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Beginning Topology (2004)
ÁöÀºÀÌ
:
Sue Goodman
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Brooks Cole
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1 edition
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256 pages
ISBN
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0534424260
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690 Point
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.
1.introduction to point set topology
2.surfaces
3.the euler characteristic
4.maps and graphs
5.vector fields on surfaces
6.the fundamental group
7.introduction to knots
"I've taught undergraduate topology from this book twice, and the students loved it both times. It has a good selection of topics from a range of areas, and, I think, adequately conveys the spirit of topology in a way that a more traditional text on point-set topology does not. Rather than getting lost in a maze of uninteresting technicalities, Goodman introduces the reader to wonderful gems like knot theory, map coloring theory, and the classification of surfaces. As a result, the text is more suited for a topics course than for a course preparing students for algebraic topology. (Although the fundamental group is covered in this book.)
In summary, I really like this book, and when I saw that it was rated 1 star by two other people, I felt like I needed to rectify the situation."
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