Math 2001: Introduction to Discrete Mathematics
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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
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