Foundations of Combinatorics with Applications (Dover Books on Mathematics)

Book Details

• Author: Edward A. Bender

• Publisher: Dover

• ISBN: 9780486446035

• Pages: 1022

• Binding: Paperback

• Edition: Illustrated

• Release Date: 18-01-2013

• Languages: English

About The Book
This comprehensive introduction to combinatorics is designed for upper-level undergraduates and graduate students in engineering, science, and mathematics. Serving as a bridge between computer science and mathematics, it provides a solid foundation for understanding the principles that underpin many areas of theoretical and applied mathematics.

The book is divided into four sections:

1. Counting and Listing: The first section covers basic counting principles, including functions, decision trees, and sieving methods, essential for understanding combinatorial structures.

2. Graph Theory: The second section delves into the fundamental concepts of graph theory, presenting key topics and their applications.

3. Applications to Computer Science and Mathematics: This part explores real-world applications, such as induction and recursion, sorting theory, and rooted plane trees, demonstrating the practical utility of combinatorics in various fields.

4. Generating Functions: The final section introduces generating functions as a powerful tool for studying counting problems, offering a deep mathematical approach to combinatorics.

Throughout the book, numerous exercises, along with notes and references, reinforce key concepts. Solutions to odd-numbered exercises and all appendix exercises are provided, making this book an invaluable resource for self-study and course work in combinatorics.