Introduction To Topology And Geometry

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Introduction to Geometry and Topology

Werner Ballmann
Introduction to Geometry and Topology Book PDF

Author : Werner Ballmann
Publisher : Birkhäuser
Page : 169 pages
File Size : 40,5 Mb
Release : 2018-07-18
Category : Mathematics
ISBN : 9783034809832

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Introduction to Geometry and Topology by Werner Ballmann Pdf

This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems. The second chapter of the book introduces manifolds and Lie groups, and examines a wide assortment of examples. Further discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets of vector fields. This discussion is deepened and expanded in the third chapter, which introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes's integral formula. The fourth and final chapter is devoted to the fundamentals of differential geometry and traces the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the book discusses connections and curvature--the central concepts of differential geometry. The discussion culminates with the Gauß equations and the version of Gauß's theorema egregium for submanifolds of arbitrary dimension and codimension. This book is primarily aimed at advanced undergraduates in mathematics and physics and is intended as the template for a one- or two-semester bachelor's course.

Introduction to Topology and Geometry

Saul Stahl,Catherine Stenson
Introduction to Topology and Geometry Book PDF

Author : Saul Stahl,Catherine Stenson
Publisher : John Wiley & Sons
Page : 430 pages
File Size : 47,8 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118546147

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Introduction to Topology and Geometry by Saul Stahl,Catherine Stenson Pdf

An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition “. . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.” —CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the Second Edition: • Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being • Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods • Bridges seemingly disparate topics by creating thoughtful and logical connections • Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.

Topology and Geometry

Glen E. Bredon
Topology and Geometry Book PDF

Author : Glen E. Bredon
Publisher : Springer Science & Business Media
Page : 580 pages
File Size : 53,6 Mb
Release : 1993-06-24
Category : Mathematics
ISBN : 9780387979267

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Topology and Geometry by Glen E. Bredon Pdf

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS

Introduction to Topology

Bert Mendelson
Introduction to Topology Book PDF

Author : Bert Mendelson
Publisher : Courier Corporation
Page : 226 pages
File Size : 51,9 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486135090

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Introduction to Topology by Bert Mendelson Pdf

Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.

Introduction to Topology

Theodore W. Gamelin,Robert Everist Greene
Introduction to Topology Book PDF

Author : Theodore W. Gamelin,Robert Everist Greene
Publisher : Courier Corporation
Page : 258 pages
File Size : 52,7 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780486320182

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Introduction to Topology by Theodore W. Gamelin,Robert Everist Greene Pdf

This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.

A Combinatorial Introduction to Topology

Michael Henle
A Combinatorial Introduction to Topology Book PDF

Author : Michael Henle
Publisher : Courier Corporation
Page : 340 pages
File Size : 44,5 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 0486679667

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A Combinatorial Introduction to Topology by Michael Henle Pdf

Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.

Geometry with an Introduction to Cosmic Topology

Michael P. Hitchman
Geometry with an Introduction to Cosmic Topology Book PDF

Author : Michael P. Hitchman
Publisher : Jones & Bartlett Learning
Page : 255 pages
File Size : 44,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9780763754570

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Geometry with an Introduction to Cosmic Topology by Michael P. Hitchman Pdf

The content of Geometry with an Introduction to Cosmic Topology is motivated by questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have and edge? Is it infinitely big? Dr. Hitchman aims to clarify this fascinating area of mathematics. This non-Euclidean geometry text is organized intothree natural parts. Chapter 1 provides an overview including a brief history of Geometry, Surfaces, and reasons to study Non-Euclidean Geometry. Chapters 2-7 contain the core mathematical content of the text, following the ErlangenProgram, which develops geometry in terms of a space and a group of transformations on that space. Finally chapters 1 and 8 introduce (chapter 1) and explore (chapter 8) the topic of cosmic topology through the geometry learned in the preceding chapters.

Introduction to Topological Manifolds

John M. Lee
Introduction to Topological Manifolds Book PDF

Author : John M. Lee
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 55,8 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387227276

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Introduction to Topological Manifolds by John M. Lee Pdf

Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.

Topology and Geometry for Physicists

Charles Nash,Siddhartha Sen
Topology and Geometry for Physicists Book PDF

Author : Charles Nash,Siddhartha Sen
Publisher : Courier Corporation
Page : 302 pages
File Size : 43,5 Mb
Release : 2013-08-16
Category : Mathematics
ISBN : 9780486318363

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Topology and Geometry for Physicists by Charles Nash,Siddhartha Sen Pdf

Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.

A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics

Antonio Sergio Teixeira Pires
A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics Book PDF

Author : Antonio Sergio Teixeira Pires
Publisher : Morgan & Claypool Publishers
Page : 171 pages
File Size : 48,7 Mb
Release : 2019-03-21
Category : Science
ISBN : 9781643273747

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A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics by Antonio Sergio Teixeira Pires Pdf

In the last years there have been great advances in the applications of topology and differential geometry to problems in condensed matter physics. Concepts drawn from topology and geometry have become essential to the understanding of several phenomena in the area. Physicists have been creative in producing models for actual physical phenomena which realize mathematically exotic concepts and new phases have been discovered in condensed matter in which topology plays a leading role. An important classification paradigm is the concept of topological order, where the state characterizing a system does not break any symmetry, but it defines a topological phase in the sense that certain fundamental properties change only when the system passes through a quantum phase transition. The main purpose of this book is to provide a brief, self-contained introduction to some mathematical ideas and methods from differential geometry and topology, and to show a few applications in condensed matter. It conveys to physicists the basis for many mathematical concepts, avoiding the detailed formality of most textbooks.

Introduction to Topology

Tej Bahadur Singh
Introduction to Topology Book PDF

Author : Tej Bahadur Singh
Publisher : Springer
Page : 452 pages
File Size : 43,8 Mb
Release : 2019-05-17
Category : Mathematics
ISBN : 9789811369544

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Introduction to Topology by Tej Bahadur Singh Pdf

Topology is a large subject with several branches, broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad range of mathematical disciplines, while algebraic topology offers as a powerful tool for studying problems in geometry and numerous other areas of mathematics. This book presents the basic concepts of topology, including virtually all of the traditional topics in point-set topology, as well as elementary topics in algebraic topology such as fundamental groups and covering spaces. It also discusses topological groups and transformation groups. When combined with a working knowledge of analysis and algebra, this book offers a valuable resource for advanced undergraduate and beginning graduate students of mathematics specializing in algebraic topology and harmonic analysis.

Knots, Molecules, and the Universe

Erica Flapan
Knots Molecules and the Universe Book PDF

Author : Erica Flapan
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 53,5 Mb
Release : 2015-12-22
Category : Algebraic topology
ISBN : 9781470425357

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Knots, Molecules, and the Universe by Erica Flapan Pdf

This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas. Though the book can be read and enjoyed by nonmathematicians, college students, or even eager high school students, it is intended to be used as an undergraduate textbook. The book is divided into three parts corresponding to the three areas referred to in the title. Part 1 develops techniques that enable two- and three-dimensional creatures to visualize possible shapes for their universe and to use topological and geometric properties to distinguish one such space from another. Part 2 is an introduction to knot theory with an emphasis on invariants. Part 3 presents applications of topology and geometry to molecular symmetries, DNA, and proteins. Each chapter ends with exercises that allow for better understanding of the material. The style of the book is informal and lively. Though all of the definitions and theorems are explicitly stated, they are given in an intuitive rather than a rigorous form, with several hundreds of figures illustrating the exposition. This allows students to develop intuition about topology and geometry without getting bogged down in technical details.

Geometry and Topology

Miles Reid,Balazs Szendroi
Geometry and Topology Book PDF

Author : Miles Reid,Balazs Szendroi
Publisher : Cambridge University Press
Page : 218 pages
File Size : 49,7 Mb
Release : 2005-11-10
Category : Mathematics
ISBN : 052184889X

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Geometry and Topology by Miles Reid,Balazs Szendroi Pdf

Geometry aims to describe the world around us. It is central to many branches of mathematics and physics, and offers a whole range of views on the universe. This is an introduction to the ideas of geometry and includes generous helpings of simple explanations and examples. The book is based on many years teaching experience so is thoroughly class-tested, and as prerequisites are minimal, it is suited to newcomers to the subject. There are plenty of illustrations; chapters end with a collection of exercises, and solutions are available for teachers.

Topology

Stefan Waldmann
Topology Book PDF

Author : Stefan Waldmann
Publisher : Springer
Page : 136 pages
File Size : 49,9 Mb
Release : 2014-08-05
Category : Mathematics
ISBN : 9783319096803

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Topology by Stefan Waldmann Pdf

This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. Therefore students will need fundamental topological notions already at an early stage in their bachelor programs. While there are already many excellent monographs on general topology, most of them are too large for a first bachelor course. Topology fills this gap and can be either used for self-study or as the basis of a topology course.

An Introduction to the Geometry and Topology of Fluid Flows

Renzo L. Ricca
An Introduction to the Geometry and Topology of Fluid Flows Book PDF

Author : Renzo L. Ricca
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401004466

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An Introduction to the Geometry and Topology of Fluid Flows by Renzo L. Ricca Pdf

Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics. Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples. In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.