Applied Combinatorics is a comprehensive guidebook to the fundamental concepts of combinatorics and their practical applications. This book covers a wide range of topics, from basic counting principles to graph theory and network analysis, making it an essential reference for students and professionals alike.
The book is divided into seven sections, each focusing on a specific area of combinatorics. The first section introduces the basic principles of counting and provides numerous examples and exercises to reinforce these concepts. The second section explores the topic of generating functions, which are powerful tools for solving combinatorial problems. The third section covers the principles of graph theory, including graph coloring, connectivity, and matching theory.
The fourth section of the book delves into the fascinating field of design theory, which is concerned with the construction of experimental designs for scientific research. The fifth section focuses on combinatorial algorithms and their applications, including the popular traveling salesman problem and the knapsack problem. The sixth section explores the intersection between combinatorics and probability theory, including topics such as random walks and Markov chains.
Finally, the seventh section of the book discusses some advanced topics in combinatorics, including the theory of partitions, the combinatorics of words, and the study of matroids.
Throughout the book, the authors emphasize the practical applications of combinatorics in a wide range of fields, from computer science to genetics to social networks. Each chapter concludes with a set of problems that challenge the reader to apply the concepts they have learned to real-world situations.
With its clear and accessible style, Applied Combinatorics is an ideal text for undergraduate and graduate courses in mathematics, computer science, and engineering. It is also a valuable resource for researchers and professionals in these fields who are seeking to deepen their understanding of combinatorial theory and its applications.