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DiscreteMath.md (5803B)


      1 # Discrete Math
      2 
      3 Discrete math related links.
      4 
      5 ## Discrete Mathematics and Its Applications (Rosen)
      6 
      7 Unit 1.1 (logic)
      8 
      9 - [Proposition](Proposition.md)
     10 - [Negation](Negation.md)
     11 - [Connectives](Connectives.md)
     12 - [Converse](Converse.md)
     13 - [Inverse](Inverse.md)
     14 - [Contrapositive](Contrapositive.md)
     15 - [Biconditional](Biconditional.md)
     16 
     17 Unit 1.2 (logic)
     18 
     19 - [Proposition](Proposition.md)
     20 - [Connectives](Connectives.md)
     21 
     22 Unit 1.3 (logic)
     23 
     24 - [Tautology](Tautology.md)
     25 - [Contradiction](Contradiction.md)
     26 - [Contingency](Contingency.md)
     27 - [DemorgansLaw](DemorgansLaw.md)
     28 - [ConditionalDisjunction](ConditionalDisjunction.md)
     29 - [DistributiveLaw](DistributiveLaw.md)
     30 - [WellDefined](WellDefined.md)
     31 - [Commutative](Commutative.md)
     32 - [Satisfiable](Satisfiable.md)
     33 
     34 Unit 1.4 (proof)
     35 
     36 - [Predicate](Predicate.md)
     37 - [PropositionalFunction](PropositionalFunction.md)
     38 - [Quantifiers](Quantifiers.md)
     39 - [Universe](Universe.md)
     40 - [Preconditions](Preconditions.md)
     41 - [Postcondition](Postcondition.md)
     42 
     43 Unit 1.5 (proof)
     44 
     45 - [NestedQuantifier](NestedQuantifier.md)
     46 
     47 Unit 1.6 (proof)
     48 
     49 - [LawOfDetachment](LawOfDetachment.md)
     50 
     51 Unit 1.7 (proof)
     52 
     53 - [DirectProof](DirectProof.md)
     54 - [Contrapositive](Contrapositive.md)
     55 - [Contradiction](Contradiction.md)
     56 - [Cases](Cases.md)
     57 - [VacuousProof](VacuousProof.md)
     58 - [ExhaustiveProof](ExhaustiveProof.md)
     59 
     60 Unit 2.1 (sets)
     61 
     62 - [Set](Set.md)
     63 - [Subset](Subset.md)
     64 - [PowerSet](PowerSet.md)
     65 - [CartesianProduct](CartesianProduct.md)
     66 - [TruthSet](TruthSet.md)
     67 - [Complement](Complement.md)
     68 - [Multiset](Multiset.md)
     69 
     70 Unit 2.3 (functions)
     71 
     72 - [Range](Range.md)
     73 - [Image](Image.md)
     74 - [Preimage](Preimage.md)
     75 - [Codomain](Codomain.md)
     76 - [Injective](Injective.md)
     77 - [Surjective](Surjective.md)
     78 - [InverseFunction](InverseFunction.md)
     79 - [Floor](Floor.md)
     80 - [Ceiling](Ceiling.md)
     81 - [Bijective](Bijective.md)
     82 
     83 Unit 2.4 (sequence + other stuff)
     84 
     85 - [Sequence](Sequence.md)
     86 - [Recurrence Relation](RecurrenceRelation.md)
     87 
     88 Unit 2.3 (computation 5th edition)
     89 
     90 - [Tractable](Tractable.md)
     91 - [Intractable](Intractable.md)
     92 - [Unsolvable](Unsolvable.md)
     93 - [NPProblem](NPProblem.md)
     94 - [PProblem](PProblem.md)
     95 - [NPComplete](NPComplete.md)
     96 
     97 Unit 2.4 (integers and division)
     98 
     99 - [Number Theory](NumberTheory.md)
    100 - [Composite Number](CompositeNumber.md)
    101 - [Prime Number](PrimeNumber.md)
    102 - [Mersenne Prime](MersennePrime.md) 
    103 - [Div](Div.md)
    104 - [Mod](Mod.md)
    105 - [Relatively Prime](RelativelyPrime.md)
    106 - [Pairwise Relatively Prime](PairwiseRelativelyPrime.md)
    107 - [Prime Factorization](PrimeFactorization.md) 
    108 - [GCD](GCD.md)
    109 - [LCM](LCM.md) 
    110 - [Congruence](Congruence.md) 
    111 - [Congruence Class](CongruenceClass.md)
    112 - [Caesar Cipher](CaesarCipher.md)
    113 - [Vigenere Cipher](VigenereCipher.md)
    114 - [Euclidean Algorithm](EuclideanAlgorithm.md) 
    115 - [Linear Combination](LinearCombination.md)
    116 - [Linear Congruence](LinearCongruence.md)
    117 
    118 Unit 2.4 (Sequences and Summations 8th edition)
    119 
    120 - [Recurrence Relation](RecurrenceRelation.md)
    121 
    122 Unit 6.1 (The Basics of Counting 8th edition)
    123 
    124 - [Combinatorics](Combinatorics.md)
    125 - [Sum Rule](SumRule.md)
    126 - [Tree Diagram](TreeDiagram.md)
    127 - [Subtraction Rule](SubtractionRule.md)
    128 - [Division Rule](DivisionRule.md)
    129 - [Sum Of Geometric Series](SumOfGeometricSeries.md)
    130 - [Counting Principle](CountingPrinciple.md)
    131 
    132 Unit 6.2 (Pigeonhole principle)
    133 
    134 - [Pigeonhole Principle](PigeonholePrinciple.md)
    135 - [Generalized Pigeonhole Principle](GeneralizedPigeonholePrinciple.md)
    136 - [Subsequence](Subsequence.md)
    137 - [Ramsey Numbers](RamseyNumbers.md)
    138 
    139 Unit 6.3 (Permutations and Combinations)
    140 
    141 - [Permutation](Permutation.md)
    142 - [RPermutation](RPermutation.md)
    143 - [Combination](Combination.md)
    144 - [RCombination](RCombination.md)
    145 - [Combinatorial Proof](CombinatorialProof.md)
    146 - [Bijective Proof](BijectiveProof.md)
    147 
    148 Unit 6.4 (Binomial Coefficient & Identities)
    149 
    150 - [Binomial Coefficient](BinomialCoefficient.md) 
    151 - [Pascals Identity](PascalsIdentity.md)
    152 - [Vandermondes Identity](VandermondesIdentity.md)
    153 - [Binomial](Binomial.md)
    154 
    155 Unit 6.5 (Generalized Permutations & Combinations)
    156 
    157 - [Distinguishable](Distinguishable.md)
    158 - [Indistinguishable](Indistinguishable.md)
    159 
    160 Unit 8.2 (Solving Linear Recurrence Relations)
    161 
    162 - [Recurrence Relation](RecurrenceRelation.md)
    163 - [Linear Combination](LinearCombination.md)
    164 - [Linear Homogeneous Recurrence Relation](LinearHomogeneousRecurrenceRelation.md)
    165 - [Characteristic Equation](CharacteristicEquation.md)
    166 - [Characteristic Roots](CharacteristicRoots.md)
    167 
    168 Unit 8.3 (Divide and Conquer)
    169 
    170 - [Divide And Conquer](DivideAndConquer.md)
    171 
    172 Unit 8.5 (Inclusion Exclusion)
    173 
    174 - [Principle Of Inclusion Exclusion](PrincipleOfInclusionExclusion.md)
    175 
    176 Unit 9.1 (Relations)
    177 
    178 - [Relation](Relation.md) (define like function)
    179 - [Relation On ASet](RelationOnASet.md) 
    180 - [Reflexive](Reflexive.md) 
    181 - [Symmetric](Symmetric.md)
    182 - [Antisymmetric](Antisymmetric.md)
    183 - [Transitive](Transitive.md)
    184 
    185 Unit 9.3 (Representing Relations)
    186 
    187 - [Zero One Matrix](ZeroOneMatrix.md)
    188 - [Digraph](Digraph.md)
    189 - [Loop](Loop.md)
    190 
    191 Unit 9.4 (Closures of Relations)
    192 
    193 - [Transitive Closure](TransitiveClosure.md)
    194 - [Reflexive Closure](ReflexiveClosure.md)
    195 - [Symmetric Closure](SymmetricClosure.md)
    196 - [Closure](Closure.md)
    197 
    198 Unit 9.5 (Equivalence Relations)
    199 
    200 - [Equivalence Relation](EquivalenceRelation.md)
    201 - [Equivalence Class](EquivalenceClass.md) ([a] notation)
    202 - [Representative](Representative.md)
    203 - [Partition](Partition.md)
    204 
    205 Unit 9.6 (Partial Orderings)
    206 
    207 - [Partially Ordered Set](PartiallyOrderedSet.md)
    208 - [Hasse Diagram](HasseDiagram.md)
    209 - [Lexicographic Ordering](LexicographicOrdering.md)
    210 
    211 Unit 10.1 (Graphs)
    212 
    213 - [Graphs](Graphs.md)
    214 - [Multigraph](Multigraph.md)
    215 - [Loop](Loop.md)
    216 - [Pseudo Graphs](PseudoGraphs.md)
    217 - [Mixed Graph](MixedGraph.md) 
    218 
    219 Unit 10.2 (Graph Terms)
    220 
    221 - [Bipartite](Bipartite.md)
    222 
    223 Unit 10.3 (Representing Graphs and Isomorphisms)
    224 
    225 - [Adjacency Matrix](AdjacencyMatrix.md) (for dense)