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Beginning Topology - 05 edition

Beginning Topology (ISBN10: 0534424260; ISBN13: 9780534424268)
ISBN13: 978-0534424268
ISBN10: 0534424260

Summary: With a nice balance of mathematical precision and accessibility, this text provides a broad introduction to the field of topology. Author Sue Goodman piques student curiosity and interest without losing necessary rigor so that they can appreciate the beauty and fun of mathematics. The text demonstrates that mathematics is an active and ever-changing field with many problems still unsolved, and students will see how the various areas of mathematics-algebra, combinator
ics, geometry, calculus, and differential equations-interact with topology. Students learn some of the major ideas and results in the field, do explorations and fairly elementary proofs, and become aware of some recent questions. By presenting a wide range of topics, exercises, and examples, Goodman creates an interactive and enjoyable atmosphere in which to learn topology.

Benefits:
  • The first three chapters provide the foundation for the course and then Chapters 4-7 branch out into some of the various fields of topology: combinatorial topology and map coloring, differential and algebraic topology, and knot theory.
  • The book introduces the flavor of topology as a whole while introducing the essentials in the context in which the students work (primarily subsets of Euclidean space).
  • A wealth of examples and exercises appear throughout each chapter (as opposed to the end of the chapter) to keep students actively involved in the process of learning and discovery.
  • The projects are designed to be less routine and are ideal for group work. They may involve some exploratory activities where there is not a simple answer, and may lead students through more complicated arguments.
...show more
Summary: With a nice balance of mathematical precision and accessibility, this text provides a broad introduction to the field of topology. Author Sue Goodman piques student curiosity and interest without losing necessary rigor so that they can appreciate the beauty and fun of mathematics. The text demonstrates that mathematics is an active and ever-changing field with many problems still unsolved, and students will see how the various areas of mathematics-algebra, combinatorics, geometry, calculus, and differential equations-interact with topology. Students learn some of the major ideas and results in the field, do explorations and fairly elementary proofs, and become aware of some recent questions. By presenting a wide range of topics, exercises, and examples, Goodman creates an interactive and enjoyable atmosphere in which to learn topology.

Benefits:
  • The first three chapters provide the foundation for the course and then Chapters 4-7 branch out into some of the various fields of topology: combinatorial topology and map coloring, differential and algebraic topology, and knot theory.
  • The book introduces the flavor of topology as a whole while introducing the essentials in the context in which the students work (primarily subsets of Euclidean space).
  • A wealth of examples and exercises appear throughout each chapter (as opposed to the end of the chapter) to keep students actively involved in the process of learning and discovery.
  • The projects are designed to be less routine and are ideal for group work. They may involve some exploratory activities where there is not a simple answer, and may lead students through more complicated arguments.
...show less

Edition/Copyright: 05
Cover: Hardback
Publisher: Brooks/Cole Publishing Co.
Year Published: 2005
International: No

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