Geometries and Transformations


Author: Norman W. Johnson

Publisher: Cambridge University Press

ISBN: 1107103401

Category: Mathematics

Page: 350

View: 7649

A readable exposition of how Euclidean and other geometries can be distinguished using linear algebra and transformation groups.

Euclidean Geometry and Transformations


Author: Clayton W. Dodge

Publisher: Courier Corporation

ISBN: 9780486434766

Category: Mathematics

Page: 295

View: 3563

This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.

Bäcklund and Darboux Transformations

The Geometry of Solitons : AARMS-CRM Workshop, June 4-9, 1999, Halifax, N.S., Canada


Author: A. A. Coley

Publisher: American Mathematical Soc.

ISBN: 9780821870259

Category: Mathematics

Page: 436

View: 2594

This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory. The book consists of two parts. The first is a series of introductory pedagogical lectures presented by leading experts in the field. They are devoted respectively to Backlund transformations of Painleve equations, to the dressing methodand Backlund and Darboux transformations, and to the classical geometry of Backlund transformations and their applications to soliton theory. The second part contains original contributions that represent new developments in the theory and applications of these transformations. Both the introductorylectures and the original talks were presented at an International Workshop that took place in Halifax, Nova Scotia (Canada). This volume covers virtually all recent developments in the theory and applications of Backlund and Darboux transformations.



Author: David A. Brannan,Matthew F. Esplen,Jeremy J. Gray

Publisher: Cambridge University Press

ISBN: 9780521597876

Category: Mathematics

Page: 497

View: 1790

Textbook for undergraduate courses on geometry or for self study that reveals the intricacies of geometry.

Geometry of M Bius Transformations, Elliptic, Parabolic and Hyperbolic Actions of Sl2r

Mathematics, Geometry


Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 1478414405

Category: Education

Page: 46

View: 8687

Facts101 is your complete guide to Geometry of M Bius Transformations, Elliptic, Parabolic and Hyperbolic Actions of Sl2r. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

A Course in Modern Geometries


Author: Judith N. Cederberg

Publisher: Springer Science & Business Media

ISBN: 1475734905

Category: Mathematics

Page: 441

View: 2418

Designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. The first chapter presents several finite geometries in an axiomatic framework, while Chapter 2 continues the synthetic approach in introducing both Euclids and ideas of non-Euclidean geometry. There follows a new introduction to symmetry and hands-on explorations of isometries that precedes an extensive analytic treatment of similarities and affinities. Chapter 4 presents plane projective geometry both synthetically and analytically, and the new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Throughout, each chapter includes a list of suggested resources for applications or related topics in areas such as art and history, plus this second edition points to Web locations of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions are available for "Cabri Geometry" and "Geometers Sketchpad".

Geometry and Topology


Author: Miles Reid,Balazs Szendroi

Publisher: Cambridge University Press

ISBN: 9780521848893

Category: Mathematics

Page: 196

View: 4523

Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the Möbius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups,having applications to relativity theory and quantum mechanics. A final chapter features historical discussions and indications for further reading. With minimal prerequisites, the book provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics. The book is based on many years' teaching experience, and is thoroughly class-tested. There are copious illustrations, and each chapter ends with a wide supply of exercises. Further teaching material is available for teachers via the web, including assignable problem sheets with solutions.

Geometry of Complex Numbers


Author: Hans Schwerdtfeger

Publisher: Courier Corporation

ISBN: 0486135861

Category: Mathematics

Page: 224

View: 7363

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Geometries and Groups


Author: Viacheslav V. Nikulin,Igor R. Shafarevich

Publisher: Springer Science & Business Media

ISBN: 9783540152811

Category: Mathematics

Page: 251

View: 3444

This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's non-Euclidean geometry. Each section is carefully motivated by discussion of the physical and general scientific implications of the mathematical argument, and its place in the history of mathematics and philosophy. The book is expected to find a place alongside classics such as Hilbert and Cohn-Vossen's "Geometry and the imagination" and Weyl's "Symmetry".

Finite Groups and Finite Geometries


Author: T. Tsuzuku

Publisher: Cambridge University Press

ISBN: 0521222427

Category: Mathematics

Page: 328

View: 8522

A 1982 introduction to developments which had taken place in finite group theory related to finite geometries.

Euclidean and Affine Transformations

Geometric Transformations


Author: P. S. Modenov,A. S. Parkhomenko

Publisher: Academic Press

ISBN: 1483261484

Category: Mathematics

Page: 170

View: 8371

Geometric Transformations, Volume 1: Euclidean and Affine Transformations focuses on the study of coordinates, trigonometry, transformations, and linear equations. The publication first takes a look at orthogonal transformations, including orthogonal transformations of the first and second kinds; representations of orthogonal transformations as the products of fundamental orthogonal transformations; and representation of an orthogonal transformation of space as a product of fundamental orthogonal transformations. The text then examines similarity and affine transformations. Topics include properties of affine mappings, Darboux's lemma and its consequences, affine transformations in coordinates, homothetic transformations, similarity transformations of the plane in coordinates, and similarity mapping. The book takes a look at the representation of a similarity transformation as the product of a homothetic transformation and an orthogonal transformation; application of affine transformations to the investigation of properties of the ellipse; and representation of any affine transformation as a product of affine transformations of the simplest types. The manuscript is a valuable reference for high school teachers and readers interested in the Euclidean and affine transformations.

College Geometry


Author: Howard Whitley Eves,Howard Eves

Publisher: Jones & Bartlett Learning

ISBN: 9780867204759

Category: Mathematics

Page: 370

View: 9316


From a Geometrical Point of View

A Study of the History and Philosophy of Category Theory


Author: Jean-Pierre Marquis

Publisher: Springer Science & Business Media

ISBN: 1402093845

Category: Science

Page: 310

View: 9706

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.

Mathematics for Quantum Chemistry


Author: Jay Martin Anderson

Publisher: Courier Corporation

ISBN: 0486151484

Category: Science

Page: 160

View: 4742

Introduction to problems of molecular structure and motion covers calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics. Answers to problems. 1966 edition.

Projective and Cayley-Klein Geometries


Author: Arkadij L. Onishchik,Rolf Sulanke

Publisher: Springer Science & Business Media

ISBN: 3540356452

Category: Mathematics

Page: 434

View: 8200

This book offers an introduction into projective geometry. The first part presents n-dimensional projective geometry over an arbitrary skew field; the real, the complex, and the quaternionic geometries are the central topics, finite geometries playing only a minor part. The second deals with classical linear and projective groups and the associated geometries. The final section summarizes selected results and problems from the geometry of transformation groups.

How to Solve Applied Mathematics Problems


Author: B. L. Moiseiwitsch

Publisher: Courier Corporation

ISBN: 0486285227

Category: Mathematics

Page: 336

View: 8295

This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.

Digital Geometry

Geometric Methods for Digital Picture Analysis


Author: Reinhard Klette,Azriel Rosenfeld

Publisher: Elsevier

ISBN: 0080477267

Category: Computers

Page: 672

View: 422

Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. Digital Geometry is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital geometry, some of which date back to ancient times, and also discusses the key processes involved, such as geometric algorithms as well as operations on pictures. *A comprehensive text and reference written by pioneers in digital geometry, image processing and analysis, and computer vision *Provides a collection of state-of-the-art algorithms for a wide variety of geometrical picture analysis tasks, including extracting data from digital images and making geometric measurements on the data *Includes exercises, examples, and references to related or more advanced work

Introduction to Crystallography


Author: Donald E. Sands

Publisher: Courier Corporation

ISBN: 0486136809

Category: Science

Page: 192

View: 4719

Clear, concise explanation of logical development of basic crystallographic concepts. Topics include crystals and lattices, symmetry, x-ray diffraction, and more. Problems, with answers. 114 illustrations. 1969 edition.

Galois Theory

Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures,


Author: Emil Artin

Publisher: Courier Corporation

ISBN: 048615825X

Category: Mathematics

Page: 86

View: 2056

Clearly presented discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.