Discrete Mathematical Structures, Sixth Edition,
offers a clear and concise presentation of the fundamental concepts of discrete mathematics. Ideal for a one-semester introductory course, this text contains more genuine computer science applications than any other text in the field. This book is written at an appropriate level for a wide variety of majors and non-majors, and assumes a college algebra course as a prerequisite. 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. New to this Edition New sections on Logic, Mathematical Statements, and Logic and Problem Solving help students understand proofs and proof techniques. Additional exercises help students develop conjectures and how to prove or disprove them. More applications, exercises, and figures have been added to help students learn and retain the material. New material on fuzzy sets and fuzzy logic introduces students to a topic that is extremely important for modern issues of automated feedback and control of processes. Popular puzzles like Sudoku and their underlying mathematical connections form a continuous thread in the text, connecting set theory, Boolean matrices, algorithms and coding, logic, the general construction of proofs, coloring problems and polynomials, and other topics in a way that students will find both interesting and instructive.
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