Discrete Mathematics with Ducks

Containing exercises and materials that engage students at all levels, Discrete Mathematics with Ducks presents a gentle introduction for students who find the proofs and abstractions of mathematics challenging. This classroom-tested text uses discrete mathematics as the context for introducing proofwriting.

Facilitating effective and active learning, each chapter contains a mixture of discovery activities, expository text, in-class exercises, and homework problems.

• Elementary exercises at the end of each expository section prompt students to review the material
• Try This! sections encourage students to construct fundamental components of the concepts, theorems, and proofs discussed.
• Sets of discovery problems and illustrative examples reinforce learning.
• Bonus sections can be used for take-home exams, projects, or further study
• Instructor Notes sections offer suggestions on how to use the material in each chapter

Discrete Mathematics with Ducks offers students a diverse introduction to the field and a solid foundation for further study in discrete mathematics and complies with SIGCSE guidelines. The book shows how combinatorics and graph theory are used in both computer science and mathematics.

Table of Contents

Part I. Theme: The Basics
Chapter 1. Counting and Proofs
Chapter 2. Sets and Logic
Chapter 3. Graphs and Functions
Chapter 4. Induction
Chapter 5. Algorithms with Ciphers

Part II. Theme: Combinatorics
Chapter 6. Binomial Coefficients and Pascal’s Triangle
Chapter 7. Balls and Boxes and PIE: Counting Techniques
Chapter 8. Recurrences
Chapter 9. Cutting Up Food: Counting and Geometry

Part III. Theme: Graph Theory
Chapter 10. Trees
Chapter 11. Euler’s Formula and Applications
Chapter 12. Graph Traversals
Chapter 13. Graph Coloring

Part IV. Other Material
Chapter 14. Probability and Expectation
Chapter 15. Fun with Cardinality

A. Additional Problems
B. Solutions to Check Yourself Problems
C. The Greek Alphabet and Some Uses for Some Letters
D. List of Symbols