Key Message: Discrete Mathematical Structures, Sixth Edition, offers a clear and concise presentation of the fundamental concepts of discrete mathematics. This introductory book contains more genuine computer science applications than any other text in the field, and will be especially helpful for readers interested in computer science. This book is written at an appropriate level for a wide variety of readers, and assumes a college algebra course as the only prerequisite. Key Topics: Fundamentals; Logic; Counting; Relations and Digraphs; Functions; Order Relations and Structures; Trees; Topics in Graph Theory; Semigroups and Groups; Languages and Finite-State Machines; Groups and Coding Market: For all readers interested in discrete mathematics.

Combining a careful selection of topics with coverage of their genuine applications in computer science, this book, more than any other in this field, is clearly and concisely written, presenting the basic ideas of discrete mathematical structures in a manner that is understandable. Limiting its scope and depth of topics to those that readers can actually utilize, this book covers first the fundamentals, then follows with logic, counting, relations and digraphs, functions, order relations and structures, trees, graph theory, semigroups and groups, languages and finite-state machines, and groups and coding. With its comprehensive appendices and index, this book can be an excellent reference work for mathematicians and those in the field of computer science.

Publisher:

Pearson Prentice Hall

ISBN:

9780132297516

Publication date:

July 2008

Length:

257mm

Width:

203mm

Thickness:

25mm

Weight:

1111g

Edition:

6th Edition

Pages:

522

Illustrations:

Illustrated

Readership:

Undergraduate

Illustrated:

Illustrated

• 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. 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 Machines 11. Groups and Coding 11.1 Coding of Binary Information and Error Detection 11.2 Decoding and Error Correction 11.3 Public Key Cryptology Appendix A: Algorithms and Pseudocode Appendix B: Additional Experiments in Discrete Mathematics Appendix C: Coding Exercises