| 1 | The Foundations: Logic and Proofs |
| 1.1 | Propositional Logic |
| 1.2 | Propositional Equivalences |
| 1.3 | Predicates and Quantifiers |
| 1.4 | Nested Quantifiers |
| 1.5 | Rules of Inference |
| 1.6 | Introduction to Proofs |
| 1.7 | Proof Methods and Strategy |
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| 2 | Basic Structures: Sets, Functions |
| 2.1 | Sets |
| 2.2 | Set Operations |
| 2.3 | Functions |
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| 3 | The Fundamentals: Algorithms |
| 3.1 | Algorithms |
| 3.2 | The Growth of Functions |
| 3.3 | Complexity of Algorithms |
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| 4 | Induction and Recursion |
| 4.1 | Mathematical Induction |
| 4.2 | Strong Induction and Well-Ordering |
| 4.3 | Recursive Definitions and Structural Induction |
| 4.4 | Recursive Algorithms |
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| 5 | Counting |
| 5.1 | The Basics of Counting |
| 5.2 | The Pigeonhole Principle |
| 5.3 | Permutations and Combinations |
| 5.4 | Binomial Coefficients |
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| 9 | Graphs |
| 9.1 | Graphs and Graph Models |
| 9.2 | Graph Terminology and Special Types of Graphs |
| 9.3 | Representing Graphs |
| 9.4 | Connectivity |
| 9.6 | Shortest-Path Problems |
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| 10 | Trees |
| 10.1 | Introduction to Trees |
| 10.2 | Application of Trees |
| 10.3 | Tree Traversal |
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| 12 | Modeling Computation (if time permits) |
| 12.1 | Languages and Grammars |
| 12.2-3 | Finite-State Machines |
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