Introduction to Differential and Algebraic Topology (Texts in the Mathematical Sciences)

Borisovich, Yu.G.; Bliznyakov, N.M.; Fomenko, T.N.; Izrailevich, Y.A.

ISBN 10: 9048145589 / ISBN 13: 9789048145584

Verlag: Springer, 2010

In. Bestandsnummer des Verkäufers ria9789048145584_new

Inhaltsangabe:

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.

Reseña del editor: 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.

Bibliografische Details

Titel: Introduction to Differential and Algebraic ...
Verlag: Springer
Erscheinungsdatum: 2010
Einband: Softcover
Zustand: New