Dernière sortie
Topology Of Surfaces, Knots, And Manifolds. A First Undergraduate Course
TOPOLOGY OF SURFACES, KNOTS, AND MANIFOLDS offers an intuitionbased and example-driven approach to the basic ideas and probleins involving Manifolds, particularly one- and two-dimensional manifolds. A blend of examples and exercises Icads the reader to anticipate general definitions and theorems concerning curves, surfaces, knots, and links - the objects of interest in the appealing set of mathematical ideas known as "rubber sheet geometry". The result is a text that is accessible to a broad range of undergraduate students, yet still provides solid coverage of the mathematics underlying these topics. Here are some of the features that make Carlson's approach work: • A student-friendly writing style provides a clear exposition of concepts. • Mathematical results are presented accurately and main definitions, theorems, and remarks are clearly highlighted for easy reference. • Carefully selected exercises, some of which require hands-on work on computer-aided visualization, reinforce the understanding of concepts or further develop ideas. • Extensive use of illustrations helps the students develop an intuitive understanding of the material. • Frequent historical references chronicle the development of the subject and highlight connections between topology and other areas of mathematics. • Chapter summary sections offer a review of each chapter's topics and a transitional look forward to the next chapter.
TOPOLOGY OF SURFACES, KNOTS, AND MANIFOLDS offers an intuitionbased and example-driven approach to the basic ideas and probleins involving Manifolds, particularly one- and two-dimensional manifolds. A blend of examples and exercises Icads the reader to anticipate general definitions and theorems concerning curves, surfaces, knots, and links - the objects of interest in the appealing set of mathematical ideas known as "rubber sheet geometry". The result is a text that is accessible to a broad range of undergraduate students, yet still provides solid coverage of the mathematics underlying these topics. Here are some of the features that make Carlson's approach work: • A student-friendly writing style provides a clear exposition of concepts. • Mathematical results are presented accurately and main definitions, theorems, and remarks are clearly highlighted for easy reference. • Carefully selected exercises, some of which require hands-on work on computer-aided visualization, reinforce the understanding of concepts or further develop ideas. • Extensive use of illustrations helps the students develop an intuitive understanding of the material. • Frequent historical references chronicle the development of the subject and highlight connections between topology and other areas of mathematics. • Chapter summary sections offer a review of each chapter's topics and a transitional look forward to the next chapter.
