# Discrete Mathematical Structures (Classic Version),6th edition

• Bernard Kolman Drexel University
• Robert Busby
• Sharon C. Ross
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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.

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 Warshallâ€™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 C: Coding Exercises

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