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.
1. Fundamentals 1.1 Sets and Subsets 1.2 Operations on Sets 1.3 Sequences 1.4 Properties of Integers 1.5 Matrices 1.6 Mathematical Structures 2. Logic 2.1 Propositions and Logical Operations 2.2 Conditional Statements 2.3 Methods of Proof 2.4 Mathematical Induction 2.5 Mathematical Statements 2.6 Logic and Problem Solving 3. Counting 3.1 Permutations 3.2 Combinations 3.3 Pigeonhole Principle 3.4 Elements of Probability 3.5 Recurrence Relations 112 4. Relations and Digraphs 4.1 Product Sets and Partitions 4.2 Relations and Digraphs 4.3 Paths in Relations and Digraphs 4.4 Properties of Relations 4.5 Equivalence Relations 4.6 Data Structures for Relations and Digraphs 4.7 Operations on Relations 4.8 Transitive Closure and Warshall's Algorithm 5. Functions 5.1 Functions 5.2 Functions for Computer Science 5.3 Growth of Functions 5.4 Permutation Functions 6. Order Relations and Structures 6.1 Partially Ordered Sets 6.2 Extremal Elements of Partially Ordered Sets 6.3 Lattices 6.4 Finite Boolean Algebras 6.5 Functions on Boolean Algebras 6.6 Circuit Design 7. Trees 7.1 Trees 7.2 Labeled Trees 7.3 Tree Searching 7.4 Undirected Trees 7.5 Minimal Spanning Trees 8. Topics in Graph Theory 8.1 Graphs 8.2 Euler Paths and Circuits 8.3 Hamiltonian Paths and Circuits 8.4 Transport Networks 8.5 Matching Problems 8.6 Coloring Graphs 9. Semigroups and Groups 9.1 Binary Operations Revisited 9.2 Semigroups 9.3 Products and Quotients of Semigroups 9.4 Groups 9.5 Products and Quotients of Groups 9.6 Other Mathematical Structures 10. Groups and Coding 10.1 Coding of Binary Information and Error Detection 10.2 Decoding and Error Correction 10.3 Public Key Cryptology 11. Languages and Finite-State Machines 11.1 Languages 11.2 Representations of Special Grammars and Languages 11.3 Finite-State Machines 11.4 Monoids, Machines, and Languages 11.5 Machines and Regular Languages 11.6 Simplification of Machines Appendix A: Algorithms and Pseudocode Appendix B: Additional Experiments in Discrete Mathematics Appendix C: Coding Exercises
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