Top Books for Discrete Mathematics: A Comprehensive Guide

Discrete mathematics is a broad and essential field for computer science, electrical engineering, and many other domains. However, with its vast range of topics, no single book can cover everything. This guide will recommend some of the best books that can help you master discrete mathematics.

1. Bóna’s “A Walk Through Combinatorics”

Discrete mathematics encompasses a wide range of topics, and one book that stands out for its thorough coverage is A Walk Through Combinatorics by Miklós Bóna. This book excels in covering enumerative combinatorics and graph theory concepts, offering a variety of exercises at different levels of difficulty. The exercises include even some open problems, which can challenge advanced readers. Each chapter is thoughtfully designed to introduce and explore these essential concepts, making it a valuable resource for both advanced students and professionals.

2. Jukna’s “Extremal Combinatorics”

Another book that stands out is Extremal Combinatorics by Stasys Jukna. This book is known for its self-contained nature, making it easy for students to follow along without needing extensive background knowledge. It focuses on providing estimates for the sizes of combinatorial objects. While it is particularly appealing to computer scientists, mathematicians can also benefit greatly from this book. The book features elegant and whimsical proofs that highlight recurring themes in the subject. The book is not only informative but also engaging, making complex concepts easier to understand.

3. Miller’s “The Probability Lifesaver”

The Probability Lifesaver by Steven J. Miller is an excellent resource for students interested in discrete mathematics. The book emphasizes four main areas:

Counting Discrete probability Continuous probability The art of problem-solving: how to write convincing proofs, how to approach complex problems, and how to use algebra as a tool

While the entire book is worth exploring, it isn't necessary to cover every chapter. Instead, pick up the book and focus on the topics that interest you the most. The book offers a practical approach to understanding probability and problem-solving techniques, making it a versatile tool for students at any level.

Additional Resources for Learning Discrete Mathematics

For those who prefer self-study or need a more structured approach, there are additional resources available online. One highly recommended resource is the MIT OpenCourseWare: Mathematics for Computer Science. This course offers a complete set of lecture notes and readings, essentially containing a book of its own. The notes are well-organized and provide clear explanations and illustrations of concepts. The lectures complement the notes, making this a comprehensive and effective learning tool for mastering discrete mathematics.

Based on personal experience, the "Kenneth H. Rosen" book has been very helpful. Although the author acknowledges that the book may not be taken seriously by all, it has proven to be a valuable resource for those looking to strengthen their understanding of discrete mathematics. Whether you're a beginner or an advanced student, there’s something in this book for everyone.

In conclusion, while no single book can cover every aspect of discrete mathematics, these recommendations should provide a solid foundation for learning and mastering the subject. Choose the books that best suit your needs and interests, and don't hesitate to explore additional resources like MIT OpenCourseWare for a more comprehensive understanding.