|Wed. 1/20||Introduction. Statements, negation, conjunction,
|Mon. 1/25||Logical equivalences, tautologies, contradictions.
Conditionals and biconditionals.
|Wed. 1/27||Conditionals and English usage.
|Mon. 2/1||Logic circuits. Sets||Secs. 1.4, 5.1|
|Wed. 2/3||Sets, predicates, truth set of a predicate.
|Secs. 5.1, 2.1-2|
|Mon. 2/8||Translation from English.|
Multiply quantified predicates.
|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.)|
|Mon. 2/15||Sets: Cartesion products, power set, partitions.
Proofs: Venn diagram, element-wise proofs,
|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.
|Secs. 3.1, 3.3, 3.4|
|Wed. 2/24||The quotient-remainder theorem.
|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.
|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?
|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
|Wed. 4/14||Equivalence relations||Sec. 10.3|
|Mon. 4/19||Partitions and equivalence relations.
Examples of equivalence relations.
|Sec 10.3 |
|Wed. 4/21||More on partially ordered sets.
|Sec. 10.5 |
|Mon. 4/26||From the addition rule to inclusion-exclusion.||Sec 6.3|
|Wed. 4/28||The rational numbers using equivalence relations.
|Sec. 10.3.10 |
|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.) |
|Mon. 5/10||From counting to probability and gambling.
|Sec. 6.4, 6.6, 6.7|
|Wed. 5/12||Questions and exam prep.||.|
|Mon. 5/17||FINAL EXAM.||Cumulative.|