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Full Description
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.
Contents
1. Fundamentals1.1 Sets and Subsets1.2 Operations on Sets1.3 Sequences1.4 Properties of Integers1.5 Matrices1.6 Mathematical Structures2. Logic2.1 Propositions and Logical Operations2.2 Conditional Statements2.3 Methods of Proof2.4 Mathematical Induction2.5 Mathematical Statements2.6 Logic and Problem Solving3. Counting3.1 Permutations3.2 Combinations3.3 Pigeonhole Principle3.4 Elements of Probability3.5 Recurrence Relations 1124. Relations and Digraphs4.1 Product Sets and Partitions4.2 Relations and Digraphs4.3 Paths in Relations and Digraphs4.4 Properties of Relations4.5 Equivalence Relations4.6 Data Structures for Relations and Digraphs4.7 Operations on Relations4.8 Transitive Closure and Warshall's Algorithm5. Functions5.1 Functions5.2 Functions for Computer Science5.3 Growth of Functions5.4 Permutation Functions6. Order Relations and Structures6.1 Partially Ordered Sets6.2 Extremal Elements of Partially Ordered Sets6.3 Lattices6.4 Finite Boolean Algebras6.5 Functions on Boolean Algebras6.6 Circuit Design7. Trees7.1 Trees7.2 Labeled Trees7.3 Tree Searching7.4 Undirected Trees7.5 Minimal Spanning Trees8. Topics in Graph Theory8.1 Graphs8.2 Euler Paths and Circuits8.3 Hamiltonian Paths and Circuits8.4 Transport Networks8.5 Matching Problems8.6 Coloring Graphs9. Semigroups and Groups9.1 Binary Operations Revisited9.2 Semigroups9.3 Products and Quotients of Semigroups9.4 Groups9.5 Products and Quotients of Groups9.6 Other Mathematical Structures10. Languages and Finite-State Machines10.1 Languages10.2 Representations of Special Grammars and Languages10.3 Finite-State Machines10.4 Monoids, Machines, and Languages10.5 Machines and Regular Languages10.6 Simplification of Machines11. Groups and Coding11.1 Coding of Binary Information and Error Detection11.2 Decoding and Error Correction11.3 Public Key CryptologyAppendix A: Algorithms and PseudocodeAppendix B: Additional Experiments in Discrete MathematicsAppendix C: Coding Exercises
