DayDateTopic5th Ed
FriJan 06Introduction. Chapter 1
MonJan 09Proofs. Logic: Statements. "Not". 1.1
WedJan 11Formal Logic: NOT, AND, OR, XOR. Properties.1.2
FriJan 13Formal Logic: Implication, biconditional. Arguments.1.2
MonJan 16Set Theory. Definition, Subset, Power Set, Empty Set.1.3
WedJan 18Operations with sets: Union, Intersection, Complement.1.3
FriJan 20Quantifiers.1.4
MonJan 23Postulates for the Integers.Complete List of Postulates
WedJan 25Postulates for the Integers: Uniqueness of the additive inverse. Order. Some notes and exercises on the postulates for the integers
FriJan 27Postulates for the Integers: Induction. 4.1
MonJan 30Postulates for the Integers: Induction. 4.1
WedFeb 01Least Integer. Gap between n and n+1. Divisibility. Even and odd. Irrationality of root 2.2.1
FriFeb 03Division Algorithm.2.1
MonFeb 06Greatest Common Divisor. Euclidean Algorithm2.2
WedFeb 08Eucliden Algoritnm. Linear Diophantine Equations. 2.2, 2.3
FriFeb 10Linear Diophantine Equations. 2.3
MonFeb 13Prime Numbers. Unique Factorization Theorem. 2.5
WedFeb 15Least Common Multiple. Integers in Different Bases.2.4
FriFeb 17Midterm 1
MonFeb 20Reading Week.
WedFeb 22Reading Week.
FriFeb 24Reading Week.
MonFeb 27Modular Arithmetic. Tests for Divisibility.3.1, 3.2
WedMar 01Modular Arithmetic: finding the remainder. Fermat's Little Theorem. 3.2, 3.4
FriMar 03Modular Arithmetic: divisors of zero and multiplicative inverses. Linear Congruences.3.4, 3.5
MonMar 06Multiple Linear Congruences.3.6
WedMar 08Chinese Remainder Theorem.3.6
FriMar 10Phi-function. Euler-Fermat. RSA Encryption.3.7
MonMar 13RSA Encryption. Cartesian Product. Relations. 7.4, 1.3, 3.3
WedMar 15Equivalence Relations.
FriMar 17No Lecture3.3
MonMar 20Equivalence Relations: Modular Classes. 3.3, 3.4
WedMar 22Equivalence Relations: Construction of the Integers.
FriMar 24Midterm 2
MonMar 27Functions. 6.1, 6.2
WedMar 29Composition of Functions. 6.3
FriMar 31Injective and Surjective Functions.6.5
MonApr 03Invertible Functions.6.5
WedApr 05Cardinality. Countable sets.6.6
FriApr 07Cardinality: Countable and Uncountable Sets. 6.6