The volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry. It presents the detailed Hecke algebra and braid representation to illustrate the original Jones polynomial (rather than the algebraic formal definition many other books and research articles use) and provides self-contained proofs of the Tait conjecture (one of the big achievements from the Jones invariant). It also presents explicit computations to the Casson-Lin invariant via braid representations.With the approach of an explicit computational point of view on knot invariants, this user-friendly volume will benefit readers to easily understand low-dimensional topology from examples and computations, rather than only knowing terminologies and theorems.

This book constitutes the refereed post-conference proceedings of the Second BenchCouncil International Federated Intelligent Computing and Block Chain Conferences, FICC 2020, held in Qingdao, China, in October/ November 2020.The 32 full papers and 6 short papers presented were carefully reviewed and selected from 103 submissions. The papers of this volume are organized in topical sections on AI and medical technology; AI and big data; AI and block chain; AI and education technology; and AI and financial technology.

The volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry. It presents the detailed Hecke algebra and braid representation to illustrate the original Jones polynomial (rather than the algebraic formal definition many other books and research articles use) and provides self-contained proofs of the Tait conjecture (one of the big achievements from the Jones invariant). It also presents explicit computations to the Casson-Lin invariant via braid representations.With the approach of an explicit computational point of view on knot invariants, this user-friendly volume will benefit readers to easily understand low-dimensional topology from examples and computations, rather than only knowing terminologies and theorems.

A tutorial on the major nonlinear systems analysis and design techniques.