

Author : Amoruso, Giuseppe
Publisher : IGI Global
Page : 924 pages
File Size : 42,9 Mb
Release : 2016-04-11
Category : Design
ISBN : 9781522500308

Get Book

Handbook of Research on Visual Computing and Emerging Geometrical Design Tools by Amoruso, Giuseppe Pdf

Visual computing and descriptive geometry are multidisciplinary fields addressing the handling of images, 3D models, and other computer graphics. These ideas are experiencing a revival due to emergent technologies and applications available to developers. Based in traditional forms of design and architecture, these fields are currently experiencing a bounty of new research based on old principles. The Handbook of Research on Visual Computing and Emerging Geometrical Design Tools seeks to add to this knowledge base by considering these technologies from a designer’s perspective rather than reiterating the principles of computer science. It combines aspects of geometry and representation with emerging tools for CAD, generation, and visualization while addressing the digital heritage of such fields. This book is an invaluable resource for developers, students of both graphic and computer-generated design, researchers, and designers.

Author : Attila Kuba,László G. Nyúl,Kálmán Palágyi
Publisher : Springer
Page : 688 pages
File Size : 42,7 Mb
Release : 2006-10-13
Category : Computers
ISBN : 9783540476528

Get Book

Discrete Geometry for Computer Imagery by Attila Kuba,László G. Nyúl,Kálmán Palágyi Pdf

This book constitutes the refereed proceedings of the 13th International Conference on Discrete Geometry for Computer Imagery, DGCI 2006, held in Szeged, Hungary in October 2006. The 28 revised full papers and 27 revised poster papers presented together with two invited papers were carefully reviewed and selected from 99 submissions.

Author : Jesper Lützen
Publisher : OUP Oxford
Page : 334 pages
File Size : 41,7 Mb
Release : 2005-05-12
Category : Science
ISBN : 9780191524349

Get Book

Mechanistic Images in Geometric Form by Jesper Lützen Pdf

This book gives an analysis of Hertz's posthumously published Principles of Mechanics in its philosophical, physical and mathematical context. In a period of heated debates about the true foundation of physical sciences, Hertz's book was conceived and highly regarded as an original and rigorous foundation for a mechanistic research program. Insisting that a law-like account of nature would require hypothetical unobservables, Hertz viewed physical theories as (mental) images of the world rather than the true design behind the phenomena. This paved the way for the modern conception of a model. Rejecting the concept of force as a coherent basic notion of physics he built his mechanics on hidden masses (the ether) and rigid connections, and formulated it as a new differential geometric language. Recently many philosophers have studied Hertz's image theory and historians of physics have discussed his forceless mechanics. The present book shows how these aspects, as well as the hitherto overlooked mathematical aspects, form an integrated whole which is closely connected to the mechanistic world view of the time and which is a natural continuation of Hertz's earlier research on electromagnetism. Therefore it is also a case study of the strong interactions between philosophy, physics and mathematics. Moreover, the book presents an analysis of the genesis of many of the central elements of Hertz's mechanics based on his manuscripts and drafts. Hertz's research program was cut short by the advent of relativity theory but its image theory influenced many philosophers as well as some physicists and mathematicians and its geometric form had a lasting influence on advanced expositions of mechanics.

Author : Kai S Lam
Publisher : World Scientific Publishing Company
Page : 592 pages
File Size : 45,9 Mb
Release : 2014-07-07
Category : Science
ISBN : 9789814551502

Get Book

Fundamental Principles of Classical Mechanics by Kai S Lam Pdf

This book is written with the belief that classical mechanics, as a theoretical discipline, possesses an inherent beauty, depth, and richness that far transcends its immediate applications in mechanical systems. These properties are manifested, by and large, through the coherence and elegance of the mathematical structure underlying the discipline, and are eminently worthy of being communicated to physics students at the earliest stage possible. This volume is therefore addressed mainly to advanced undergraduate and beginning graduate physics students who are interested in the application of modern mathematical methods in classical mechanics, in particular, those derived from the fields of topology and differential geometry, and also to the occasional mathematics student who is interested in important physics applications of these areas of mathematics. Its main purpose is to offer an introductory and broad glimpse of the majestic edifice of the mathematical theory of classical dynamics, not only in the time-honored analytical tradition of Newton, Laplace, Lagrange, Hamilton, Jacobi, and Whittaker, but also the more topological/geometrical one established by Poincare, and enriched by Birkhoff, Lyapunov, Smale, Siegel, Kolmogorov, Arnold, and Moser (as well as many others).

Author : Marc Frantz,Annalisa Crannell
Publisher : Princeton University Press
Page : 248 pages
File Size : 44,8 Mb
Release : 2011-07-05
Category : Mathematics
ISBN : 140083905X

Get Book

Viewpoints by Marc Frantz,Annalisa Crannell Pdf

An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students. Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery. Classroom-tested activities and problem solving Accessible problems that move beyond regular art school curriculum Multiple solutions of varying difficulty and applicability Appropriate for students of all mathematics and art levels Original and exclusive essays by contemporary artists Forthcoming: Instructor's manual (available only to teachers)

Author : Arnout Jozef Ceulemans
Publisher : Springer Nature
Page : 352 pages
File Size : 44,6 Mb
Release : 2024-06-03
Category : Electronic
ISBN : 9789402422450

Get Book

Group Theory Applied to Chemistry by Arnout Jozef Ceulemans Pdf

Author : Marciel Agop,Ioan Merches
Publisher : CRC Press
Page : 280 pages
File Size : 54,7 Mb
Release : 2018-09-25
Category : Mathematics
ISBN : 9780429679971

Get Book

Operational Procedures Describing Physical Systems by Marciel Agop,Ioan Merches Pdf

The authors examine topics in modern physics and offer a unitary and original treatment of the fundamental problems of the dynamics of physical systems, as well as a description of the nuclear matter within a framework of general relativity. They show that some physical phenomena studied at two different resolution scales (e.g. microscale, cosmological scale), apparently with no connection between them, become compatible by means of the operational procedures, acting either as some ”hidden” symmetries, or harmonic-type mappings. The book is addressed to the students, researchers and university/high school teachers working in the fields of mathematics, physics, and chemistry.

Author : James J. Callahan
Publisher : Springer Science & Business Media
Page : 526 pages
File Size : 47,5 Mb
Release : 2010-09-09
Category : Mathematics
ISBN : 9781441973320

Get Book

Advanced Calculus by James J. Callahan Pdf

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 : Marcelo Epstein
Publisher : Cambridge University Press
Page : 325 pages
File Size : 44,9 Mb
Release : 2010-07-26
Category : Science
ISBN : 9781139490467

Get Book

The Geometrical Language of Continuum Mechanics by Marcelo Epstein Pdf

Epstein presents the fundamental concepts of modern differential geometry within the framework of continuum mechanics. Divided into three parts of roughly equal length, the book opens with a motivational chapter to impress upon the reader that differential geometry is indeed the natural language of continuum mechanics or, better still, that the latter is a prime example of the application and materialisation of the former. In the second part, the fundamental notions of differential geometry are presented with rigor using a writing style that is as informal as possible. Differentiable manifolds, tangent bundles, exterior derivatives, Lie derivatives, and Lie groups are illustrated in terms of their mechanical interpretations. The third part includes the theory of fiber bundles, G-structures, and groupoids, which are applicable to bodies with internal structure and to the description of material inhomogeneity. The abstract notions of differential geometry are thus illuminated by practical and intuitively meaningful engineering applications.

Author : Gabriele Cornelli,Richard McKirahan,Constantinos Macris
Publisher : Walter de Gruyter
Page : 551 pages
File Size : 54,6 Mb
Release : 2013-10-29
Category : Philosophy
ISBN : 9783110318500

Get Book

On Pythagoreanism by Gabriele Cornelli,Richard McKirahan,Constantinos Macris Pdf

The purpose of the conference “On Pythagoreanism”, held in Brasilia in 2011, was to bring together leading scholars from all over the world to define the status quaestionis for the ever-increasing interest and research on Pythagoreanism in the 21st century. The papers included in this volume exemplify the variety of topics and approaches now being used to understand the polyhedral image of one of the most fascinating and long-lasting intellectual phenomena in Western history. Cornelli’s paper opens the volume by charting the course of Pythagorean studies over the past two centuries. The remaining contributions range chronologically from Pythagoras and the early Pythagoreans of the archaic period (6th-5th centuries BCE) through the classical, hellenistic and late antique periods, to the eighteenth century. Thematically they treat the connections of Pythagoreanism with Orphism and religion, with mathematics, metaphysics and epistemology and with politics and the Pythagorean way of life.