Knots and Surfaces
By N. D. Gilbert, T. Porter, N.d. Gilbert
* Publisher: Oxford University Press, USA
* Number Of Pages: 268
* Publication Date: 1994-01-15
* ISBN-10 / ASIN: 0198533977
* ISBN-13 / EAN: 9780198533979
* Binding: Hardcover
Product Description:
This highly readable text details the interaction between the mathematical theory of knots and the theories of surfaces and group presentations. It expertly introduces several topics critical to the development of pure mathematics while providing an account of math "in action" in an unusual context. Beginning with a simple diagrammatic approach to the study of knots that reflects the artistic and geometric appeal of interlaced forms, Knots and Surfaces takes the reader through recent research advances. Topics include topological spaces, surfaces, the fundamental group, graphs, free groups, and group presentations. The authors skillfully combine these topics to form a coherent and highly developed theory to explore and explain the accessible and intuitive problems of knots and surfaces to students and researchers in mathematics.
Summary: Unique approach; vibrant and captivating
Rating: 5
This unique and vibrant book is an introductory book on knot theory that somehow sneaks in a lot more rigorous mathematics than you would expect. Without seeming overly difficult, it somehow manages to include a concise introduction to the basics of knot theory, basic topology, and even a little bit of graph theory, algebraic topology and the necessary algebra.
While assuming little background, this book covers an extraordinarily diverse range of material, and ties it all together. The book is written so that a third-year undergraduate could understand it, but it's interesting enough that a graduate student will still find it fascinating.
What I love most about this book is the choice and ordering of topics--the authors dive right into the material, going to some depth in exploring polynomial invariants before they even touch any "abstract nonsense" so to speak; the machinery is developed throughout the book, as it is needed, and as a result seems natural and fully motivated.
I think this book is excellent for self-study; it would also make a great textbook for a course, although to some extent the material in the course would be dictated by what the book covers. I also think that someone teaching a topology or graph theory courses should keep this book in mind and recommend it to any students inquiring about connections to knot theory.
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