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Books
Differential Geometry
Modern Geometry―Methods and Applications: Part III: Introduction to Homology Theory (Graduate Texts in Mathematics)
Lowest new price: $45.00
Lowest used price: $29.67
List price: $95.00
Author: B.A. Dubrovin
Brand: B A Dubrovin

Focuses on homology theory This volume contains introductions to the contemporary methods for the calculation of homology groups and the classification of manifesto It is suitable for both scientists and students of mathematics as well as theoretical physics Over the past fifteen years the geometrical and topological methods of the theory of manifolds have as sumed a central role in the most advanced areas of pure and applied mathematics as well as theoretical physics The three volumes of Modern Geometry Methods and Applicationscontain a concrete exposition of these methods together with their main applications in mathematics and physics This third volume presented in highly accessible languages concentrates in homology theory It contains introductions to the contemporary methods for the calculation of homology groups and the classification of manifesto Both scientists and students of mathematics as well as theoretical physics will find this book to be a valuable reference and text
Features:
 Modern Geometry Methods and Applications Part 3 Introduction to Homology Theory
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A Geometric Approach to Differential Forms
Lowest new price: $38.08
Lowest used price: $36.49
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Author: David Bachman
Brand: David Bachman

This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.
Features:
 A Geometric Approach to Differential Forms
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The Geometry of Spacetime: An Introduction to Special and General Relativity (Undergraduate Texts in Mathematics)
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Author: James J. Callahan
Brand: James J Callahan

Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.
Features:
 The Geometry of Spacetime An Introduction to Special and General Relativity
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Geometrical Methods of Mathematical Physics
Lowest new price: $45.33
Lowest used price: $25.00
List price: $54.99
Author: Bernard F. Schutz
Brand: Brand: Cambridge University Press

In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, highenergy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods  in particular Lie derivatives, Lie groups and differential forms  and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced puremathematical expositions.
Features:
 Used Book in Good Condition
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Characteristic Classes. (AM76)
Lowest new price: $93.35
Lowest used price: $55.38
List price: $115.00
Author: John Milnor
Brand: Princeton University Press

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds.
In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of StiefelWhitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers.
Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.
Features:
 Used Book in Good Condition
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Differential Geometry of Curves and Surfaces
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Lowest used price: $42.12
List price: $45.00
Author: Masaaki Umehara
Brand: Ingramcontent

This engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a universitylevel course, without the need for referencing other texts, as it is completely selfcontained. More advanced material in the second half of the book, including appendices, also serves more experienced students well. Furthermore, this text is also suitable for a seminar for graduate students, and for selfstudy. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates. Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities. In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field.
Features:
 Differential Geometry of Curves and Surfaces
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Differential Forms and the Geometry of General Relativity
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List price: $59.95
Author: Tevian Dray

Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity. The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible. The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.
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A Comprehensive Introduction to Differential Geometry, Vol. 4, 3rd Edition
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List price: $45.00
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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 A Comprehensive Introduction to Differential Geometry, Vol. 3, 3rd Edition
 A Comprehensive Introduction to Differential Geometry, Vol. 5, 3rd Edition
 A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition
 A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd Edition
 Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus
 Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)
 Physics for Mathematicians, Mechanics I
 Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218)
 Calculus, 4th edition
 Geometry of Differential Forms (Translations of Mathematical Monographs, Vol. 201)


Michael Atiyah: Collected Works: Volume 4: Index Theory: 2 Volume 4: Index Theory: 2
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Lowest used price: $302.79
List price: $275.00
Author: Michael Atiyah
Brand: Brand: Oxford University Press, USA

Professor Atiyah is one of the greatest living mathematicians and is well known throughout the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still at the peak of his career. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into six volumes, divided thematically for easy reference by individuals interested in a particular subject. Volumes III and IV cover papers written in 196384 and are the result of a long collaboration with I. M. Singer on the Index Theory of elliptic operators.
Features:
 Used Book in Good Condition


Elementary Differential Geometry, Revised 2nd Edition, Second Edition
Lowest new price: $84.99
Lowest used price: $47.00
List price: $96.95
Author: Barrett O'Neill

Written primarily for students who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Revised 2nd Edition, provides an introduction to the geometry of curves and surfaces. The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text.  Over 36,000 copies sold worldwide
 Accessible, practical yet rigorous approach to a complex topicalso suitable for selfstudy
 Extensive update of appendices on Mathematica and Maple software packages
 Thorough streamlining of second edition's numbering system
 Fuller information on solutions to oddnumbered problems
 Additional exercises and hints guide students in using the latest computer modeling tools
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