Kolman, Bernard, Busby, R., Ross, S.C. 　著

目次

1. Fundamentals. Sets and Subsets. Operations on Sets. Sequences.Division in the Integers. Matrices. Mathematical Structures. 2. Logic.Propositions and Logical Operations. Conditional Statements. Methods ofProof. Mathematical Induction. 3. Counting. Permutations. Combinations. ThePigeonhole Principle. Elements of Probability. Recurrence Relations. 4.Relations and Digraphs. Product Sets and Partitions. Relations and Digraphs.Paths in Relations and Digraphs. Properties of Relations. EquivalenceRelations. Computer Representation of Relations and Digraphs. Operations onRelations. Transitive Closure and Warshall's Algorithm. 5. Functions.Functions. Functions for Computer Science. Growth of Functions. PermutationFunctions. 6. Order Relations and Structures. Partially Ordered Sets.Extremal Elements of Partially Ordered Sets. Lattices. Finite BooleanAlgebras. Functions on Boolean Algebras. Circuit Design. 7. Trees. Trees.Labeled Trees. Tree Searching. Undirected Trees. Minimal Spanning Trees. 8.Topics in Graph Theory. Graphs. Euler Paths and Circuits. Hamiltonian Pathsand Circuits. Transport Networks. Matching Problems. Coloring Graphs. 9.Semigroups and Groups. Semigroups. Products and Quotients of Semigroups.Groups. Products and Quotients of Groups. 10. Languages and Finite-StateMachines. Languages. Representations of Special Grammars. And Languages.Finite-State Machines. Semigroups, Machines, and Languages. Machines andRegular Languages. Simplification of Machines. 11. Groups and Coding.Coding of Binary Information and Error Detection. Decoding and ErrorCorrection. Appendix A: Algorithms and Pseudocode. Appendix B:Experiments in Discrete Mathematics.