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Intuitive Topology
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Book Synopsis Intuitive Topology by : Viktor Vasilʹevich Prasolov
Download or read book Intuitive Topology written by Viktor Vasilʹevich Prasolov and published by American Mathematical Soc.. This book was released on 1995 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Intuitive Concepts in Elementary Topology by : B.H. Arnold
Download or read book Intuitive Concepts in Elementary Topology written by B.H. Arnold and published by Courier Corporation. This book was released on 2015-02-23 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Topology: An Intuitive Approach by : Hajime Satō
Download or read book Algebraic Topology: An Intuitive Approach written by Hajime Satō and published by American Mathematical Soc.. This book was released on 1999 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Intuitive Combinatorial Topology by : V.G. Boltyanskii
Download or read book Intuitive Combinatorial Topology written by V.G. Boltyanskii and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. ISBN 13 :9780821886250 Total Pages :432 pages Book Rating :4.8/5 (862 download)
Book Synopsis Elementary Topology by : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Download or read book Elementary Topology written by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov and published by American Mathematical Soc.. This book was released on with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elementary Concepts of Topology by : Paul Alexandroff
Download or read book Elementary Concepts of Topology written by Paul Alexandroff and published by Courier Corporation. This book was released on 2012-08-13 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topology Now! written by Robert Messer and published by American Mathematical Soc.. This book was released on 2018-10-10 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Counterexamples in Topology by : Lynn Arthur Steen
Download or read book Counterexamples in Topology written by Lynn Arthur Steen and published by Courier Corporation. This book was released on 2013-04-22 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.
Book Synopsis Differential Topology by : Morris W. Hirsch
Download or read book Differential Topology written by Morris W. Hirsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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
Book Synopsis A First Course in Topology by : Robert A Conover
Download or read book A First Course in Topology written by Robert A Conover and published by Courier Corporation. This book was released on 2014-05-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Knots, Molecules, and the Universe by : Erica Flapan
Download or read book Knots, Molecules, and the Universe written by Erica Flapan and published by American Mathematical Soc.. This book was released on 2015-12-22 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Combinatorial Introduction to Topology by : Michael Henle
Download or read book A Combinatorial Introduction to Topology written by Michael Henle and published by Courier Corporation. This book was released on 1994-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Elements of Homology Theory by : Viktor Vasilʹevich Prasolov
Download or read book Elements of Homology Theory written by Viktor Vasilʹevich Prasolov and published by American Mathematical Soc.. This book was released on 2007 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Topology by : Bert Mendelson
Download or read book Introduction to Topology written by Bert Mendelson and published by Courier Corporation. This book was released on 2012-04-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Topology by : V. A. Vasilʹev
Download or read book Introduction to Topology written by V. A. Vasilʹev and published by American Mathematical Soc.. This book was released on 2001 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, homology and cohomology, intersection index, etc. The author notes, "The lecture note origins of the book left a significant imprint on itsstyle. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs." He concludes, "As a rule, only those proofs (or sketches of proofs) that are interesting per se and have importantgeneralizations are presented."
Book Synopsis Experiments in Topology by : Stephen Barr
Download or read book Experiments in Topology written by Stephen Barr and published by Courier Corporation. This book was released on 2012-12-04 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Intuitive Topology by : Viktor Vasilʹevich Prasolov
Download or read book Intuitive Topology written by Viktor Vasilʹevich Prasolov and published by . This book was released on 1991 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt:
