Discrete Mathematics for Computer Science

Discrete mathematics becomes easier to grasp when you get to test an idea before someone names it. This problem-led introduction builds mathematical thinking for computer science through puzzles, proofs, counterexamples, and short Python explorations. Its focus is the course Mathematical Thinking in Computer Science, the first course in the related Coursera specialization.

Rather than treating mathematics as a collection of results to memorize, the book invites you to work through a question, look for a pattern, and then examine the reasoning behind a solution. That makes it a useful fit for learners who want to strengthen both their mathematical arguments and their computational intuition.

Reason your way through proofs and puzzles

The chapters introduce proof techniques, existence arguments, examples and counterexamples, logic, and reductio ad absurdum. Later topics include recursion and induction, double counting, invariants, and termination. Together, these ideas offer several ways to approach a problem when the answer is not immediately obvious.

See discrete mathematics at work in computer science

Python code snippets connect mathematical concepts with computation, while the book’s project chapters use the 15-puzzle to explore permutations, solvability, and implementation. Further examples introduce SAT solvers and integer linear programming, showing how formal tools can help investigate problems beyond pencil-and-paper calculations.

Learn by trying, not just reading

Active learning is central to the book’s structure: readers encounter problems before the explanations, and many exercises include solutions. The text also describes interactive puzzles and automatically graded quizzes associated with the course. The book itself remains self-contained for readers who prefer to work through the material independently.

A thoughtful starting point for computer science students

Students and independent learners looking for a guided introduction to mathematical reasoning will find a clear path through foundational topics, with programming used as a way to test and illuminate ideas—not as a substitute for understanding them.