Combinatorics [Hardcover]

This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course.

Features retained from the first edition:

• Lively and engaging writing style
• Timely and appropriate examples
• Numerous well-chosen exercises
• Flexible modular format
• Optional sections and appendices

Highlights of Second Edition enhancements:

• Smoothed and polished exposition, with a sharpened focus on key ideas
• Expanded discussion of linear codes
• New optional section on algorithms
• Greatly expanded hints and answers section
• Many new exercises and examples

Chapter 1: The Mathematics of Choice.

1.1. The Fundamental Counting Principle.

1.2. Pascal’s Triangle.

*1.3. Elementary Probability.

*1.4. Error-Correcting Codes.

1.5. Combinatorial Identities.

1.6. Four Ways to Choose.

1.7. The Binomial and Multinomial Theorems.

1.8. Partitions.

1.9. Elementary Symmetric Functions.

*1.10. Combinatorial Algorithms.

Chapter 2: The Combinatorics of Finite Functions.

2.1. Stirling Numbers of the Second Kind.

2.2. Bells, Balls, and Urns.lS