Discrete Mathematical Structures
United States Edition
5th Edition
Published on 14. November 2003
Book
Hardback
528 pages
978-0-13-045797-4 (ISBN)
Description
For one- or two-term freshman/sophomore-level courses in Discrete Mathematics.
Combining a careful selection of topics with previews of their genuine applications in computer science, this text, more than any other book in its field, is written at an elementary level with a strong pedagogical focus. It limits its area and coverage of topics to those that students will actually utilize, and emphasizes both basic theory and applications, giving a firm foundation for more advanced courses, as well as providing an excellent reference work for those courses.
Combining a careful selection of topics with previews of their genuine applications in computer science, this text, more than any other book in its field, is written at an elementary level with a strong pedagogical focus. It limits its area and coverage of topics to those that students will actually utilize, and emphasizes both basic theory and applications, giving a firm foundation for more advanced courses, as well as providing an excellent reference work for those courses.
More details
Edition
5th edition
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
Professional and scholarly
Dimensions
Height: 273 mm
Width: 209 mm
Thickness: 25 mm
Weight
1164 gr
ISBN-13
978-0-13-045797-4 (9780130457974)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Bernard Kolman | Robert Busby | Sharon C. Ross
Discrete Mathematical Structures
Book
08/2008
6th Edition
Pearson
€151.02
Article exhausted; check for reprint
Previous edition
Bernard Kolman | Robert C. Busby | Sharon Cutler Ross
Discrete Mathematical Structures
United States Edition
Book
12/1999
4th Edition
Pearson
€89.12
Article exhausted; check for reprint
Content
1. Fundamentals.
Sets and Subsets. Operations on Sets. Sequences. Properties of Integers. Matrices. Mathematical Structures.
2. Logic.
Propositions and Logical Operations. Conditional Statements. Methods of Proof. Mathematical Induction.
3. Counting.
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.
5. Functions.
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.
7. Trees.
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.
Sets and Subsets. Operations on Sets. Sequences. Properties of Integers. Matrices. Mathematical Structures.
2. Logic.
Propositions and Logical Operations. Conditional Statements. Methods of Proof. Mathematical Induction.
3. Counting.
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.
5. Functions.
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.
7. Trees.
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.