Completely up-to-date, illustrated throughout, and written in an accessible style, Knots and Surfaces is an account of the mathematical theory of knots and its interaction with related fields. This is an area of intense research activity, and this text provides the advanced undergraduate with a superb introduction to this exciting field. Beginning with a simple diagrammatic approach, the book proceeds through recent advances to areas of current research. Topics including topological spaces, surfaces, the fundamental group, graphs, free groups, and group presentations combine to form a coherent and highly developed theory with which to explore and explain the accessible and intuitive problems of knots and surfaces. - ;The main theme of this book is the mathematical theory of knots and its interaction with the theory of surfaces and of group presentations. Beginning with a simple diagrammatic approach to the study of knots, reflecting the artistic and geometric appeal of interlaced forms, Knots and Surfaces takes the reader through recent advances in our understanding to areas of current research. Topics included are straightforward introductions to topological spaces, surfaces, the fundamental group, graphs, free groups, and group presentations. These topics combine into a coherent and highly developed theory to explore and explain the accessible and intuitive problems of knots and surfaces. Both as an introduction to several areas of prime importance to the development of pure mathematics today, and as an account of pure mathematics in action in an unusual context, this book presents novel challenges to students and other interested readers. -
Genera of the Arborescent Links
... by Philip J. Davis Celestial Mechanics, by Harry Pollard Field Theory and its Classical Problems, by Charles Robert Hadlock The Generalized Riemann Integral, by Robert M. McLeod From Error-Correcting Codes through Sphere Packings to ...
Quandles are essentially knots translated into algebra. This book provides an accessible introduction to quandle theory for readers with a background in linear algebra.
MR1238875(94i:57007) [6] J. Scott Carter and Masahico Saito, Knotted surfaces and their diagrams, Mathematical Surveys and Monographs, vol. 55, American Mathematical Society, Providence, RI, 1998. MR1487374 (98m:57027) [7] R. H. Fox, ...
Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds.
The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
... Introduction to Analytic and Probabilistic Number Theory, Third Edition, 2015 Firas Rassoul-Agha and Timo Seppäläinen, A Course on Large Deviations with an Introduction to Gibbs Measures, 2015 Diane Maclagan and Bernd Sturmfels, ...
Knots Unravelled: From String to Mathematics