Download or read book Riemannian Geometry written by Isaac Chavel and published by Cambridge University Press. This book was released on 2006-04-10 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.
Download or read book A Modern Introduction to Geometries written by Annita Tuller and published by . This book was released on 1967 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Course in Modern Geometries written by Judith N. Cederberg and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 introduces Euclid's geometry and the basic ideas of non-Euclidean geometry. The synthetic approach of Chapters 1 - 2 is followed by the analytic treatment of transformations of the Euclidean plane in Chapter 3. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3 - 4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. Each chapter includes a list of suggested sources for applications and/or related topics.
Download or read book Symmetry in Mechanics written by Stephanie Frank Singer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: "And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has taught: talented but ap preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning. To suit this audience, the author eschews density of topics and efficiency of presentation in favor of a gentler tone, a coherent story, digressions on mathe maticians, physicists and their notations, simple examples worked out in detail, and reinforcement of the basics. Dense and efficient texts play a crucial role in the education of budding (and budded) mathematicians and physicists. This book does not presume to improve on the classics in that genre. Rather, it aims to provide those classics with a large new generation of appreciative readers. This text introduces some basic constructs of modern symplectic geometry in the context of an old celestial mechanics problem, the two-body problem. We present the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation, first in the style of an undergraduate physics course, and x Preface then again in the language of symplectic geometry. No previous exposure to symplectic geometry is required: we introduce and illustrate all necessary con structs.
Download or read book Modern Geometries written by Michael Henle and published by Pearson. This book was released on 2001 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation. Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems. For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists.
Download or read book Riemannian Geometry written by Isaac Chavel and published by . This book was released on 1995 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Modern View of Geometry written by Leonard M. Blumenthal and published by Courier Dover Publications. This book was released on 2017-04-19 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elegant exposition of postulation geometry of planes offers rigorous, lucid treatment of coordination of affine and projective planes, set theory, propositional calculus, affine planes with Desargues and Pappus properties, more. 1961 edition.
Download or read book Introduction to Classical Geometries written by Ana Irene Ramírez Galarza and published by Springer Science & Business Media. This book was released on 2007-05-02 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the geometric intuition of the reader by examining the symmetries (or rigid motions) of the space in question. This approach introduces in turn all the classical geometries: Euclidean, affine, elliptic, projective and hyperbolic. The main focus is on the mathematically rich two-dimensional case, although some aspects of 3- or $n$-dimensional geometries are included. Basic notions of algebra and analysis are used to convey better understanding of various concepts and results. Concepts of geometry are presented in a very simple way, so that they become easily accessible: the only pre-requisites are calculus, linear algebra and basic analytic geometry.
Download or read book Applied Differential Geometry written by Vladimir G. Ivancevic and published by World Scientific. This book was released on 2007 with total page 1346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator ? ?Human Biodynamics Engine?, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools ? this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.
Download or read book A Survey of Classical and Modern Geometries written by Arthur Baragar and published by Pearson. This book was released on 2001 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes the beauty of geometry using a modern approach. Models & computer exercises help readers to cultivate geometric intuition. Topics include Euclidean Geometry, Hand Constructions, Geometer's Sketch Pad, Hyperbolic Geometry, Tilings & Lattices, Spherical Geometry, Projective Geometry, Finite Geometry, and Modern Geometry Research. Ideal for geometry at an intermediate level.
Download or read book Geometry a Very Short Introduction written by Maciej Dunajski and published by Oxford University Press. This book was released on 2022-01-27 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof - deductive reasoning from a set of axioms - first arose. To this day geometry remains a very active area of research in mathematics.This Very Short Introduction covers the areas of mathematics falling under geometry, starting with topics such as Euclidean and non-Euclidean geometries, and ranging to curved spaces, projective geometry in Renaissance art, and geometry of space-time inside a black hole. Starting from the basics,Maciej Dunajski proceeds from concrete examples (of mathematical objects like Platonic solids, or theorems like the Pythagorean theorem) to general principles. Throughout, he outlines the role geometry plays in the broader context of science and art.Very Short Introductions: Brilliant, Sharp, InspiringABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.
Download or read book A Course in Modern Geometries written by Judith N. Cederberg and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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".
Download or read book Geometry Euclid and Beyond written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.
Download or read book Modern Geometries written by James R. Smart and published by Cengage Learning. This book was released on 1998 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive, best-selling text focuses on the study of many different geometries -- rather than a single geometry -- and is thoroughly modern in its approach. Each chapter is essentially a short course on one aspect of modern geometry, including finite geometries, the geometry of transformations, convexity, advanced Euclidian geometry, inversion, projective geometry, geometric aspects of topology, and non-Euclidean geometries. This edition reflects the recommendations of the COMAP proceedings on Geometry's Future, the NCTM standards, and the Professional Standards for Teaching Mathematics. References to a new companion text, Active Geometry by David A. Thomas encourage students to explore the geometry of motion through the use of computer software. Using Active Geometry at the beginning of various sections allows professors to give students a somewhat more intuitive introduction using current technology before moving on to more abstract concepts and theorems.
Download or read book College Geometry written by Nathan Altshiller-Court and published by Courier Corporation. This book was released on 2012-06-29 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.
Download or read book Non Euclidean Geometries written by András Prékopa and published by Springer Science & Business Media. This book was released on 2006-06-03 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: "From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.
Download or read book Applied Differential Geometry written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
