ABSTRACT

Discrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels.  

The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they’ve learned.  As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems. 

The author’s lively and friendly writing style is appealing to both instructors and students alike and encourages readers to learn. The book’s light-hearted approach to the subject is a guiding principle and helps students learn mathematical abstraction. 

Features:

  • The book’s Try This! sections encourage students to construct components of discussed concepts, theorems, and proofs
  • Provided sets of discovery problems and illustrative examples reinforce learning
  • Bonus sections can be used by instructors as part of their regular curriculum, for projects, or for further study

part 1|2 pages

Part I Theme: The Basics

chapter 1|24 pages

Counting and Proofs

chapter 2|38 pages

Sets and Logic

chapter 3|38 pages

Graphs and Functions

chapter 4|24 pages

Induction

chapter 5|36 pages

Algorithms with Ciphers

chapter |10 pages

Theme I Supplement

part 2|2 pages

Part II Theme: Combinatorics

chapter 8|32 pages

Recurrences

chapter 9|24 pages

Cutting Up Food: Counting and Geometry

part |2 pages

Part III Theme: Graph Theory

chapter 10|38 pages

Trees

chapter 11|24 pages

Euler’s Formula and Applications

chapter 12|32 pages

Graph Traversals

chapter 13|32 pages

Graph Coloring

part 4|2 pages

Part IV Other Material

chapter 14|36 pages

Probability and Expectation

chapter 15|30 pages

Fun with Cardinality

chapter 16|22 pages

Number Theory

chapter 17|26 pages

Computational Complexity