Knots and Links [Paperback]

A richly illustrated 2004 textbook on knot theory; minimal prerequisites but modern in style and content.Knot theory is a subject in which naturally occurring questions are often so simple to state that they can be explained to a child. Yet finding answers may require ideas from the forefront of research. Peter Cromwell has written a textbook designed for use at advanced undergraduate or beginning graduate level courses. Numerous examples and exercises serve to help students through the material, and an instructor's manual is available online.Knot theory is a subject in which naturally occurring questions are often so simple to state that they can be explained to a child. Yet finding answers may require ideas from the forefront of research. Peter Cromwell has written a textbook designed for use at advanced undergraduate or beginning graduate level courses. Numerous examples and exercises serve to help students through the material, and an instructor's manual is available online.Knot theory is the study of embeddings of circles in space. Peter Cromwell has written a textbook on knot theory designed for use in advanced undergraduate or beginning graduate-level courses. The exposition is detailed and careful yet engaging and full of motivation. Numerous examples and exercises serve to help students through the material, while an instructor's manual is available online.Preface; 1. Introduction; 2. A topologist's toolkit; 3. Link diagrams; 4. Constructions and decompositions of links; 5. Spanning surfaces and genus; 6. Matrix invariants; 7. The Alexander-Conway polynomial; 8. Rational tangles; 9. More polynomials; 10. Closed braids and arc presentations; Appendix A. Knot diagrams; Appendix B. Numerical invariants; Appendix C. Properties; Appendix D. Polynomials; Appendix E. Polygon coordinates; Appendix F. Family properties; Bibliography; Index. The book has a satisfying, unifying goalclear prose, systematic rigor, attractive layout, and copious diagrams all add to thl3*