The book introduces you to discrete mathematics, emphasizing the main topics and the reasoning on which mathematical thinking is based. It teaches you to think abstractly as you study the concepts of logic and proof. You will become familiar with logical circuits, algorithm analysis, recursive thinking, computability, cryptography, and combinatorics, discovering that the concepts of discrete mathematics underpin all modern science and technology, and you will build the necessary background for higher-level computer science and mathematics courses. Suzanna Epp examines the difficulties in understanding logic and language, with an approach that helps students of different knowledge levels grasp the basics of mathematical reasoning, enabling them to construct well-structured mathematical arguments. With definitions, theorems, over 2500 exercises and problems for practice, and 500 solved examples, the book serves as a comprehensive reference manual to which you will systematically refer when attending advanced courses. The proofs are developed so that you can resort to either a shorter or a more detailed guidance, depending on your level of understanding. With the book's flexible structure, instructors can combine core topics with optional material to cover different curricula and emphasize different course requirements. Contents: Mathematical language Logic of compound statements Logic of quantified statements Elementary number theory and methods of proof Sequences, mathematical induction, and recursion Set theory Properties of functions Properties of relations Counting and probability Graph and tree theory Algorithm efficiency analysis Regular expressions and finite state automata Appendix A: Properties of real numbers Appendix B: Solutions and hints for selected exercises