Discrete Mathematical Structures (Classic Version)

Discrete Mathematical Structures (Classic Version), 6th edition

  • Bernard Kolman, 
  • Robert Busby, 
  • Sharon C. Ross

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Overview

Discrete Mathematical Structures presents the fundamental concepts of discrete mathematics, while focusing on computer science applications. The authors treat relations and digraphs as two aspects of the same fundamental idea, which is then used as the basis of virtually all concepts in the text.

Published by Pearson (July 14th 2021) - Copyright © 2009

ISBN-13: 9780137538782

Table of contents

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

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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