Math 2001: Introduction to Discrete Mathematics

Monday, January 17 : First Day of Class......Page 7
Sets and Subsets......Page 8
Subsets......Page 10
Russell's Paradox......Page 11
Cardinality, informally......Page 13
The Cartesian Product......Page 14
Note on the empty set......Page 17
Power Set......Page 18
Intersections, Unions, Difference and Complements......Page 19
Venn Diagrams......Page 21
Index Sets......Page 22
Statements......Page 26
And, Or......Page 28
Not......Page 29
LaTeX......Page 31
Conditional Statements......Page 32
The Converse......Page 36
The Contrapositive......Page 37
Biconditional Statements......Page 38
Negating statements......Page 39
Friday, February 9......Page 41
Quantifyers......Page 42
Logical Inference......Page 45
Broad Strokes for the Topic of Proofs......Page 47
Friday, February 16......Page 49
Monday, February 19......Page 50
Preliminaries......Page 51
Examples of Direct and Contrapositive Proofs......Page 52
Wednesday, February 21......Page 53
Cases......Page 54
Without Loss of Generality......Page 55
Without Loss of generality continued......Page 57
Proof by Contradiction......Page 58
Proof by Contradiction Continued......Page 60
Congruence of Integers......Page 61
If and only if, and the following are equivalent.......Page 62
Friday, March 2......Page 64
Monday, March 5......Page 65
The following are equivalent (TFAE)......Page 66
Existence Proofs......Page 68
Existence and Uniqueness Proofs......Page 69
Proving xX......Page 71
Proving X Y......Page 72
Proving X Y......Page 73
Proving X = Y......Page 74
(Weak) Mathematical Induction......Page 77
Strong Mathematical Induction Continued......Page 82
Friday, March 23......Page 86
Relations......Page 87
Equivalence Relations......Page 88
Equivalence classes......Page 90
Friday, April 6......Page 93
Partitions......Page 94
Partitions, continued......Page 96
Integers modulo n......Page 97
Integers modulo n finished......Page 99
Functions......Page 100
Functions continued......Page 102
Injectivity and Surjectivity......Page 103
Injectivity and Surjectivity......Page 105
Friday, April 20......Page 107
The Pigeon-Hole Principle......Page 108
Image and Preimage......Page 110
Composition......Page 111
Inverses......Page 113
Cardinality......Page 114
Cardinality Continued......Page 116
Cardinality Continued......Page 118
Review......Page 123