离散数学结构 Discrete Mathematical Structures9不是PDF格式)
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【推荐级别】
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☆☆☆☆☆
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49 次 |
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【文件格式】 |
PDF
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【ISBN】 |
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【资料语言】 |
英文
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【文件大小】 |
29.81MB
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【上传时间】 |
2008-05-16
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【共享者】 |
kemin
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资料说明：
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Discrete Mathematical Structures, 6/E
Bernard Kolman
Robert Busby
Sharon C. Ross
ISBN-10: 0132297515
ISBN-13: 9780132297516
Publisher: Prentice Hall
Copyright: 2009
Format: Cloth; 552 pp
Estimated Availability: 07/24/2008
Suggested retail price: $123.00 (*Price subject to change)
This item is not yet available for purchase. See estimated availability date above.
* The focus on computer science prepares students for future computer science careers.
* The emphasis on proof lays the foundation for mathematical thinking.
* Clear organization of topics prevents students from being overwhelmed. The authors treat relations and digraphs as two aspects of the same fundamental idea, which is then used as the basis of virtually all the concepts introduced in the book.
* Vignettes of mathematical history open each chapter, providing students with a practical background of how these ideas were developed.
* Additional number theory coverage provides more information on the properties of integers, including base n representations, and gives more contexts for isomorphism.
* Cryptology is explored throughout the book, introducing students to this exciting field.
* Coverage of coding provides students with a full picture of all of its aspects, including efficiency, effectiveness, and security. A set of coding exercises for each chapter is also included in Appendix C.
* Exercises emphasize multiple representations of concepts, and provide practice on reading and writing mathematical proofs.
* Experiments provide opportunities for in-depth exploration and discovery, as well as for writing and for working in groups. Topics include weighted voting systems, Petri nets, Catalan numbers, and others.
* End-of-chapter material includes Tips for Proofs, a summary of Key Ideas, and a Self-Test, which contains a set of conceptual review questions to help students identify and synthesize the main ideas of each chapter.
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
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