PrefaceA Word to Students1 Fundamentals 1.1 Sets and Subsets 1.2 Operations on Sets 1.3 Sequences 13 1.4 Division in the Integers 1.5 Matrices 32 1.6 Mathematical Structures2 Logic 50 2.1 Propositions and Logical Operations 2.2 Conditional Statements 2.3 Methods of Proof 2.4 Mathematical Induction3 Counting 3.1 Permutations 3.2 Combinations 3.3 Pigeonhole Principle 3.4 Elements of Probability 3.5 Recurrence Relations4 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 Computer Representation of 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 Functions6 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 Design7 Trees 7.1 Trees 7.2 Labeled Trees 7.3 Tree Searching 7.4 Undirected Trees 7.5 Minimal Spanning Trees8 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 Graphs9 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 Structures10 Languages and Finite-State Machines 10.1 Languages 10.2 Representations of Special Grammars and Languages 10.3 Finite-State Machines 10.4 Monoids, Machines, and Languages 10.5 Machines and Regular Languages 10.6 Simplification of Machines11 Groups and CodingAppendix A:Aigorithms and PsenudocodeAppendix B:Additionol Experiments in Discrete MathematicsAnswers to Odd-Numberde ExercisesAnswers to Chapter Self-TestsGlossaryIndexPhoto Credits