Discrete Mathematics with Ducks

Discrete mathematics brings together ideas that help explain counting, logical reasoning, networks, and the structure of algorithms. In Discrete Mathematics with Ducks, Sarah-Marie Belcastro makes those ideas approachable through lively presentation and a steady emphasis on doing mathematics: exploring a question, testing a pattern, and learning how to make a convincing argument.

Build the foundations: logic, counting, and proof

The book begins with counting principles and proof, then develops sets, logic, functions, and graphs. Its sequence gives learners opportunities to connect abstract definitions with problems and examples, while building habits of mathematical reasoning along the way.

Follow the ideas into algorithms and ciphers

Induction, algorithms, modular arithmetic, and classical ciphers extend the opening foundations into new settings. These topics show how discrete structures support both formal arguments and procedures for solving problems.

Explore combinatorics and graph theory

Later material turns to binomial coefficients, Pascal’s triangle, counting techniques, recurrences, and graph theory. The contents also reach probability, number theory, cardinality, and computational complexity, offering a broad view of the subject rather than a single narrow strand.

Learning by trying, not just reading

“Try This!” activities, discovery problems, examples, projects, exercises, and supplementary problem sets make active problem-solving part of the reading experience. The book also includes separate guidance for students and instructors, with suggestions for classroom use and self-study.

A thoughtful companion for discrete mathematics study

This second edition is suited to students learning discrete mathematics and to instructors looking for material that supports discussion and active practice. Its light touch gives the subject personality, while the mathematical content keeps the focus on concepts, problems, and proofs.