Introduction To Geometry And Topology

Introduction to Geometry and Topology PDF
Author: Werner Ballmann
Publisher: Birkhäuser
ISBN: 3034809832
Size: 42.35 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 169
View: 2018

Get Book



Book Description:

Introduction To Geometry And Topology

by Werner Ballmann, Introduction To Geometry And Topology Book available in PDF, EPUB, Mobi Format. Download Introduction To Geometry And Topology books, 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.







Einf Hrung In Die Geometrie Und Topologie

Einf  hrung in die Geometrie und Topologie PDF
Author: Werner Ballmann
Publisher: Springer-Verlag
ISBN: 3034809018
Size: 31.34 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : de
Pages : 162
View: 5276

Get Book



Book Description:

Einf Hrung In Die Geometrie Und Topologie

by Werner Ballmann, Einf Hrung In Die Geometrie Und Topologie Book available in PDF, EPUB, Mobi Format. Download Einf Hrung In Die Geometrie Und Topologie books, Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik- und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein- oder zweisemestrige Vorlesungen geeignet.







Introduction To Topology And Geometry

Introduction to Topology and Geometry PDF
Author: Saul Stahl
Publisher: John Wiley & Sons
ISBN: 1118546148
Size: 24.78 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 536
View: 3163

Get Book



Book Description:

Introduction To Topology And Geometry

by Saul Stahl, Introduction To Topology And Geometry Book available in PDF, EPUB, Mobi Format. Download Introduction To Topology And Geometry books, 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.







Knots Molecules And The Universe

Knots  Molecules  and the Universe PDF
Author: Erica Flapan
Publisher: American Mathematical Soc.
ISBN: 1470425351
Size: 61.67 MB
Format: PDF, ePub, Mobi
Category : Algebraic topology
Languages : en
Pages : 386
View: 3246

Get Book



Book Description:

Knots Molecules And The Universe

by Erica Flapan, Knots Molecules And The Universe Book available in PDF, EPUB, Mobi Format. Download Knots Molecules And The Universe books, 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.







A Combinatorial Introduction To Topology

A Combinatorial Introduction to Topology PDF
Author: Michael Henle
Publisher: Courier Corporation
ISBN: 9780486679662
Size: 16.61 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 310
View: 5035

Get Book



Book Description:

A Combinatorial Introduction To Topology

by Michael Henle, A Combinatorial Introduction To Topology Book available in PDF, EPUB, Mobi Format. Download A Combinatorial Introduction To Topology books, 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.







Introduction To Topology

Introduction to Topology PDF
Author: Bert Mendelson
Publisher: Courier Corporation
ISBN: 9780486663524
Size: 40.88 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 206
View: 4786

Get Book



Book Description:

Introduction To Topology

by Bert Mendelson, Introduction To Topology Book available in PDF, EPUB, Mobi Format. Download Introduction To Topology books, Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.







A Topological Introduction To Nonlinear Analysis

A Topological Introduction to Nonlinear Analysis PDF
Author: Robert F. Brown
Publisher: Springer
ISBN: 3319117947
Size: 23.99 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 240
View: 2502

Get Book



Book Description:

A Topological Introduction To Nonlinear Analysis

by Robert F. Brown, A Topological Introduction To Nonlinear Analysis Book available in PDF, EPUB, Mobi Format. Download A Topological Introduction To Nonlinear Analysis books, This third edition is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. Included in this new edition are several new chapters that present the fixed point index and its applications. The exposition and mathematical content is improved throughout. This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply focused and highly readable view of nonlinear analysis by a practicing topologist who has seen a clear path to understanding. "For the topology-minded reader, the book indeed has a lot to offer: written in a very personal, eloquent and instructive style it makes one of the highlights of nonlinear analysis accessible to a wide audience."-Monatshefte fur Mathematik (2006)







Introduction To Topological Manifolds

Introduction to Topological Manifolds PDF
Author: John Lee
Publisher: Springer Science & Business Media
ISBN: 1441979409
Size: 27.66 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 433
View: 2659

Get Book



Book Description:

Introduction To Topological Manifolds

by John Lee, Introduction To Topological Manifolds Book available in PDF, EPUB, Mobi Format. Download Introduction To Topological Manifolds books, This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.







Introduction To Differential And Algebraic Topology

Introduction to Differential and Algebraic Topology PDF
Author: Yu.G. Borisovich
Publisher: Springer Science & Business Media
ISBN: 9401719594
Size: 66.80 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 493
View: 4039

Get Book



Book Description:

Introduction To Differential And Algebraic Topology

by Yu.G. Borisovich, Introduction To Differential And Algebraic Topology Book available in PDF, EPUB, Mobi Format. Download Introduction To Differential And Algebraic Topology books, Topology as a subject, in our opinion, plays a central role in university education. It is not really possible to design courses in differential geometry, mathematical analysis, differential equations, mechanics, functional analysis that correspond to the temporary state of these disciplines without involving topological concepts. Therefore, it is essential to acquaint students with topo logical research methods already in the first university courses. This textbook is one possible version of an introductory course in topo logy and elements of differential geometry, and it absolutely reflects both the authors' personal preferences and experience as lecturers and researchers. It deals with those areas of topology and geometry that are most closely related to fundamental courses in general mathematics. The educational material leaves a lecturer a free choice in designing his own course or his own seminar. We draw attention to a number of particularities in our book. The first chap ter, according to the authors' intention, should acquaint readers with topolo gical problems and concepts which arise from problems in geometry, analysis, and physics. Here, general topology (Ch. 2) is presented by introducing con structions, for example, related to the concept of quotient spaces, much earlier than various other notions of general topology thus making it possible for students to study important examples of manifolds (two-dimensional surfaces, projective spaces, orbit spaces, etc.) as topological spaces, immediately.







An Illustrated Introduction To Topology And Homotopy

An Illustrated Introduction to Topology and Homotopy PDF
Author: Sasho Kalajdzievski
Publisher: CRC Press
ISBN: 1482220814
Size: 35.18 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 485
View: 3217

Get Book



Book Description:

An Illustrated Introduction To Topology And Homotopy

by Sasho Kalajdzievski, An Illustrated Introduction To Topology And Homotopy Book available in PDF, EPUB, Mobi Format. Download An Illustrated Introduction To Topology And Homotopy books, An Illustrated Introduction to Topology and Homotopy explores the beauty of topology and homotopy theory in a direct and engaging manner while illustrating the power of the theory through many, often surprising, applications. This self-contained book takes a visual and rigorous approach that incorporates both extensive illustrations and full proofs