# Lecture Notes

Lectures were prepared in Apple Keynote (.key files) and are given here as .pdf files. The schedule was adjusted due to weather cancellations or other changes in the syllabus.

1. Sets and Strings (22 Jan) (.pdf)
2. Propositions and Boolean Operations (24 Jan) (.pdf)
3. Set Operations and Truth Tables (27 Jan) (.pdf)
4. Rules for Propositional Proofs (29 Jan) (.pdf)
5. Propositional Proof Strategies (31 Jan) (.pdf)
6. Predicates and Relations (3 Feb) (.pdf)
7. Quantifiers and Languages (7 Feb) (.pdf)
8. Proofs With Quantifiers (10 Feb) (.pdf)
9. Relations and Functions (12 Feb) (.pdf)
10. Partial Orders and Equivalence Relations (14 Feb) (.pdf)
11. (Lecture 11 merged into Lecture 10)
12. Divisibility and Primes (18 Feb) (.pdf)
13. Modular Arithmetic (19 Feb) (.pdf)
14. The Chinese Remainder Theorem (21 Feb) (.pdf)
15. The Fundamental Theorem of Arithmetic (24 Feb) (.pdf)
16. Recursive Definition (26 Feb) (.pdf)
17. Proof by Induction for Naturals (28 Feb) (.pdf)
18. Variations on Induction fof Naturals (3 Mar) (.pdf)
19. Proving the Basic Facts of Arithmetic (5 Mar) (.pdf)
20. Strings and String Operations (7 Mar) (.pdf)
21. Induction for Problem Solving (10 Mar) (.pdf)
22. Graphs, Paths, and Trees (12 Mar) (.pdf)
23. Recursion on Trees (14 Mar) (.pdf)
24. General, Breadth-First, and Depth-First Search (24 Mar) (.pdf)
25. BFS and DFS on Graphs (26 Mar) (.pdf)
26. Uniform-Cost and A* Search (28 Mar) (.pdf)
27. Games and Adversary Search (31 Mar) (.pdf)
28. Regular Expressions and Their Languages (2 Apr) (.pdf)
29. Proving Regular Expression Identities (4 Apr) (.pdf)
30. Proving Properties of the Regular Languages (7 Apr) (.pdf)
31. What DFA's Can and Can't Do (9 Apr) (.pdf)
32. The Myhill-Nerode Theorem (11 Apr) (.pdf)
33. NFA's and the Subset Construction (14 Apr) (.pdf)
34. Killing λ-Moves: λ-NFA's to NFA's (16 Apr) (.pdf)
35. Constructing NFA's From Regular Expressions (18 Apr) (.pdf)
36. State Elimination: NFA's to Regular Expressions (23 Apr) (.pdf)
37. Two-Way Automato and Turing Machines (25 Apr) (.pdf)
38. Turing Machine Semantics (28 Apr) (.pdf)
39. The Halting Problem and Unsolvability (30 Apr) (.pdf)