Quandles: An Introduction to the Algebra of Knots (Student Mathematical Library)

La 4e de couv. indique : "From prehistory to the present, knots have been used for purposes both artistic and practical. The modern science of Knot Theory has ramifications for biochemistry and mathematical physics and is a rich source of research projects for undergraduate and graduate students and professionals alike. Quandles are essentially knots translated into algebra. This book provides an accessible introduction to quandle theory for readers with a background in linear algebra. Important concepts from topology and abstract algebra motivated by quandle theory are introduced along the way. With elementary self-contained treatments of topics such as group theory, cohomology, knotted surfaces and more, this book is perfect for a transition course, an upper-division mathematics elective, preparation for research in knot theory, and any reader interested in knots." Quandles And Their Kin--kei Racks, Biquandles, And Biracks--are Algebraic Structures Whose Axioms Encode The Movement Of Knots In Space, Say Elhamdadi And Nelson, In The Same Way That Groups Encode Symmetry And Orthogonal Transformations Encode Rigid Motion. They Introduce Quandle Theory To Readers Who Are Comfortable With Linear Algebra And Basic Set Theory But May Have No Previous Exposure To Abstract Algebra, Knot Theory, Or Topology. They Cover Knots And Links, Quandles, Quandles And Groups, Generalizations Of Quandles, Enhancements, And Generalized Knots And Links. Knots And Links -- Algebraic Structures -- Quandles -- Quandles And Groups -- Generalizations Of Quandles -- Enhancements -- Generalized Knots And Links. Mohamed Elhamdadi, Sam Nelson. Includes Bibliographical References (pages 237-241) And Index. Provides an accessible introduction to quandle theory for readers with a background in linear algebra. Important concepts from topology and abstract algebra motivated by quandle theory are introduced along the way. Includes elementary self-contained treatments of topics such as group theory, cohomology, knotted surfaces and more. Content: * Knots and links* Algebraic structures* Quandles* Quandles and groups* Generalizations of quandles* Enhancements* Generalizd knots and links* Bibliography* Index