This textbook presents all the fundamental topics of discrete mathematics that are introduced from the perspectives of a pure mathematician and an applied computer scientist. The integration of the two perspectives is seen throughout the book; key concepts are motivated and explained through real-world examples, and yet are still formalized with mathematical rigor. Thus, it is an excellent introduction to computer science and software engineering. The first author is a leading mathematician in the area of logic, computability, and theoretical computer science, with more than 25 years of teaching and research experience. The second author is a computer science PhD student at the University of Washington specializing in database systems. The father-and-daughter team bring together two different perspectives to create a unified book for students interested in learning discrete mathematics, connections between discrete mathematics and computer science, and the mathematical foundations of computer science. Readers will learn how to formally define abstract concepts, reason about objects (e.g., programs, graphs and numbers), investigate properties of algorithms, and prove their correctness. The textbook concentrates on the study of several well-known algorithmic problems (e.g., the path problem for graphs and finding the greatest common divisor), inductive definitions, proofs of correctness of algorithms via loop invariants and induction, the basics of formal methods (e.g., propositional logic), finite state machines, counting, probability, and the foundations of databases (e.g., relational calculus). Key Features • The father-daughter co-authorship offers complementary views on the subject. The synergy between these two perspectives is seen throughout the book; along with every definition there is an example, for every proof there is a discussion, and every chapter comes with at least one real-world programming exercise • This book is compact and easy-to-read, unlike many existing discrete mathematics textbooks that tend to be close to 1,000 pages long • The organization of the textbook differs from standard discrete mathematics textbooks in various ways. First, the book starts with a discussion of graphs, trees, and algorithms on these structures. These structures relate directly to real-world problems, and are thus more interesting and easier to understand. In contrast, most discrete mathematics textbooks introduce set theory and functions first, even though these are conceptually more abstract and difficult. Second, sets and operations on sets are introduced with the goal of explaining relational calculus as a foundation to databases. Often, this connection is not made in discrete mathematics textbooks. Our textbook makes this connection to immediately see the application of sets to something concrete and useful. Third, the book connects functions and the transition tables of automata. This link between different concepts in the book will help the reader better understand the topic. Finally, throughout the textbook, the induction principles are emphasized. For example, many abstract objects are defined inductively, program correctness is analyzed through loop invariants and there are many proofs that are based on mathematical induction

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