Topology: An Introduction with Application to Topological Groups
Idioma: inglés
Editorial: Dover Publications Inc., 2011
- Tapa blanda
- Usado
Librería: World of Books (was SecondSale), Montgomery, IL, Estados Unidos de AmericaWorld of Books (was SecondSale)
Vendedor de AbeBooks desde 20 de diciembre de 2007
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EUR 4,47
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Admirably meets the topology requirements for the pregraduate training of research mathematicians. American Mathematical MonthlyTopology, sometimes described as rubber-sheet geometry, is crucial to modern mathematics and to many other disciplines from quantum mechanics to sociology. This stimulating introduction to the field will give the student a familiarity with elementary point set topology, including an easy acquaintance with the line and the plane, knowledge often useful in graduate mathematics programs.The book is not a collection of topics, rather it early employs the language of point set topology to define and discuss topological groups. These geometric objects in turn motivate a further discussion of set-theoretic topology and of its applications in function spaces. An introduction to homotopy and the fundamental group then brings the student's new theoretical knowledge to bear on very concrete problems: the calculation of the fundamental group of the circle and a proof of the fundamental theorem of algebra. Finally, the abstract development is brought to satisfying fruition with the classification of topological groups by equivalence under local isomorphism. Throughout the book there is a sustained geometric development a single thread of reasoning which unifies the topological course.One of the special features of this work is its well-chosen exercises, along with a selection of problems in each chapter that contain interesting applications and further theory. Careful study of the text and diligent performance of the exercises will enable the student to achieve an excellent working knowledge of topology and a useful understanding of its applications. Moreover, the author's unique teaching approach lends an extra dimension of effectiveness to the books: Of particular interest is the remarkable pedagogy evident in this work. The author converses with the reader on a personal basis. He speaks with him, questions him, challenges him, and best of all occasionally leaves him to his own devices. American Scientist.…
N° de ref. del artículo 00105874733
- Título
- Topology: An Introduction with Application to Topological Groups
- Autor
- George Mccarty
- Editorial
- Dover Publications Inc.
- Año de publicación
- 2011
- Estado
- Good
- Encuadernación
- Paperback
- Idioma
- inglés
- ISBN 10
- 0486656330
- ISBN 13
- 9780486656335
“Sinopsis” puede pertenecer a otra edición de este título.
De la contraportada
Topology, sometimes described as "rubber-sheet geometry," is crucial to modern mathematics and to many other disciplines from quantum mechanics to sociology. This stimulating introduction to the field will give the student a familiarity with elementary point set topology, including an easy acquaintance with the line and the plane, knowledge often useful in graduate mathematics programs.
The book is not a collection of topics, rather it early employs the language of point set topology to define and discuss topological groups. These geometric objects in turn motivate a further discussion of set-theoretic topology and of its applications in function spaces. An introduction to homotopy and the fundamental group then brings the student's new theoretical knowledge to bear on very concrete problems: the calculation of the fundamental group of the circle and a proof of the fundamental theorem of algebra. Finally, the abstract development is brought to satisfying fruition with the classification of topological groups by equivalence under local isomorphism. Throughout the book there is a sustained geometric development a single thread of reasoning which unifies the topological course.
One of the special features of this work is its well-chosen exercises, along with a selection of problems in each chapter that contain interesting applications and further theory. Careful study of the text and diligent performance of the exercises will enable the student to achieve an excellent working knowledge of topology and a useful understanding of its applications. Moreover, the author's unique teaching approach lends an extra dimension of effectiveness to the books: "Of particular interest is the remarkable pedagogy evident in this work. The author converses with the reader on a personal basis. He speaks with him, questions him, challenges him, and best of all occasionally leaves him to his own devices." American Scientist
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World of Books (was SecondSale)
Montgomery, IL, Estados Unidos de America
Vendedor de AbeBooks desde 20 de diciembre de 2007
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