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Discrete Mathematical Structures, 5/e by Bernard Kolman, Robert C. Busby, Sharon Cutler Ross, Prentice Hall, 2004, ISBN 0-13-045797-3

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1. Fundamentals.
   • Sets and Subsets.
     1. Real Analysis: Sets and Relations
   • Operations on Sets.
     1. Venn Diagrams
     2. Interactive Venn Diagrams
   • Sequences.
   • Properties of Integers.
     1. Sieve of Eratosthenes
     2. Divisibility Criteria
     3. Divisibility Rules
     4. Notes and Literature on Prime Numbers
     5. The Prime Pages
     6. GIMPS Home Page
     7. Number Guessing Game
     8. Napier Bones
     9. Introduction to Cryptography
   • Matrices.
   • Mathematical Structures
   .
2. Logic.
   • Propositions and Logical Operations.
     1. Factasia Logic
     2. Lewis Carroll's Game of Logic
     3. According to the Rules
   • Conditional Statements.
     1. Truth Table
   • Methods of Proof.
     1. Proofs in Mathematics
   • Mathematical Induction
     1. Breaking Chocolate Bars
   .
3. Counting.
   • Permutations.
     1. Information on Permutations
   • Combinations.
     1. Information on Combinations of a Set
   • Pigeonhole Principle.
     1. The Puzzlers' Pigeonhole
   • Elements of Probability.
   • Recurrence Relations
     1. Recurrence Relations
     2. Fibonacci Numbers and the Golden Section
     3. The Tower of Hanoi
     4. Tower of Hanoi Facts
     5. The Tower of Hanoi -- recursive solutions
     6. Tower of Hanoi (TH) on the Web
     7. Huffman Code Generator
   .
4. Relations and Digraphs.
   • Product Sets and Partitions.
   • Relations and Digraphs.
     1. Real Analysis: Sets and Relations
   • Paths in Relations and Digraphs.
   • Properties of Relations.
   • Equivalence Relations.
     1. Equivalence Relations
   • Computer Representation of Relations and Digraphs.
   • Operations on Relations.
   • Transitive Closure and Warshall's Algorithm.
     1. Transitive closure
5. Functions.
   • Functions.
   • Functions for Computer Science.
   • Growth of Functions.
     1. Big-O
   • 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.
     1. Depth First Search
     2. Depth First Search
     3. Breadth First Search
   • Undirected Trees.
   • Minimal Spanning Trees.
8. Topics in Graph Theory.
   • Graphs.
     1. Graph Theory Lessons
   • Euler Paths and Circuits.
     1. Eulerian Cycle / Chinese Postman
   • Hamiltonian Paths and Circuits.
     1. The Hamiltonian Page
   • Transport Networks.
   • Matching Problems.
   • Coloring Graphs.
     1. Graph Coloring Page
     2. http://www.cs.sunysb.edu/~algorith/files/vertex-coloring.shtml (1.5.7 Vertex Coloring)

     3. http://www.cs.sunysb.edu/~algorith/files/edge-coloring.shtml (1.5.8 Edge Coloring)

     4. http://www.math.gatech.edu/~thomas/FC/fourcolor.html (The Four Color Theorem)

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.

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