| Day | Topics | Preparation | |
|---|---|---|---|
| Wed. 1/22 | Introduction. Statements, negation, conjunction, disjunction. | Sec. 1.1 | |
| Fri. 1/24 | Logical equivalences, tautologies, contradictions.
Conditionals |
Secs. 1.1-2 | |
| Mon. 1/27 | Conditionals and English usage, biconditionals.
Logical arguments. |
Secs. 1.2-3 | |
| Wed. 1/29 | Logical arguments. | Sec. 1.3 | |
| Fri. 1/31 | Logic circuits. Predicates and quantifiers. | Secs. 1.4, 2.1 | |
| Mon. 2/3 | Predicates, quantifiers. | Secs. 2.1 | |
| Wed. 2/5 | Predicates and quantifiers: Translation from English, truth sets, compound predicates. |
Sec. 2.2 | |
| Fri. 2/7 | Conditional predicates. Multiply quantified statements. Arguments with quantified predicates. |
Sec.2.3 | |
| Mon. 2/10 | A logic problem (2.3#27).
Logical arguments and proof. |
Sec.2.3 | |
| Wed. 2/12 | 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. |
Secs. 3.1, 3.3, 3.4 | |
| Fri. 2/14 | Three theorems we assume: The quotient-remainder theorem. If prime p divides ab then p divides a or b Unique factorization of integers. |
Secs. 3.4, 3.3, | |
| Mon. 2/17 | Questions?
Proof of biconditionals. Proof using the contrapositve. |
Sec. 3.5 | |
| Wed. 2/19 | Floor and ceiling functions. | Sec. 3.5 | |
| Fri. 2/21 | Proof by contradiction and two classy theorems. Irrationality of sqrt(2), the infinitude of primes |
Secs. 3.6,7 | |
| Mon. 2/24 | Questions? Problems from 3.6, and 3.7. | . | |
| Wed. 2/26 | EXAM | Secs. 1.1-4; 2.1-2; 3.1, 3.3-7; | |
| Fri. 2/28 | Sets: the basics. | Sec. 5.1 | |
| Mon. 3/3 | Intersection, union, empty set, universal set. | Secs. 5.2-3 | |
| Wed. 3/5 | Main Properties of Sets (Theorem 5.2.2) | Secs. 5.2, 3 | |
| Fri. 3/7 | Set difference, algebra of sets. Partitions, power set. |
Secs. 5.1-3 | |
| Mon. 3/10 | Two partitions of the power set.
Cartesian product, relations. |
Sec. 5.1, 10.1 | |
| Wed. 3/12 | Three representations of relations: set, table, arrow diagram. Examples: functions, mod n |
10.1, p. 559, Example 10.3.8 | |
| Fri. 3/14 | Properties of relations: reflexive, symmetric, transitive |
Sec. 10.2 | |
| Mon. 3/17 | Equivalence relations | Sec. 10.3 | |
| Wed. 3/19 | Some important equivalence relations: mod n, the rationals, topology |
Sec. 10.3 (10.3.10 and Exercises. 26, 34) | |
| Fri. 3/21 | Partially ordered sets. | Sec. 10.5 | |
| Mon. 3/24 | More on Posets | Sec. 10.5 | |
| Wed. 3/26 | Functions, one to one and onto. | Ch. 10 Sec. 7.1,3 | |
| Fri. 3/28 | The pigeonhole principle. Inverse functions. | Sec. 7.3, 4, | |
| Mon. 4/7 | Sequences, summation and product notation. | Sec. 4.1 | |
| Wed. 4/9 | EXAM | Primarily Secs. 3.6,7; Ch. 5; Ch. 10. | |
| Fri. 4/11 | Sequences. Summation and product notation | Sec. 4.1 | |
| Mon. 4/14 | The well ordering principle. Induction. | Sec. 4.2, p. 217-218. | |
| Wed. 4/16 | Induction, the quotient remainder theorem | Secs. 4.2-3 and p. 418 | |
| Fri. 4/18 | Strong induction, recursion | Secs. 4.4, 8.1 | |
| Mon. 4/21 | Solving a recurrence relation.
Proving the formula. |
Sec. 8.2 | |
| Wed. 4/23 | Multiplication rule. Language of probability | Sec 6.1-2 | |
| Fri. 4/25 | Counting, the basics. Inclusion, exculsion. | Secs. 6.2-3 | |
| Mon. 4/28 | Four ways to choose, and how to count them. | Secs. 6.3-4 | |
| Wed. 4/30 | Poker hands. | Sec. 6.3-4 | |
| Fri. 5/2 | EXAM. | Secs. 4.1-4; 8.1-2. | |
| Mon. 5/5 | The binomial theorem and Pascal's triangle. | Secs. 6.6, 6.7 | |
| Wed. 5/7 | Return of exam and review. | . |