| Day | Topics | Preparation | |
|---|---|---|---|
| Wed. 9/4 | Introduction. Statements, negation, conjunction, disjunction. | Sec. 1.1 | |
| Fri. 9/6 | Logical equivalences, tautologies, contradictions.
Conditionals |
Sec. 1.1-2 | |
| Mon. 9/9 | Conditionals and English usage, biconditionals.
Logical arguments. |
Sec. 1.2-3 | |
| Wed. 9/11 | Class canceled | . | |
| Fri. 9/13 | Logical arguments. | Sec. 1.3 | |
| Mon. 9/16 | Logic circuits. Predicates and quantifiers. | Sec. 1.4, 2.1 | |
| Wed. 9/18 | Predicates, quantifiers, truth sets. | Secs. 2.1 | |
| Fri. 9/20 | Conditional predicates. Multiply quantified statements. |
Sec. 2.2 | |
| Mon. 9/23 | Arguments with quantified predicates. A logic problem.(2.3#27) |
Sec.2.3 | |
| Wed. 9/25 | Three proofs: The sum of evens is even. If a divides b and b divides c then a divides c. Consecutive integers have opposite parity. |
Sec. 3.1, 3.3, 3.4 | |
| Fri. 9/27 | Three theorems we assume: The quotient-remainder theorem. If prime p divides ab then p divides a or b |
Sec. 3.4, 3.3, | |
| Mon. 9/30 | Questions?.. Unique factorization of integers. (leftover from Fri.) Proof of biconditionals. Proof using the contrapositve. |
Sec. 3.5 | |
| Wed. 10/2 | EXAM | Secs. 1.1-4; 2.1-2; 3.1, 3.3-4; | |
| Fri. 10/4 | Floor and ceiling functions. | Sec. 3.5 | |
| Mon. 10/7 | Proof by contradiction. Two classy theorems. |
Sec. 3.6,7 | |
| Wed. 10/9 | Review exam. | . | |
| Fri. 10/11 | Irrationality of sqrt(2)
Sets: the basics. |
Secs. 3.7 Sec. 5.1 | |
| Mon. 10/14 | Properties of Sets | Sec. 5.2-3 | |
| Wed. 10/16 | Problems from 3.6, and 3.7. | . | |
| Fri. 10/18 | Set difference, algebra of sets. Partitions, power set. |
Sec. 5.2, 3 | |
| Mon. 10/21 | Two partitions of the power set Cartesian product, relations. |
Sec. 5.1, 5.3, 10.1 | |
| Wed. 10/23 | Arrow diagrams, tables of relations Functions, mod n |
Sec. 10.1, p. 559, Example 10.3.8 | |
| Fri. 10/25 | Properties of relations: reflexive, symmetric, transitive |
Sec. 10.2 | |
| Mon. 10/28 | Equivalence relations | Sec. 10.3 | |
| Wed. 10/30 | Partially ordered sets. | Sec. 10.5 | |
| Fri. 11/1 | Partially ordered sets. The rational numbers. |
Sec. 10.5 10.3.10 and 10.3 ex. 34 | |
| Mon. 11/4 | Questions? Functions, one to one and onto. |
Ch. 10 Sec. 7.1,3 | |
| Wed. 11/6 | EXAM | Primarily Secs. 3.6,7; Ch. 5; Ch. 10. | |
| Fri. 11/8 | Functions, one-to-one, onto and both. | Sec. 7.3 Sec. 4.1 | |
| Mon. 11/11 | Sequences, summation and product notation. | Sec. 4.1 | |
| Wed. 11/13 | The well ordering principle. Induction. | Sec. 4.2, p. 217-218. | |
| Fri. 11/15 | Induction, the quotient remainder theorem | Sec. 4.2-3 and p. 418 | |
| Mon. 11/18 | Strong induction, recursion | Sec. 4.4, 8.1 | |
| Wed. 11/20 | Recursion. | Sec. 8.2 | |
| Fri. 11/22 | Probability and counting. | Sec. 6.1 | |
| Mon. 11/25 | Multiplication rule | Sec 6.2 | |
| Wed. 11/27 | EXAM (a second try!). | Primarily Secs. 3.6,7; Ch. 5; Ch. 10. | |
| Mon. 12/2 | Counting. | Sec. 6.2-3 | |
| Wed. 12/4 | Review of induction. Return of 2nd exam, take 2. |
. | |
| Fri. 12/6 | EXAM. | Secs. 4.1-4; 8.1-2. | |
| Mon. 12/9 | Poker hands. The binomial theorem and Pascal's triangle. | Sec. 6.4, 6.6, 6.7 | |
| Wed. 12/11 | Return of exam and review. | . |