Discrete mathematical Structure

1. Fundamentals
2. Logic
3. Counting
4. Relations and Digraphs
5. Functions
6. Order Relations and Structures
7. Trees
8. Topics in Graph Theory
9. Semigroups and Groups
10. Groups and Coding
11. Languages and Finite-State Machines


Salient Features
• The focus on computer science prepares students for future computer science careers.
• The emphasis on proof lays the foundation for mathematical thinking.
• Clear organization of topics prevents students from being overwhelmed. The authors treat relations and digraphs as two aspects of the same fundamental idea, which is then used as the basis of virtually all the concepts introduced in the book.
• Vignettes of mathematical history open each chapter, providing students with a practical background of how these ideas were developed.
• Additional number theory coverage provides more information on the properties of integers, including base n representations, and gives more contexts for isomorphism.
• Cryptology is explored throughout the book, introducing students to this exciting field.
• Coverage of coding provides students with a full picture of all of its aspects, including efficiency, effectiveness, and security. A set of coding exercises for each chapter is also included in Appendix C.
• Exercises emphasize multiple representations of concepts, and provide practice on reading and writing mathematical proofs.
• Experiments provide opportunities for in-depth exploration and discovery, as well as for writing and for working in groups. Topics include weighted voting systems, Petri nets, Catalan numbers, and others.
• End-of-chapter material includes Tips for Proofs, a summary of Key Ideas, and a Self-Test, which contains a set of conceptual review questions to help students identify and synthesize the main ideas of each chapter.