Intuitive Topology

Author : Viktor Vasilʹevich Prasolov
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 53,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803561

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Intuitive Topology by Viktor Vasilʹevich Prasolov Pdf

This book is an introduction to elementary topology presented in an intuitive way, emphasizing the visual aspect. Examples of nontrivial and often unexpected topological phenomena acquaint the reader with the picturesque world of knots, links, vector fields, and two-dimensional surfaces. The book begins with definitions presented in a tangible and perceptible way, on an everyday level, and progressively makes them more precise and rigorous, eventually reaching the level of fairly sophisticated proofs. This allows meaningful problems to be tackled from the outset. Another unusual trait of this book is that it deals mainly with constructions and maps, rather than with proofs that certain maps and constructions do or do not exist. The numerous illustrations are an essential feature. The book is accessible not only to undergraduates but also to high school students and will interest any reader who has some feeling for the visual elegance of geometry and topology.

Author : V.V. Prasolov
Publisher : Universities Press
Page : 108 pages
File Size : 48,5 Mb
Release : 1998
Category : Electronic
ISBN : 8173711186

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Intuitive Topology by V.V. Prasolov Pdf

This is an introductory course on topology and begins by defining the main notions in a tangible and perceptible way, and then progressing to more precise and rigorous definitions and results, reaching the level of fairly sophisticated yet completely understandable proofs.

Author : Viktor Vasilʹevich Prasolov
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 45,5 Mb
Release : 1995
Category : Mathematics
ISBN : 0821803565

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Intuitive Topology by Viktor Vasilʹevich Prasolov Pdf

This book is an introduction to elementary topology presented in an intuitive way, emphasizing the visual aspect. Examples of nontrivial and often unexpected topological phenomena acquaint the reader with the picturesque world of knots, links, vector fields, and two-dimensional surfaces. The book begins with definitions presented in a tangible and perceptible way, on an everyday level, and progressively makes them more precise and rigorous, eventually reaching the level of fairly sophisticated proofs. This allows meaningful problems to be tackled from the outset. Another unusual trait of this book is that it deals mainly with constructions and maps, rather than with proofs that certain maps and constructions do or do not exist. The numerous illustrations are an essential feature. The book is accessible not only to undergraduates but also to high school students and will interest any reader who has some feeling for the visual elegance of geometry and topology.

Author : B.H. Arnold
Publisher : Courier Corporation
Page : 192 pages
File Size : 47,7 Mb
Release : 2015-02-23
Category : Mathematics
ISBN : 9780486275765

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Intuitive Concepts in Elementary Topology by B.H. Arnold Pdf

Classroom-tested and much-cited, this concise text is designed for undergraduates. It offers a valuable and instructive introduction to the basic concepts of topology, taking an intuitive rather than an axiomatic viewpoint. 1962 edition.

Author : Hajime Satō
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 50,5 Mb
Release : 1999
Category : Mathematics
ISBN : 0821810464

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Algebraic Topology: An Intuitive Approach by Hajime Satō Pdf

The single most difficult thing one faces when one begins to learn a new branch of mathematics is to get a feel for the mathematical sense of the subject. The purpose of this book is to help the aspiring reader acquire this essential common sense about algebraic topology in a short period of time. To this end, Sato leads the reader through simple but meaningful examples in concrete terms. Moreover, results are not discussed in their greatest possible generality, but in terms of the simplest and most essential cases. In response to suggestions from readers of the original edition of this book, Sato has added an appendix of useful definitions and results on sets, general topology, groups and such. He has also provided references. Topics covered include fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. Objects and examples considered in the text include the torus, the Möbius strip, the Klein bottle, closed surfaces, cell complexes and vector bundles.

Author : V.G. Boltyanskii,V.A. Efremovich
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 48,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475756043

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Intuitive Combinatorial Topology by V.G. Boltyanskii,V.A. Efremovich Pdf

Topology is a relatively young and very important branch of mathematics, which studies the properties of objects that are preserved through deformations, twistings, and stretchings. This book deals with the topology of curves and surfaces as well as with the fundamental concepts of homotopy and homology, and does this in a lively and well-motivated way. This book is well suited for readers who are interested in finding out what topology is all about.

Author : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 46,5 Mb
Release : 2024-06-23
Category : Mathematics
ISBN : 0821886258

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Elementary Topology by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov Pdf

This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.

Author : Viktor Vasilʹevich Prasolov
Publisher : Unknown
Page : 95 pages
File Size : 52,8 Mb
Release : 1991
Category : Electronic
ISBN : OCLC:173164887

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Intuitive Topology by Viktor Vasilʹevich Prasolov Pdf

Author : Morris W. Hirsch
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494495

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Differential Topology by Morris W. Hirsch Pdf

"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." —MATHEMATICAL REVIEWS

Author : Robert Messer,Philip Straffin
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 55,9 Mb
Release : 2018-10-10
Category : Electronic
ISBN : 9781470447816

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Topology Now! by Robert Messer,Philip Straffin Pdf

Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting world of topology now(!) rather than later. Students using this textbook should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs.

Author : Stephen Barr
Publisher : Courier Corporation
Page : 244 pages
File Size : 41,7 Mb
Release : 2012-12-04
Category : Mathematics
ISBN : 9780486152745

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Experiments in Topology by Stephen Barr Pdf

Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.

Author : Viktor Vasilʹevich Prasolov
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 50,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821838129

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Elements of Homology Theory by Viktor Vasilʹevich Prasolov Pdf

The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.

Author : Paul Alexandroff
Publisher : Courier Corporation
Page : 68 pages
File Size : 51,9 Mb
Release : 2012-08-13
Category : Mathematics
ISBN : 9780486155067

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Elementary Concepts of Topology by Paul Alexandroff Pdf

Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.

Author : Paul L. Shick
Publisher : John Wiley & Sons
Page : 291 pages
File Size : 50,6 Mb
Release : 2011-10-14
Category : Mathematics
ISBN : 9781118030585

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Topology by Paul L. Shick Pdf

The essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn. This approach includes many more examples, allowing students to develop more sophisticated intuition and enabling them to learn how to write precise proofs in a brand-new context, which is an invaluable experience for math majors. Along with the standard point-set topology topics—connected and path-connected spaces, compact spaces, separation axioms, and metric spaces—Topology covers the construction of spaces from other spaces, including products and quotient spaces. This innovative text culminates with topics from geometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental group), which provide instructors with the opportunity to choose which "capstone" best suits his or her students. Topology: Point-Set and Geometric features: A short introduction in each chapter designed to motivate the ideas and place them into an appropriate context Sections with exercise sets ranging in difficulty from easy to fairly challenging Exercises that are very creative in their approaches and work well in a classroom setting A supplemental Web site that contains complete and colorful illustrations of certain objects, several learning modules illustrating complicated topics, and animations of particularly complex proofs

Author : Robert A Conover
Publisher : Courier Corporation
Page : 276 pages
File Size : 50,5 Mb
Release : 2014-05-21
Category : Mathematics
ISBN : 9780486780016

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A First Course in Topology by Robert A Conover Pdf

Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com