Schedule

Definition of the rational numbers.

Partial order relations.

Day | Topics | Preparation | |
---|---|---|---|

Wed. 7/13 | Introduction. Statements, negation, conjunction,
disjunction. Logical equivalence, Theorem 1.1.1 |
Sec. 1.1 | |

Th. 7/14 | Conditionals, converse, inverse, contrapositve and biconditional.
Logic circuits |
Sec. 1.1-2 Sec. 1.4 | |

Mon. 7/18 | Conditionals and English usage.
Logical arguments. |
Sec. 1.2-3 | |

Tu. 7/19 | A bit about sets. Predicates and their truth sets. Quantified predicates. |
Sec. 5.1 Sec. 2.1 | |

Wed. 7/20 | Quantified predicates: negation and multiple quantifiers. Arguments with predicates. |
Sec. 2.2, 3 2.4 | |

Th. 7/21 | Fundamental properties of the integers. Divisibility theorems and proofs. | Sec. 3.1 3.3, | |

Mon. 7/25 |
Three theorems we assume: The quotient-remainder theorem. If prime p divides ab then p divides
a or b
Unique factorization of integers. |
Secs. 3.4 Sec. 3.5 | |

Tues. 7/26 | Exam: Logic Unique factorization of integers. Rational numbers. |
Ch. 1, 2 Sec. 3.3,5 | |

Wed. 7/27 | The floor and ceiling functions. Proof by contraposition and contradiction. Three classic theorems. |
Sec. 3.5 Secs. 3.6,7 | |

Thurs. 7/28 | Infinitude of primes Properties of Sets: The empty set; Theorems 5.2.2 and 5.3.3 |
Sec. 5.1-3 | |

Mon. 8/1 | Set difference and symmetric difference. Algebraic proofs of set properties. Partitions of a set The power set of a set. | Sec. 5.1-3 | |

Tues. 8/2 | Exam: Integers and proof strategies The Cartesian product of sets. Relations from to A ,
and functions.B |
Secs. 3.1, 3.3-7 Secs. 10.1, 7.1 | |

Wed. 8/3 | Relations and functions: inverse relation, injective, surjective functions. Relations on a set :A Reflexive, symmetric, transitive properties. |
Sec. 7.1-3, Sec. 10.2 | |

Thurs. 8/4 | Transitive closure. Equivalence relations and partitions. | Sec. 10.2 Sec 10.3 | |

Mon. 8/8 | Examples of equivalence relations: integers mod n, the Mobius strip. |
Sec. 10.3 Sec 10.5 | |

Tues. 8/9 | Partially ordered sets. Sequences, summation and product notation. |
Sec. 10.5 Sec. 4.1 | |

Wed. 8/10 | EXAM The well ordering principle. Induction. |
Sec 5.1-3, 7.1-3, 10-1,2,3,5 Sec. 4.2, p. 240-241. | |

Thurs. 8/11 | Some induction proofs. | Sec. 4.2-3. Secs 8.2. | |

Mon. 8/15 | Recursively defined sequences and formulas for them. Arithmetic, geometric and other sequences. Strong induction. |
Sec. 8.1,2, 4.4 | |

Tues. 8/16 | Some strong induction proofs. Counting the basics |
Sec. 4.4, 8.1,2 6.1,2 | |

Wed. 8/17 | EXAM. Inclusion/exclusion principle. |
Secs. 4.1-4, 8.1-2. Sec. 6.3,4. | |

Thurs. 8/18 | 4 ways to choose. Binomial coefficients. Pascal's triangle. |
Sec. 6.4, 6.6, 6.7 | |

Mon. 8/22 | Probability, poker hands. Questions?, Review. |
Sec . 6.4. | |

Tues. 8/23 | Final Exam. | . |