Homotopy Theory And Related Topics

by Philip Hackney (Author), Marcy Robertson (Author), Donald Yau (Author)
Studies topics that are somewhat ignored in the existent literature on properads
Contains important results, especially concerning the combinatorics of graphs and graphs substitution
Analyses technical and conceptual difficulties in an easy-to-read manner

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then, It is that they can't see the problem. one day, perhaps you will find the final G.K. Chesterton, The Scandal of Fa­ question. ther Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R.

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then It is that they can't see the problem. one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Min­ kowsky lemma, coding theory and the structure of water meet one another in packing and covering theory: quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

Authors: Adhikari, Mahima Ranjan
Discusses the basic concepts of algebraic topology with numerous related illustrations and applications
Approaches the topic nearly “from scratch” and accompanies students through its natural development
Provides examples and step-by-step instructions and explains problem-solving techniques for a better grasp of the topic
Integrates various concepts of algebraic topology, examples, exercises, applications, and historical notes
Reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to pursue further study

Authors: Adhikari, Mahima Ranjan
Discusses the basic concepts of algebraic topology with numerous related illustrations and applications
Approaches the topic nearly “from scratch” and accompanies students through its natural development
Provides examples and step-by-step instructions and explains problem-solving techniques for a better grasp of the topic
Integrates various concepts of algebraic topology, examples, exercises, applications, and historical notes
Reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to pursue further study