| Day | Topics | Preparation | |
|---|---|---|---|
| Wed. 9/3 | Introduction. Statements, negation, conjunction, disjunction. | Sec. 1.1 | |
| Fri. 9/5 | Logical equivalences, tautologies, contradictions.
Conditionals |
Sec. 1.1-2 | |
| Mon. 9/8 | Conditionals and English usage, biconditionals.
Logical arguments. |
Sec. 1.2-3 | |
| Wed. 9/10 | Logical arguments. | Sec. 1.3 | |
| Fri. 9/12 | Logic circuits. Predicates and quantifiers. | Sec. 1.4, 2.1 | |
| Mon. 9/15 | Predicates, quantifiers, truth sets. | Secs. 2.1 | |
| Wed. 9/17 | Translation from English. Compound predicates. Multiply quantified predicates. |
Secs. 2.1,2 | |
| Fri. 9/19 | Arguments with quantified predicates.
A logic problem.(2.3#27) |
Sec. 2.3 | |
| Mon. 9/22 | Fundamental properties of the integers.
First proof: The sum of evens is even. |
Sec.2.3 | |
| Wed. 9/24 | Two more proofs: 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. 9/26 | Three theorems we assume: The quotient-remainder theorem. If prime p divides ab then p divides a or b Unique factorization of integers. |
Sec. 3.4, 3.3, | |
| Mon. 9/29 | Questions? Rational numbers. The floor and ceiling functions. |
Sec. 3.5 | |
| Wed. 10/1 | Sets: the basics | Sec. 5.1 | |
| Fri. 10/3 | Your opportunity to ask questions. | . | |
| Mon. 10/6 | EXAM | Secs. 1.1-4; 2.1-2; 3.1, 3.3-4; | |
| Wed. 10/8 | Proof by contradiction. Two classy theorems: The sum of a rational and an irrational. Irrationality of sqrt(2). |
Secs. 3.7 | |
| Fri. 10/10 | Another classy theorem:
The infinitude of primes.
Intersection and union of sets. |
Sec. 3.7 Sec. 5.1 | |
| Mon. 10/13 | Properties of Sets:
The empty set; Theorems 5.2.2 and 5.3.3 Set difference and symmetric difference |
Sec. 5.1-3 | |
| Wed. 10/15 | Algebraic proofs of set equalities,
Venn diagrams as an aid. Power set, partitions. |
Secs. 5.2,3 | |
| Fri. 10/17 | More on partitions. Two partitions of the power set. |
Secs. 5.2, 3 | |
| Mon. 10/20 | Cartesian product. Relations | Sec. 5.1, 5.3, 10.1 | |
| Wed. 10/22 | Arrow diagrams, tables of relations Functions, mod n |
Sec. 10.1, p. 559, Example 10.3.8 | |
| Fri. 10/24 | Properties of relations: reflexive, symmetric, transitive |
Sec. 10.2 | |
| Mon. 10/27 | Class cancelled due to fire. | . | |
| Wed. 10/29 | Class cancelled due to fire. | . | |
| Fri. 10/31 | Equivalence relations | Sec. 10.3 | |
| Mon. 11/3 | Partitions and equivalence relations. | Sec 10.3 | |
| Wed. 11/5 | Examples of equivalence relations The Mobius strip, the rational numbers. Partially ordered sets. |
10.3.10 and 10.3 ex. 34 Sec. 10.5 | |
| Fri. 11/7 | Partially ordered sets. | Sec. 10.5 | |
| Mon. 11/10 | Functions, one-to-one, onto and both. | Sec. 7.1,3 Sec. 4.1 | |
| Wed. 11/12 | . | . | |
| Fri. 11/14 | EXAM | Primarily Secs. 3.6,7; Ch. 5; Ch. 10. | |
| Mon. 11/17 | The well ordering principle. Induction. | Sec. 4.2, p. 217-218. | |
| Wed. 11/19 | Some induction proofs. | Sec. 4.2-3, p. 217-218. | |
| Fri. 11/21 | Induction proofs. | Sec. 4.4 | |
| Mon. 11/24 | Recursively defined functions. Strong induction . | Sec. 4.4, 8.1 | |
| Wed. 11/26 | Strong induction, the Fibonacci numbers. | Secs 8.1-2. | |
| Mon. 12/1 | Counting and probability. | Sec. 6.1-2 | |
| Wed. 12/3 | EXAM. | Secs. 4.1-4; 8.1-2. | |
| Fri. 12/5 | Inclusion/exclusion principle.
4 ways to choose. |
Sec. 6.3,4. | |
| Mon. 12/8 | Binomial coefficients.
Pascal's triangle. |
Sec. 6.4, 6.6, 6.7 | |
| Wed. 12/10 | Poker hands. The binomial theorem. | . | |
| Fri. 12/12 | Review for final. | . |