| Date | Lecture Slides | Sections from text to be completed BEFORE class |
|---|
| W, 9/7 | L1: Intro to Language of Math | R1: 1.1 Variables, Universal, Existential and Conditional Statements |
| F, 9/9 | L2: Sets and Ordered Pairs | R2: 1.2 the language of Sets |
| | |
| M, 9/12 | No Class! | |
| W, 9/14 | D1: Translating between English and Math | |
| W, 9/14 | L3: Relations and Functions | R3: 1.3: Relations &
Functions; R3 Quiz Preamble |
| F, 9/16 | L4: PropLogic | R4: 2.1 Logical Form and Equivalence |
| | |
| M, 9/19 | L5: Conditionals and Intro to Natural Deduction | R5: 2.2 Conditional Statements |
| W, 9/21 | D2: Translating between English and PropCalc | |
| W, 9/21 | L6: CNF and Natural Deduction | R6: 2.3 Valid and Invalid arguments |
| F, 9/23 | L7: PredCalc with Equality | R7: 3.1 Predicates and Quantified Statements I |
| | |
| M, 9/26 | L8: More PredCalc | Hw1 due; R8: 3.2 Predicates and Quantified Statements II |
| W, 9/28 | D3: PropCalc Natural Deduction Proofs | |
| W, 9/28 | L9: Tarski's Definition of Truth | R9: 3.3 Statements with multiple quantifiers |
| F, 9/30 | L10: Nat. Ded. Rules: =-i, =-e, ∀-e, ∃-i | R10: 3.4 Arguments with quantifiers.
R10 Preamble |
| | |
| M, 10/3 | No Class! | |
| W, 10/5 | D4: Disc4: Review including answers to Hw2 | |
| W, 10/5 | Chapt 4: Number Theory and Proof Methods | R11: 4.1 Direct Proof and Counterexample I |
| Th 10/6, 7 - 9p.m. | First Test | ISB 135 |
| F, 10/7 | L12: Last 2 Natural Deduction Rules | R12: 4.2 Direct Proof and Counterexample II: Rational Numbers |
| | |
| Tu, 10/11 | L13: Divisiblity Proofs | R13: 4.3 Direct Proof and Counterexample III: Divisibility |
| W, 10/12 | No Class and No Discussion! | |
| F, 10/14 | L14: Division and Modular Arithmetic | R14: 4.4 Direct Proof and Counterexample IV: argument by cases and quotient/remainder theorem |
| | |
| M, 10/17 | L15: Rings, Commutative Rings and Fields | R15: 4.5 Direct Proof and Counterexample V: Floor and Ceiling |
| W, 10/19 | D5. Disc 5: Z/mZ | |
| W, 10/19 | L16: Square root of 2 is irrational; There are
infinitely many primes | R16: 4.6, 4.7 Indirect Proof |
| F, 10/21 | L17: Euclid's Algorithm | R17:4.8 Euclid's Algorithm |
| | |
| M, 10/24 | L18: Mathematical Induction | Chapt 5 Mathematical Induction R18: 5.1 |
| W, 10/26 | D6. Disc 6: Induction | |
| W, 10/26 | L19: Eulerian Walks | R19:5.2 Mathematical Induction II |
| F, 10/28 | L20: Complete Induction | R20: 5.3 Mathematical Induction III |
| | |
| M, 10/31 | L21: Euler's Formula and Well Ordering | Hw3 due; R21: 5.4 Strong Mathematical Induction and the Well-Ordering Principle |
| W, 11/2 | D7. Disc 7: Unique Factorization Thm,
Disc 7 Ans | |
| W, 11/2 | L22: Inductive Definitions and Structural Induction | R22: 5.9 Recursive Definitions and Structural Induction |
| F, 11/4 | L23: Truth Game | R23: 7.1 |
| | |
| M, 11/7 | L24: Functions | R24: 7.2, 7.3 1:1, onto, composition and inverse of functions |
| W, 11/9 | D8. Review | Hw4 due; |
| W, 11/9 | No Class! | |
| Th 11/10, 7 - 9p.m. | Second
Test | THOM 104 |
| | |
| M, 11/14 | L25: Relations and Digraphs | R25: 8.1, 8.2 Relations |
| W, 11/16 | L26: Equivalence Relations and
Fermat's Thm | R26: 8.3 Equivalence Relations |
| F, 11/18 | L27: Cryptography and
RSA | R27: 8.4 RSA; Rivest,
Shamir & Adelman explain RSA |
| | |
| | Thanksgiving Recess | |
| | |
| M, 11/28 | L28: DFS on Undirected Graphs | R28: 10.1, 10.2: Graphs and Euler Paths |
| W, 11/30 | D9. No discussion meeting today | |
| W, 11/30 | L29: DFS on Directed Graphs | R29: 10.5, 10.6 trees |
| Th, 12/1 | | Hw5 due |
| F, 12/2 | L30: Deterministic Finite Automata (DFA) | R30: 12.1: just skim |
| | |
| M, 12/5 | L31: The DFA Pumping Lemma | R31: 12.1 |
| W, 12/7 | D10. Disc 10: Regular or Not? | |
| W, 12/7 | L32: Nondeterministic Finite Automata (NFA) | R32: 12.2 |
| F, 12/9 | L33: Kleene's Theorem | R33: 12.3 |
| | |
| M, 12/12 | L34: Turing Machines & Unsolvability
of Halting | |
| W, 12/14 | D11. Review hw5 Ans, Disc 10 Ans | |
| W, 12/14 | L35: Summary and Review | |
| | |
| W, 12/21 | Final | 1 - 3 pm, Marcus 131 |