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Inhaltsangabe
In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.
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Reseña del editor
In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.
Reseña del editor
This is a well-balanced introduction to topology that stresses geometric aspects. Focusing on historical background and visual interpretation of results, it emphasizes spaces with few dimensions, where visualization is possible, and interaction with combinatorial group theory via the fundamental group. It also present algorithms for topological problems. Most of the results and proofs are known, but some have been simplified or placed in a new perspective. Over 300 illustrations, many interesting exercises, and challenging open problems are included. New in this edition is a chapter on unsolvable problems, which includes the first textbook proof that the main problem of topology, the homeomorphism problem, is unsolvable.
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- VerlagSpringer
- Erscheinungsdatum1995
- ISBN 10 0387979700
- ISBN 13 9780387979700
- EinbandTapa dura
- SpracheEnglisch
- Auflage2
- Anzahl der Seiten352
- Kontakt zum HerstellerNicht verfügbar
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Classical Topology and Combinatorial Group Theory - Second edition
Verlag:
New York : Springer-Verlag, 1993
ISBN 10: 0387979700
ISBN 13: 9780387979700
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Zustand: Good. 2nd Edition. Original boards, illustrated with numerous equations, graphs and diagrams, 8vo. Graduate texts in mathematics, 72.; Spine slightly discoloured, name in pen on title page. Bestandsnummer des Verkäufers 342253-ZA24
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Classical Topology and Combinatorial Group Theory.
ISBN 10: 0387979700
ISBN 13: 9780387979700
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Zustand: Gut. Formateinband: Pappband / gebundene Ausgabe XII, 334 S. (24 cm) 1st Edition; Guter und sauberer Zustand. Sprache: Englisch Gewicht in Gramm: 800 [Stichwörter: Klassische Topologie und kombinatorische Gruppentheorie]. Bestandsnummer des Verkäufers 77370
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Classical Topology and Combinatorial Group Theory
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Zustand: Gut. Zustand: Gut | Seiten: 352 | Sprache: Englisch | Produktart: Bücher. Bestandsnummer des Verkäufers 1543453/203
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Classical Topology and Combinatorial Group Theory
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Hardcover. Zustand: Near fine. Second Edition. Graduate Texts in Mathematics 72. xii, 334 p. 24 cm. 312 figures. Yellow hardcover. Small mark on text block edge. Bestandsnummer des Verkäufers 149127
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Classical Topology and Combinatorial Group Theory
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Zustand: Good. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. In good all round condition. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,700grams, ISBN:9780387979700. Bestandsnummer des Verkäufers 5953876
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Classical Topology and Combinatorial Group Theory
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Hardcover. Zustand: Very Good. 2nd edition; text clean and tight; no dust jacket; Graduate Texts In Mathematics, 72; 8vo 8" - 9" tall; 348 pages. Bestandsnummer des Verkäufers 239164
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Classical Topology and Combinatorial Group Theory
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Gebunden. Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler s polyhedron formula, and knots, the student is led to expect that these picturesque ideas will co. Bestandsnummer des Verkäufers 5913149
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Classical Topology and Combinatorial Group Theory (Second Edition)
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Hard cover. Zustand: Very good. No jacket. Second Edition. Cover boards and spine are lightly sunned, not affecting legibility. Stickers from previous seller's on front and back cover, not covering text. Spine is shaken, but binding is tight. Name of previous owner in ink on inside front cover, front endpaper, and bottom edge of text block. Pages are clean and unmarked. Bestandsnummer des Verkäufers 1138144
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Classical Topology and Combinatorial Group Theory
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Springer New York, Springer New York Mär 1993, 1993
ISBN 10: 0387979700
ISBN 13: 9780387979700
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Buch. Zustand: Neu. Neuware -In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment 'undergraduate topology' proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 352 pp. Englisch. Bestandsnummer des Verkäufers 9780387979700
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Classical Topology and Combinatorial Group Theory
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Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment 'undergraduate topology' proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject. 352 pp. Englisch. Bestandsnummer des Verkäufers 9780387979700
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