| Day | Topics | Preparation | |
|---|---|---|---|
| Mon. 8/29 | Introduction. Statements, negation, conjunction, disjunction. | Sec. 2.1 | |
| Wed. 8/31 | Logical equivalences, tautologies, contradictions.
Conditionals and biconditionals. |
Secs. 2.1-2 | |
| Fri. 9/2 | Conditionals and English usage. Logical arguments. |
Secs. 2.2-3 | |
| Wed. 9/7 | Negation Logical arguments Circuits. |
Secs. 2.2-3 | |
| Fri. 9/9 | Class cancelled: power outage. | . | |
| Mon. 9/12 | Logical puzzle (2.3 #37,38).
Disjunctive normal form (2.4 #18, 20) |
Secs. 2.3-4 | |
| Wed. 9/15 | TEST: Logic | Secs. 2.1-4 | |
| Fri. 9/17 | Sets: subset, union, intersection. | Secs. 1.1-2, 6.1-2 (pp. 336-344) | |
| Mon. 9/19 | Predicates, truth set of a predicate. Quantified predicates. |
Secs. 1.1-2, 3.1 | |
| Wed. 9/21 | Translation from English and negation. Multiply quantifed predicates. |
Secs. 3.2-3 | |
| Fri. 9/23 | Arguments with quantified predicates.
Logic puzzles. |
Sec. 3.4 (2nd Ed. 2.3#27, 3rd 2.4#31, 4th. Ed 3.4#31.) | |
| Mon. 9/26 | Proving theorems about sets | Secs. 6.1-2 | |
| Wed. 9/28 | Disproof by counterexample.
Algebraic proofs |
Secs. 6.3 | |
| Fri. 9/30 | Partitions, the addition rule, inclusion/exclusion | Secs. 6.1 (p. 344-348), 9.3 | |
| Mon. 10/3 | Cartesian product, the multiplication rule. Power set. |
Secs. 6.1 (p. 344-348), 9.2 (525-529) | |
| Wed. 10/5 | Mathematics: Axiom, Definition, Theorem, Proof
Axioms for the integers. |
Ch. 3.1 (and my lecture notes Ch 3. | |
| Fri. 10/7 | TEST: Sets, proofs, counting. | Ch 3, 6, Secs. 9.2, 9.3 | |
| Mon. 10/10 | The Quotient Remainder Theorem. The Euclidean algorithm. |
Sec. 4.4 Sec. 4.8 | |
| Wed. 10/12 | Representation of integers in binary, octal, etc. Primes and the Unique Factorization Theorem. |
3rd E.: Sec. 1.5 (pp. 57-60, 70-73) 4.1 (pp. 211-213) 3.3
(pp. 153-4).
4th Ed.: Sec. 2.5 (pp. 78-81, 91-93), 5.1 (pp. 240-242), 4.3 (pp.176-7) | |
| Fri. 10/14 | Primes and the Unique Factorization Theorem.
Rational numbers and irrational numbers. Proof by contradiction. |
3rd Ed. Sec. 3.3 (pp. 153-4); 4th Ed. 4.3 (pp.176-7) Secs. 4.2, 4.6 | |
| Mon. 10/17 | Floor and ceiling functions. | Secs. 4.5. | |
| Wed. 10/19 | Question before the test? Sequences, summation and product notation. |
Sec. 5.1 | |
| Fri. 10/21 | TEST. | Ch. 4 | |
| Mon. 10/24 | Summation and product notation.
Explicitly defined sequences and recursively defined sequences |
Sec. 5.1, 5.6 | |
| Wed. 10/26 | The well ordering principle. Induction. | Sec. 5.2, 5.4. | |
| Fri. 10/28 | Proof by mathematical induction. | Sec. 5.2-3, | |
| Mon. 10/31 | Induction proofs for divisibility and inequalities | Sec. 5.2-3 | |
| Wed. 11/2 | Recursively defined functions and strong induction. | Sec. 5.4 | |
| Fri. 11/4 | Solving recursive sequences. | Sec. 5.6,7 | |
| Mon. 11/7 | Functions and relations. | Sec. 7.1, 8.1. | |
| Wed. 11/9 | TEST. | Ch 5. | |
| Fri. 11/11 | Veteran's day: no class. | . | |
| Mon. 11/14 | Relations, functions.
The inverse of a relation. |
Sec. 7.1, 8.1. | |
| Wed. 11/16 | Functions: injective, surjective, bijective.
Composition of functions. | >
Sec. 7.2,3. | |
| Fri. 11/18 | Relations on a set.
Properties: reflexive, symmetric, transitive |
Sec. 8.2 | |
| Mon. 11/21 | Equivalence relations and partitions. | Sec. 8.3 | |
| Wed. 11/23 | Equivalence relations: important examples. | Sec. 8.3 | |
| Mon. 11/28 | Antisymmetric relations. Partial orders. |
Sec 8.5 | |
| Wed. 11/30 | Partial orders. | Sec 8.5 | |
| Fri. 12/2 | TEST | Secs 7.1-3, 8.1-3, 8.5. | |
| Mon. 12/5 | Four ways to count. | Sec. 6.2,5 | |
| Wed. 12/7 | From counting to probability. Poker hands. |
Sec. 9.1,2,5 | |
| Fri. 12/10 | Binomial theorem. Pascal's triangle. Questions and exam prep. | Sec. 9.7 | |
| Fri. 12/16 (10:30-12:30) | FINAL EXAM. | Cumulative. See Review Sheet |