Notes on Introductory Discrete Mathematics by V.K. Balakrishnan

Overview

• Title: Introductory Discrete Mathematics
• Author: V.K. Balakrishnan
• Publisher: Dover (affordable reprint of an older book)
• Target Audience: Beginners in mathematics, especially useful for computer science students
• Personal Experience: The speaker has owned the book for over a decade and has read portions of it.

Key Features

• Affordability: Priced reasonably due to being a Dover reprint.
• Availability: Readily available copies.
• Reading Level: Not the easiest book, but the author finds it helpful.
• Format: Softcover, suitable for reading in bed or on the go.

Content Overview

Topics Covered

• Set Theory: Basics of sets; foundational for advanced mathematics.
• Combinatorics:
  • Basic counting rules
  • Permutations and combinations
  • Pigeonhole principle
  • Inclusion-exclusion principle
• Graph Theory:
  • Introduction to graphs and digraphs
  • Trees and applications, such as spanning tree problems and shortest path problems
• Advanced Topics:
  • Generating functions
  • Recurrence relations
  • MP completeness

Structure of the Book

• Readability: Generally readable with worked-out examples; definitions are highlighted.
• Exercises: Found at the end of each chapter with varying levels of difficulty; answers provided for some exercises.
• Different Approach: Emphasizes a different way of thinking compared to other math fields, like statistics.

Personal Insights

• Recommended for self-study or as a supplement for classes.
• The author enjoys the exercises and finds them engaging, noting that it can be fun to read and learn math in casual settings (e.g., at a mechanic's shop).

Additional Resources

• Courses: The speaker offers math courses on their website (mathsorcerer.com), including topics like algebra and calculus.
• YouTube Channel: The speaker has another channel called "The Internet Sorcerer," offering diverse content.

Conclusion

• The speaker highly recommends Introductory Discrete Mathematics for anyone interested in learning discrete math, especially for computer science students.
• Emphasizes the book's affordability, readability, and engaging approach to mathematics.