Some lecture entries list exercises from relevant sections in Epp that we will discuss.
| Day | Topics | Preparation |
|---|---|---|
| Tu. 8/28 | Introduction. Statements, negation, conjunction,
disjunction. Logical equivalences, tautologies, contradictions. |
Sec. 2.1 |
| Th. 8/30 | Conditionals and biconditionals. Inverse, converse, contrapositive. | Secs. 2.1-2 |
| Tu. 9/4 | Conditionals and English usage. (2.2 #16-19, 37-46) Logical arguments (2.3 #41, 43). |
Secs. 2.2-3 |
| Th 9/6 | Logical arguments and puzzles (2.3 #37,38). Circuits. Disjunctive normal form (2.4 #18, 20). |
Secs. 2.3-4 |
| Tu. 9/11 | Sets: subset, union, intersection., difference.
Predicates and truth sets. |
Secs. 1.1-2, 6.1-2 (pp. 336-344)
Sec. 3.1 |
| Th. 9/13 | Predicates and English. Quantified predicates. Negation. QUIZ: Logic |
Secs. 1.1-2, 3.1-3 Ch. 2 |
| Tu. 9/18 | Multiply quantified predicates.
Arguments with quantified predicates. Logic puzzles. |
Sec. 3.4 (2nd Ed. 2.3#27, 3rd 2.4#31, 4th. Ed 3.4#31.) |
| Th. 9/20 | Proving theorems about sets.
The Cartesian product and the multiplication rule. |
Secs. 6.1-2 Sec. 9.2 (or my notes 02d.) |
| Tu. 9/25 | Disproof by counterexample. Algebraic proofs.
Partitions and inclusion/exclusion. The power set of a set. |
Secs. 6.3 Sec. 9.3 (or my notes 02d) Sec. 6.1 |
| Th. 9/27 | Mathematics: Axiom, Definition, Theorem, Proof
Axioms for the integers. |
Ch. 3.1 (and my lecture notes 03). |
| Tu. 10/2 | TEST: Logic, Sets, Predicates, Counting | Ch. 2, 3, 6 and 9.2,3 |
| Th. 10/4 | Divisibility. The Quotient Remainder Theorem. |
Sec. 4.3 Sec. 4.4 |
| Tu. 10/9 | The Euclidean algorithm. Representation of integers in binary, octal, etc. Primes and the Unique Factorization Theorem. |
Sec 4.8 Sec. 2.5 (pp. 78-81, 91-93), 5.1 (pp. 240-242), 4.3 (pp.176-7) |
| Th. 10/11 | Primes and the Unique Factorization Theorem.
Theorems about primes. Proof by contradiction. |
Sec. 4.3 (pp.176-7) Secs. 4.6,7 |
| Tu. 10/16 | Rational numbers and irrational numbers. Floor and ceiling functions. |
Secs. 4.5, 4.7. |
| Th. 10/18 | Sequences, summation and product notation.
Explicitly defined sequences and recursively defined sequences. The Well-Ordering Principle. |
Sec. 5.1 |
| Tu. 10/23 | The Principle of Induction. Proof by mathematical induction. |
Secs. 5.2, 5.4 |
| Th. 10/25 | Induction proofs for divisibility and inequalities Recursively defined functions and strong induction. |
Sec. 5.3 |
| Tu. 10/30 | Questions before the exam? | . |
| Th. 11/1 | TEST. | Ch 4, 5. |
| Tu. 11/6 | Functions and relations. The inverse of a relation |
Sec. 7.1, 8.1. |
| Th. 11/8 | Functions: injective, surjective, bijective.
Composition of functions. | >
Sec. 7.2,3. |
| Tu. 11/13 | Relations on a set.
Properties: reflexive, symmetric, transitive |
Sec. 8.2 |
| Th. 11/15 | Equivalence relations and partitions. Equivalence relations: important examples. QUIZ: induction proof. |
Sec. 8.3 |
| Tu. 11/20 | Antisymmetric relations. Partial orders. |
Sec 8.5 |
| Tu. 11/27 | Four ways to count. The Binomial theorem. Pascal's triangle. |
Sec. 6.2,5 Sec. 9.7 |
| Th. 11/29 | TEST | Secs 7.1-3, 8.1-3, 8.5. |
| Tu. 12/4 | From counting to probability. Poker hands. |
Sec. 9.1,2,5 |
| Th. 12/6 | Questions and exam prep. | . |
| Th. 12/13 (10:30-12:30) | FINAL EXAM. | Cumulative. See Review Sheet |