| Day | Topics | Preparation | |
|---|---|---|---|
| Mon. 8/30 | Introduction. Statements, negation, conjunction, disjunction. | Sec. 1.1 | |
| Wed. 9/1 | Logical equivalences, tautologies, contradictions.
Conditionals and biconditionals. |
Secs. 1.1-2 | |
| Fri. 9/3 | Conditionals and English usage. Logical arguments. |
Secs. 1.2-3 | |
| Wed. 9/8 | Logical arguments. Logic circuits. |
Secs. 1.3-4 | |
| Fri. 9/10 | Logic puzzles | Secs. 1.3-4 | |
| Mon. 9/13 | Sets: subset, union, intersection. Predicates, truth set of a predicate. |
Secs. 5.1, 2.1-2 | |
| Wed. 9/15 | Quantified predicates. Negation. Translation from English. |
Secs. 5.1, 2.1-2 | |
| Fri. 9/17 | Multiply quantified predicates. | Secs. 2.3 | |
| Mon. 9/20 | Arguments with quantified predicates.
Logic puzzles.(2nd Ed. 2.3#27, 3rd Ed. 2.4#31) |
Secs. 2.3 (2nd Ed) 2.4 (3rd Ed.) | |
| Wed. 9/22 | Cartesian product, power set, partitions. Theorem 5.2.2: Properties of sets. Proving theorems about sets. |
Secs. 5.1-3 | |
| Fri. 9/24 | Disproof by counterexample.
Partition of a set. The power set. |
Secs. 5.1-3 | |
| Mon. 9/27 | Mathematics: Axiom, Definition, Theorem, Proof
Axioms for the integers. |
Ch. 3.1 (and my lecture notes Ch 3. | |
| Wed. 9/29 | Questions before the exam? Properties of order and divisibility. |
Ch. 3.1,3 (and my lecture notes) | |
| Fri. 10/1 | EXAM | Ch. 1, 2, 5 | |
| Mon. 10/4 | Divisibility The Quotient Remainder Theorem. |
Sec. 3.3 (1st part). | |
| Wed. 10/6 | The Quotient Remainder Theorem. The Euclidean algorithm. |
Sec. 3.4 Sec. 3.8 | |
| Fri. 10/8 | Primes and the Unique Factorization Theorem.
Proof by contradiction. |
Secs. 3.3.3, 3.6 | |
| Mon. 10/11 | Rational numbers and irrational numbers.
Proof by contractiction. |
Secs. 3.5. | |
| Wed. 10/13 | Representation of integers in binary, octal, etc. Floor and ceiling functions. |
1.5, 4.1 (just one page). Sec. 3.7 | |
| Fri. 10/15 | Sequences, summation and product notation. | Sec. 4.1, Sec 8.1 | |
| Mon. 10/18 | Explicitly defined sequences and recursively defined sequences |
Sec. 4.1, Sec 8.1 | |
| Wed. 10/20 | The well ordering principle. Induction. | Sec. 4.2,4. | |
| Fri. 10/22 | Proof by mathematical induction. Some induction proofs. |
Sec. 4.2-3, p. 217-218. | |
| Mon. 10/25 | EXAM | Ch. 3 | |
| Wed. 10/27 | Induction proofs for divisibility and inequalities | Sec. 4.2-3 | |
| Fri. 10/29 | Recursively defined functions and strong induction. | Sec. 4.4, 8.1 | |
| Mon. 11/1 | Functions | Sec. 7.1, 10.1 | |
| Wed. 11/3 | Relations and functions. The inverse of a relation. |
Sec. 7.1, 10.1-2. | |
| Fri. 11/5 | Functions: injective, surjective, bijective. | Sec. 7.1-2. | |
| Mon. 11/8 | Composition of functions. | Sec. 7.4. | |
| Wed. 11/10 | Questions before the exam? | . | |
| Fri. 11/12 | EXAM. | Secs. 4.1-4; 8.1-2. | |
| Mon. 11/15 | Properties of relations on a set:
reflexive, symmetric, transitive |
Sec. 10.2 | |
| Wed. 11/17 | Equivalence relations | Sec. 10.3 | |
| Fri. 11/19 | Equivalence relations | Sec. 10.3 | |
| Mon. 11/22 | Partial orders. | Sec 10.5 | |
| Wed. 11/24 | Partial orders. | Sec 10.5 | |
| Mon. 10/29 | Counting: The multiplication rule, the addition rule. Possibility trees. |
Sec. 6.2-3 | |
| Wed. 12/1 | From the addition rule to inclusion-exclusion. | Sec 6.3 | |
| Fri. 12/3 | EXAM | Secs 7.1,2,4 (1,3,5 in 2nd Ed.) Secs 10.1,2,3,5. | |
| Mon. 12/6 | Four ways to count. | Sec. 6.1,4 | |
| Wed. 12/8 | From counting to probability. Poker hands. Binomial theorem. Pascal's triangle. |
Sec. 6.4, 6.6, 6.7 | |
| Fri. 12/10 | Questions and exam prep. | . | |
| Mon. 12/13 (10:30-12:30) | FINAL EXAM. | Cumulative. |