Description
Book SynopsisTable of Contents1. 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. Groups and Coding
10.1 Coding of Binary Information and Error Detection
10.2 Decoding and Error Correction
10.3 Public Key Cryptology
11. Languages and Finite-State Machines
11.1 Languages
11.2 Representations of Special Grammars and Languages
11.3 Finite-State Machines
11.4 Monoids, Machines, and Languages
11.5 Machines and Regular Languages
11.6 Simplification of Machines
Appendix A: Algorithms and Pseudocode
Appendix B: Additional Experiments in Discrete Mathematics
Appendix C: Coding Exercises
