| Day | Topics | Preparation | |
|---|---|---|---|
| Wed. 1/20 | Introduction. Statements, negation, conjunction,
disjunction. Logical equivalences |
Sec. 1.1 | |
| Mon. 1/25 | Logical equivalences, tautologies, contradictions.
Conditionals and biconditionals. |
Secs. 1.1-2 | |
| Wed. 1/27 | Conditionals and English usage.
Logical arguments. |
Secs. 1.2-3 | |
| Mon. 2/1 | Logic circuits. Sets | Secs. 1.4, 5.1 | |
| Wed. 2/3 | Sets, predicates, truth set of a predicate.
Quantified predicates. |
Secs. 5.1, 2.1-2 | |
| Mon. 2/8 | Translation from English. Multiply quantified predicates. | Secs. 2.3-4 | |
| Wed. 2/10 | Arguments with quantified predicates.
Logic puzzles.(2nd Ed. 2.3#27, 3rd Ed. 2.4#31) Proving theorems about sets. |
Secs. 2.3 (2nd Ed) 2.4 (3rd Ed.) Secs. 5.2-3 | |
| Mon. 2/15 | Sets: Cartesion products, power set, partitions. Proofs: Venn diagram, element-wise proofs, algebraic proofs. |
Secs. 5.1-3 | |
| Wed. 2/17 | Practice with proofs of set theorems.
Mathematics: Axiom, Definition, Theorem, Proof The sum of evens is even, etc. |
Secs. 5.2-3 | | |
| Mon. 2/22 | Fundamental properties of the integers.
Divisibility |
Secs. 3.1, 3.3, 3.4 | |
| Wed. 2/24 | The quotient-remainder theorem. Unique Factorization. |
Secs. 3.1, 3.3, 3.5 | |
| Mon. 3/1 | EXAM | Ch. 1, 2, 5 | |
| Wed. 3/3 | Rational numbers and real numbers. The floor and ceiling functions. Proof by contraposition and contradiction. |
Secs. 3.5,6,7 | |
| Mon. 3/8 | Irrationality of sqrt(2). Sequences, summation and product notation. |
Sec. 3.7 Sec. 4.1, Sec 8.1 | |
| Wed. 3/10 | The well ordering principle. Induction. | Sec. 4.2,4. | |
| Mon. 3/15 | Proof by mathematicalinduction. Some induction proofs. |
Sec. 4.2-3, p. 217-218. | |
| Wed. 3/17 | Recursively defined functions and strong induction. | Sec. 4.2-3 | |
| Mon. 3/22 | A bit more on induction. Functions and Relations |
Sec. 7.1, 8.1 | |
| Wed. 3/24 | Functions: injective, surjective, bijective. | Sec. 7.1-2. | |
| Mon. 4/5 | Questions before the exam? Functions: composition. |
7.4. | |
| Wed. 4/7 | EXAM. | Secs. 3.1-7, 4.1-4; 8.1-2. | |
| Mon. 4/12 | Properties of relations on a set:
reflexive, symmetric, transitive |
Sec. 10.2 | |
| Wed. 4/14 | Equivalence relations | Sec. 10.3 | |
| Mon. 4/19 | Partitions and equivalence relations.
Examples of equivalence relations. Partial orders. |
Sec 10.3 10.5 | |
| Wed. 4/21 | More on partially ordered sets.
Counting. |
Sec. 10.5 6.1-3 | |
| Mon. 4/26 | From the addition rule to inclusion-exclusion. | Sec 6.3 | |
| Wed. 4/28 | The rational numbers using equivalence relations.
Possibility trees. |
Sec. 10.3.10 Sec 6.2-3. | |
| Mon. 5/3 | Four ways to count. From counting to probability. | Sec. 6.2,4 | |
| Wed. 5/5 | EXAM. | Secs 7.1,2,4 (1,3,5 in 2nd Ed.) Secs 10.1,2,3,5. Inclusion-exclusion. | |
| Mon. 5/10 | From counting to probability and gambling. Binomial theorem. Pascal's triangle. |
Sec. 6.4, 6.6, 6.7 | |
| Wed. 5/12 | Questions and exam prep. | . | |
| Mon. 5/17 | FINAL EXAM. | Cumulative. |