What you will learn in Discrete Mathematics & Mathematical Logic

1. 1. Statements and Truth Tables

   What can be true or false, and how to check every case at once.

2. 2. Logical Connectives

   And, or, not — and the or that ordinary English does not have.

3. 3. Implication and Its Relatives

   Four statements that look alike, and the one that says the same thing.

4. 4. Quantifiers and Their Negation

   For all, there exists — and why the order of two of them changes everything.

5. 5. Direct Proof

   Assume the hypothesis, derive the conclusion, and write it down.

6. 6. Proof by Contradiction and Contrapositive

   Assume the opposite, and see what breaks.

7. 7. Mathematical Induction

   One domino, a rule about the next one, and both are needed.

8. 8. Counterexamples and Refutation

   One case refutes; no number of cases proves.

9. 9. Inclusion–Exclusion

   Count everything, then take back what you counted twice.

10. 10. The Pigeonhole Principle

    Existence from counting alone — and it will not say which.

11. 11. Modular Arithmetic

    Arithmetic that wraps around, and the one chapter here on a syllabus.

12. 12. Graphs and Networks

    Dots, lines, and the seven bridges of Königsberg.

13. 13. Trees and Traversals

    Connected with no cycles — and how to walk a network.

14. 14. Recurrence Relations

    A rule for the next term, and the discrete twin of module 21.

15. 15. Boolean Algebra and Logic Circuits

    Truth tables with wires, and the algebra that shrinks them.

16. 16. Counting Steps: an Introduction to Complexity

    How the work grows, and why hardware is not the answer.