Formal Knot Theory (Dover Books on Mathematics) by Louis H. Kauffman (PDF)

Description

This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students. The author, Louis H. Kauffman, is a professor in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago. Kauffman draws upon his work as a topologist to illustrate the relationships between knot theory and statistical mechanics, quantum theory, and algebra, as well as the role of knot theory in combinatorics.Featured topics include state, trails, and the clock theorem; state polynomials and the duality conjecture; knots and links; axiomatic link calculations; spanning surfaces; the genus of alternative links; and ribbon knots and the Arf invariant. Key concepts are related in easy-to-remember terms, and numerous helpful diagrams appear throughout the text. The author has provided a new supplement, entitled “Remarks on Formal Knot Theory,” as well as his article, “New Invariants in the Theory of Knots,” first published in The American Mathematical Monthly, March 1988.

User’s Reviews

Opiniones editoriales About the Author Louis H. Kauffman is a professor in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a modern introduction into a field that takes a different perspective to knot theory. It is written for advanced Undergraduates or beginning graduates. Knowledge of Topology would be useful but not needed. It is self contained. What you should get from this book is the intuition that Kauffman brings to the table. It has been updated with papers that he has written on ArXiv. The printing of the book is top notch and it is an excellent Dover publication.You can tell this is an older book by looking at the font and quality of the printing. It is low quality. I havn’t looked into the book too much, so I can’t comment on quality of the information, but it seems to be fairly standard in what it talks about. More of an upper lever introductory text. I would suggest looking into Livingston’s book or Adams’ as these are much more basic. However Livingston doens’t include proofs as much and is kindof unclear on the geometrical approach. Still all are good books.An excellent introduction to the mathematics of knots. An introductory chapter sets up the start of knot theory and the basics. Additional chapters deveolp the basic laws, or eauations, of the theory. A good introduction for the amateur or as an adjunct foro a formal cokurse.学習者に分かりやすいようにという意図をもって書かれた本ではない。著者はこの分野では有名だが、この本はとてもお勧めできない。

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