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Differential Geometry


A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd Edition

A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd Edition Lowest new price: $40.00
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Author: Michael Spivak
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Book by Michael Spivak, Spivak, Michael

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Differential Geometry: Connections, Curvature, and Characteristic Classes (Graduate Texts in Mathematics)

Differential Geometry: Connections, Curvature, and Characteristic Classes (Graduate Texts in Mathematics) Lowest new price: $61.40
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Author: Loring W. Tu

This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of  de Rham cohomology is required for the last third of the text.

Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included.

Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields.  The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.

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Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218)

Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218) Lowest new price: $47.22
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Author: John Lee
Brand: Brand: Springer

This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer.

This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard’s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures.

Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.

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The Wheel Of Time: The Shamans Of Mexico Their Thoughts About Life Death And The Universe

The Wheel Of Time: The Shamans Of Mexico Their Thoughts About Life Death And The Universe Lowest new price: $9.26
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Author: Carlos Castaneda
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World-renowned bestselling author Carlos Castaneda's Selection of his wrtings on the shamans of ancient Mexico.

Originally drawn to Yaqui Indian spiritual leader don Juan Matus for his knowledge of mind-altering plants, bestselling author Carlos Castaneda soon immersed himself in the sorcerer’s magical world entirely. Ten years after his first encounter with the shaman, Castaneda examines his field notes and comes to understand what don Juan knew all along—that these plants are merely a means to understanding the alternative realities that one cannot fully embrace on one’s own. In Journey to Ixtlan, Carlos Castaneda introduces readers to this new approach for the first time and explores, as he comes to experience it himself, his own final voyage into the teachings of don Juan, sharing with us what it is like to truly “stop the world” and perceive reality on his own terms.

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A Comprehensive Introduction to Differential Geometry, Vol. 5, 3rd Edition

A Comprehensive Introduction to Differential Geometry, Vol. 5, 3rd Edition Lowest new price: $50.00
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Author: Michael Spivak
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Spivak's 5 volume set is a classic and overall the best and most thorough treatment of differential geometry

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Differential Geometry (Dover Books on Mathematics)

Differential Geometry (Dover Books on Mathematics) Lowest new price: $11.34
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Author: Erwin Kreyszig
Brand: Dover Publications

An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures, and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods, and results involved. With problems and solutions. Includes 99 illustrations.

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Riemannian Geometry

Riemannian Geometry Lowest new price: $37.99
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Author: Manfredo Perdigao do Carmo

Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text.

A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.

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A Comprehensive Introduction to Differential Geometry, Vol. 4, 3rd Edition

A Comprehensive Introduction to Differential Geometry, Vol. 4, 3rd Edition Lowest new price: $35.38
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Author: Michael Spivak

Spivak's 5 volume set is a classic and overall the best and most thorough treatment of differential geometry

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Analysis On Manifolds (Advanced Books Classics)

Analysis On Manifolds (Advanced Books Classics) Lowest new price: $78.76
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Author: James R. Munkres

A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.

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The Geometry of Physics: An Introduction

The Geometry of Physics: An Introduction Lowest new price: $62.90
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Author: Theodore Frankel
Brand: Brand: Cambridge University Press

This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles, and Chern forms that are helpful for a deeper understanding of both classical and modern physics and engineering. It is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study.

A main addition introduced in this Third Edition is the inclusion of an Overview, which can be read before starting the text. This appears at the beginning of the text, before Chapter 1. Many of the geometric concepts developed in the text are previewed here and these are illustrated by their applications to a single extended problem in engineering, namely the study of the Cauchy stresses created by a small twist of an elastic cylindrical rod about its axis.

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