Day | Date | Topic | 5th Ed | |

Fri | Jan 06 | Introduction. | Chapter 1 | |

Mon | Jan 09 | Proofs. Logic: Statements. "Not". | 1.1 | |

Wed | Jan 11 | Formal Logic: NOT, AND, OR, XOR. Properties. | 1.2 | |

Fri | Jan 13 | Formal Logic: Implication, biconditional. Arguments. | 1.2 | |

Mon | Jan 16 | Set Theory. Definition, Subset, Power Set, Empty Set. | 1.3 | |

Wed | Jan 18 | Operations with sets: Union, Intersection, Complement. | 1.3 | |

Fri | Jan 20 | Quantifiers. | 1.4 | |

Mon | Jan 23 | Postulates for the Integers. | | Complete List of Postulates |

Wed | Jan 25 | Postulates for the Integers: Uniqueness of the additive inverse. Order. | Some notes and exercises on the postulates for the integers | |

Fri | Jan 27 | Postulates for the Integers: Induction. | 4.1 | |

Mon | Jan 30 | Postulates for the Integers: Induction. | 4.1 | |

Wed | Feb 01 | Least Integer. Gap between n and n+1. Divisibility. Even and odd. Irrationality of root 2. | 2.1 | |

Fri | Feb 03 | Division Algorithm. | 2.1 | |

Mon | Feb 06 | Greatest Common Divisor. Euclidean Algorithm | 2.2 | |

Wed | Feb 08 | Eucliden Algoritnm. Linear Diophantine Equations. | 2.2, 2.3 | |

Fri | Feb 10 | Linear Diophantine Equations. | 2.3 | |

Mon | Feb 13 | Prime Numbers. Unique Factorization Theorem. | 2.5 | |

Wed | Feb 15 | Least Common Multiple. Integers in Different Bases. | 2.4 | |

Fri | Feb 17 | Midterm 1 | | |

Mon | Feb 20 | Reading Week. | | |

Wed | Feb 22 | Reading Week. | | |

Fri | Feb 24 | Reading Week. | | |

Mon | Feb 27 | Modular Arithmetic. Tests for Divisibility. | 3.1, 3.2 | |

Wed | Mar 01 | Modular Arithmetic: finding the remainder. Fermat's Little Theorem. | 3.2, 3.4 | |

Fri | Mar 03 | Modular Arithmetic: divisors of zero and multiplicative inverses. Linear Congruences. | 3.4, 3.5 | |

Mon | Mar 06 | Multiple Linear Congruences. | 3.6 | |

Wed | Mar 08 | Chinese Remainder Theorem. | 3.6 | |

Fri | Mar 10 | Phi-function. Euler-Fermat. RSA Encryption. | 3.7 | |

Mon | Mar 13 | RSA Encryption. Cartesian Product. Relations. | 7.4, 1.3, 3.3 | |

Wed | Mar 15 | Equivalence Relations. | | |

Fri | Mar 17 | *No Lecture* | 3.3 | |

Mon | Mar 20 | Equivalence Relations: Modular Classes. | 3.3, 3.4 | |

Wed | Mar 22 | Equivalence Relations: Construction of the Integers. | | |

Fri | Mar 24 | Midterm 2 | | |

Mon | Mar 27 | Functions. | 6.1, 6.2 | |

Wed | Mar 29 | Composition of Functions. | 6.3 | |

Fri | Mar 31 | Injective and Surjective Functions. | 6.5 | |

Mon | Apr 03 | Invertible Functions. | 6.5 | |

Wed | Apr 05 | Cardinality. Countable sets. | 6.6 | |

Fri | Apr 07 | Cardinality: Countable and Uncountable Sets. | 6.6 | |