Sets and Subsets. Operations on Sets. Sequences. Properties of Integers. Matrices. Mathematical Structures.
Propositions and Logical Operations. Conditional Statements. Methods of Proof. Mathematical Induction.
Permutations. Combinations. Pigeonhole 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. Equivalence Relations. Computer Representation of Relations and Digraphs. Operations on Relations. Transitive Closure and Warshall's Algorithm.
Functions. Functions for Computer Science. Growth of Functions. Permutation Functions.
6. Order Relations and Structures.
Partially Ordered Sets. Extremal Elements of Partially Ordered Sets. Lattices. Finite Boolean Algebras. Functions on Boolean Algebras. Circuit Design.
Trees. Labeled Trees. Tree Searching. Undirected Trees. Minimal Spanning Trees.
8. Topics in Graph Theory.
Graphs. Euler Paths and Circuits. Hamiltonian Paths and Circuits. Transport Networks. Matching Problems. Coloring Graphs.
9. Semigroups and Groups.
Binary Operations, Revisited. Semigroups. Products and Quotients of Semigroups. Groups. Products and Quotients of Groups.
10. Languages and Finite-State Machines.
Languages. Representations of Special Grammars and Languages. Finite-State Machines. Semigroups, Machines, and Languages. Machines and Regular Languages. Simplification of Machines.
11. Groups and Coding.
Coding of Binary Information and Error Detection. Decoding and Error Correction. Public Key Cryptology.
Appendix A: Algorithms and Pseudocode. Appendix B: Additional Experiments in Discrete Mathematics. Answers to Odd-Numbered Exercises. Answers to Chapter Tests. Index.
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