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Differential Geometry


Lost in Math: How Beauty Leads Physics Astray

Lost in Math: How Beauty Leads Physics Astray Lowest new price: $19.92
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Author: Sabine Hossenfelder

A contrarian argues that modern physicists' obsession with beauty has given us wonderful math but bad science

Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.


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Special Relativity and Classical Field Theory: The Theoretical Minimum

Special Relativity and Classical Field Theory: The Theoretical Minimum Lowest new price: $14.99
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Author: Leonard Susskind

The third volume in the bestselling physics series cracks open Einstein's special relativity and field theory


Physicist Leonard Susskind and data engineer Art Friedman are back. This time, they introduce readers to Einstein's special relativity and Maxwell's classical field theory. Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It's a must-read for both devotees of the series and any armchair physicist who wants to improve their knowledge of physics' deepest truths.

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Geometric Formulas (Quick Study: Academic)

Geometric Formulas (Quick Study: Academic) Lowest new price: $4.76
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Author: Inc. BarCharts
Brand: Brand: QuickStudy

6-page laminated guide includes:
·general terms
·lines
·line segments
·rays
·angles
·transversal line angles
·polygons
·circles
·theorems & relationships
·postulates
·geometric formulas

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  • Used Book in Good Condition

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Geometry Part 2 (Quickstudy Reference Guides - Academic)

Geometry Part 2 (Quickstudy Reference Guides - Academic) Lowest new price: $4.76
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Author: Inc. BarCharts
Brand: Bar Charts

Part 2 of our coverage of the fundamental structure of geometry.

 

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Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)

Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics) Lowest new price: $17.62
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Author: Manfredo P. do Carmo

One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems.
The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.

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Introduction to Differential Geometry of Space Curves and Surfaces: Differential Geometry of Curves and Surfaces

Introduction to Differential Geometry of Space Curves and Surfaces: Differential Geometry of Curves and Surfaces Lowest new price: $14.53
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Author: Taha Sochi

This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.

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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: $38.95
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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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An Introduction to Manifolds (Universitext)

An Introduction to Manifolds (Universitext) Lowest new price: $47.94
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Author: Loring W. Tu

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

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Introduction to Tensor Analysis and the Calculus of Moving Surfaces

Introduction to Tensor Analysis and the Calculus of Moving Surfaces Lowest new price: $37.70
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Author: Pavel Grinfeld
Brand: Springer

This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds.

 

Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations.

 

The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject.

 

The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.

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  • Springer

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Surveys in Differential Geometry, Vol. 11: Metric and comparison geometry (2010 re-issue)

Surveys in Differential Geometry, Vol. 11: Metric and comparison geometry (2010 re-issue) Lowest new price: $39.00
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Author: [various]

Contents Collapsed Manifolds with Bounded Sectional Curvature and Applications (by Xiaochun Rong) Nonnegatively and Positively Curved Manifolds (by Burkhard Wilking) Examples of Manifolds with Non-negative Sectional Curvature (by Wolfgang Ziller) Perelman's Stability Theorem (by Vitali Kapovitch) Semiconcave Functions in Alexandrov's Geometry (by Anton Petrunin) Manifolds with a lower Ricci Curvature Bound (by Guofang Wei) Optimal Transport and Ricci Curvature for Metric- Measure Spaces (by John Lott) Manifolds of Positive Scalar Curvature: A Progress Report (by Jonathan Rosenberg) Spaces of Curvature Bounded Above (by S. Buyalo & V. Schroeder) Negative Curvature and Exotic Topology (by F.T. Farrell, L.E. Jones & P. Ontaneda)


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