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