| Day | Topics | Preparation | |
|---|---|---|---|
| Mon. 1/12 | Introduction. Statements, negation, conjunction, disjunction. | Sec. 1.1 | |
| Wed. 1/14 | Logical equivalences, tautologies, contradictions.
Conditionals |
Sec. 1.1-2 | |
| Fri. 1/18 | Conditionals and English usage, biconditionals.
Logical arguments. |
Sec. 1.2-3 | |
| Wed. 1/21 | Logical arguments. | Sec. 1.3 | |
| Fri. 1/23 | Logic puzzles. Logic circuits. | Sec. 1.4, 2.1 | |
| Mon. 1/26 | Sets, predicates, truth set of a predicate.
Quantified predicates. |
Secs. 2.1 | |
| Wed. 1/28 | Quantified predicates. Translation from English. Multiply quantified predicates. |
Secs. 2.1,2 | |
| Fri. 1/30 | Arguments with quantified predicates.
A logic problem.(2.3#27) |
Sec. 2.3 | |
| Mon. 2/2 | Fundamental properties of the integers.
First proofs: The sum of evens is even. If a divides b and b divides c then a divides c. |
Sec. 3.1, 3.3, 3.4 | |
| Wed. 2/4 | Three theorems we assume: The quotient-remainder theorem. If prime p divides ab then p divides a or b Unique factorization of integers. |
Sec. 3.3, 3.4, | |
| Fri. 2/6 | Divisibility theorems and proofs. | Sec. 3.4 | |
| Mon. 2/9 | Rational numbers. The floor and ceiling functions. |
Sec. 3.5 | |
| Wed. 2/11 | Proof by contraposition. More on sets |
Sec. 3.6 Sec. 5.1 | |
| Fri. 2/13 | Properties of Sets:
The empty set; Theorems 5.2.2 and 5.3.3 Set difference and symmetric difference |
Sec. 5.1-3 | |
| Mon. 2/16 | Proof by contradiction. Two classy theorems: The sum of a rational and an irrational. Irrationality of sqrt(2). |
Secs. 3.7 | |
| Wed. 2/18 | Another classy theorem: The infinitude of primes. | Secs. 3.7 | |
| Fri. 2/20 | Practice Test | Secs. 1.1-4, 2.1-3 3.1, 3.3-6 | |
| Mon. 2/23 | EXAM | Secs. 1.1-4, 2.1-3 3.1, 3.3-6 | |
| Wed. 2/25 | Algebraic proofs of set equalities. Partition of a set, power set, Cartesian product. |
Secs. 5.1-3 | |
| Fri. 2/27 | Relations. Arrow diagrams, tables of relations. Functions. |
Sec. 10.1 | |
| Mon. 3/1 | Properties of relations on a set:
reflexive, symmetric, transitive |
Sec. 10.2 | |
| Wed. 3/3 | Equivalence relations | Sec. 10.3 | |
| Fri. 3/5 | Partitions and equivalence relations.
Examples of equivalence relations: integers mod n, the Mobius strip. |
Sec 10.3 | |
| Mon. 3/8 | Partially ordered sets. | Sec. 10.5 | |
| Wed. 3/10 | Partially ordered sets. | Sec. 10.5 | |
| Fri. 3/12 | Functions, one-to-one, onto and both. | Sec. 7.1,3 Sec. 4.1 | |
| Mon. 3/22 | Inverse functions. Cardinality Pigeonhole principle. |
Sec. 7.3, 4 | |
| Wed. 3/24 | Definition of the rational numbers. Sequences, summation and product notation. |
Sec 7.6 Sec. 4.1 | |
| Fri. 3/26 | Practice exam. | Secs. 3.6,7; Ch. 5; Ch. 10. | |
| Mon. 3/29 | EXAM | Secs. 3.6,7; Ch. 5; Ch. 10. | |
| Fri. 4/2 | The well ordering principle. Induction. | Sec. 4.2, p. 217-218. | |
| Mon. 4/5 | Some induction proofs. | Sec. 4.2-3, p. 217-218. | |
| Wed. 4/7 | Induction proofs. | Sec. 4.2-3 | |
| Fri. 4/9 | Using the well ordering principle. | Sec. 4.4, 8.1 | |
| Mon. 4/12 | Recursively defined functions. Strong induction . | Secs 8.2. | |
| Wed. 4/14 | Strong induction. Second order recurrence relations. | Secs 8.2,3. | |
| Fri. 4/16 | Counting and probability. | Sec. 6.1-2 | |
| Mon. 4/19 | Inclusion/exclusion principle.
4 ways to choose. |
Sec. 6.3,4. | |
| Wed. 4/21 | EXAM. | Secs. 4.1-4; 8.1-2. | |
| Fri. 4/23 | Binomial coefficients.
Pascal's triangle. |
Sec. 6.4, 6.6, 6.7 |