This book has two primary objectives: It teaches students fundamental concepts in discrete mathematics (from counting to basic cryptography to graph theory), and it teaches students proof-writing skills. With a wealth of learning aids and a clear presentation, the book teaches students not only how to write proofs, but how to think clearly and present cases logically beyond this course. Overall, this book is an introduction to mathematics. In particular, it is an introduction to discrete mathematics. All of the material is directly applicable to computer science and engineering, but it is presented from a mathematician's perspective. While algorithms and analysis appear throughout, the emphasis is on mathematics. Students will learn that discrete mathematics is very useful, especially those whose interests lie in computer science and engineering, as well as those who plan to study probability, statistics, operations research, and other areas of applied mathematics.

Benefits:

• NEW! Self Tests: A self test appears at the end of every chapter. The problems are of various degrees of difficulty, and complete answers appear in Appendix B.
• Flexible Coverage: The topics can be arranged in various ways, allowing instructors to take a computer science and engineering focus, an abstract algebra focus, a discrete structures focus, or a broad focus.
• NEW! Induction: The sections on mathematical induction have been reworked with new motivational material, more examples, and more problems. The induction section is now essentially independent of the proof by smallest counterexample section.
• NEW! New Sections: The book includes new sections covering topics such as recurrence relations and combinatorial proof.
• NEW! New Opening: The introductory section, "Joy," motivates students by describing the pleasure of doing mathematics.
• NEW! Examples: New and revised explanations, examples, and exercises appear throughout the text. New proofs appear in sections 4 and 26.
• Proof Templates: Proof templates appear throughout the book and give students the basic skeleton of the proof as well as boilerplate language.
• Growing Proofs: The author teaches students how to write proofs by instructing them to begin their proofs by first writing the first sentence and next writing the last sentence. Students then work the proof from both ends until they meet in the middle.
• Mathspeak: Marginal notes explain many of the idiosyncrasies of mathematical English.
• Hints: Appendix A contains an extensive collection of hints (and some answers when necessary) that point students in the correct direction.