2nd Edition

Discrete Mathematics with Ducks

By Sarah-Marie Belcastro Copyright 2019
    700 Pages
    by Chapman & Hall

    700 Pages 518 B/W Illustrations
    by Chapman & Hall

    700 Pages 518 B/W Illustrations
    by Chapman & Hall

    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. 


    • 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

    Preface for Instructors and Other Teachers

    Preface for Students and Other Learners

    Theme: The Basics

    1 Counting and Proofs

    2 Sets and Logic

    3 Graphics and Functions

    4 Induction

    5 Algorithms with Ciphers

    Theme I Supplement

    6 Binomial Coefficients and Pascal’s Triangle

    7 Balls and Boxes and PIE: Counting Techniques

    8 Recurrences

    9 Cutting Up Food: Counting and Geometry

    III Theme: Graph Theory

    10 Trees

    11 Euler’s Formula and Applications

    12 Graph Traversals

    13 Graph Coloring

    Theme III Supplement: Problems on the Theme of Graph Theory

    IV Other Material

    14 Probability and Expectation

    15 Fun with Cardinality

    16 Number Theory

    17 Computational Complexity

    A Solutions to Check Yourself Problems

    B Solutions to Bonus Check-Yourself Problems

    C The Greek Alphabet and Some Uses for Some Letters

    D List of Symbols




    sarah-marie belcastro is a free-range mathematician who works primarily in topological graph theory.  She enjoys connecting people to each other, connecting ideas to each other, and connecting people to ideas. Among her many non-pure-mathematics interests are the mathematics of knitting, pharmacokinetics, dance (principally ballet and modern), and changing the world. sarah-marie did her undergraduate work at Haverford College and her Ph.D. at the University of Michigan. She currently directs the summer program MathILy.