PART 1. FUNDAMENTALS OF DISCRETE MATHEMATICS.

1. Fundamental Principles of Counting.
The Rules of Sum and Product.Permutations.Combinations: The Binomial Theorem.Combinations with [...] Catalan Numbers (Optional).Summary and Historical Review.2. Fundamentals of Logic.
Basic Connectives and Truth Tables.Logical Equivalence: The Laws of Logic.Logical Implication: Rules of [...] Use of Quantifiers.Quantifiers, Definitions, and the Proofs of Theorems.Summary and Historical Review.3. Set Theory.
Sets and [...] Operations and the Laws of Set Theory.Counting and Venn Diagrams.A First Word on [...] Axioms of Probability (Optional).Conditional Probability: Independence (Optional).Discrete Random Variables (Optional).Summary and Historical Review.4. Properties of the Integers: Mathematical Induction.
The Well-Ordering Principle: Mathematical Induction.Recursive [...] Division Algorithm: Prime [...] Greatest Common Divisor: The Euclidean [...] Fundamental Theorem of Arithmetic.Summary and Historical Review.5. Relations and Functions.
Cartesian Products and Relations.Functions: Plain and [...] Functions: Stirling Numbers of the Second Kind.Special [...] Pigeonhole Principle.Function Composition and Inverse Functions.Computational Complexity.Analysis of Algorithms.Summary and Historical Review.6. Languages: Finite State Machines.
Language: The Set Theory of Strings.Finite State Machines: A First Encounter.Finite State Machines: A Second Encounter.Summary and Historical Review.7. Relations: The Second Time Around.
Relations Revisited: Properties of Relations.Computer Recognition: Zero-One Matrices and Directed Graphs.Partial Orders: Hasse Diagrams.Equivalence Relations and Partitions.Finite State Machines: The Minimization Process.Summary and Historical Review.

PART 2. FURTHER TOPICS IN ENUMERATION.

8. The Principle of Inclusion and Exclusion.
The Principle of Inclusion and Exclusion.Generalizations of the Principle.Derangements: Nothing Is in Its Right [...] Polynomials.Arrangements with Forbidden Positions.Summary and Historical Review.9. Generating Functions.
Introductory Examples.Definition and Examples: Calculational Techniques.Partitions of [...] Exponential Generating [...] Summation Operator.Summary and Historical Review.10. Recurrence Relations.