Muy chévere.
Gracias
2012/4/6 Owen Densmore
> A couple of friends from Silicon Valley are taking the Stanford Algorithms
> course with me. One of the "readings" for the class is:
>
> Mathematics for Computer Science
> Eric Lehman and Tom Leighton
> 2004
> http://www.cs.princeton.edu/courses/archive/spr10/cos433/mathcs.pdf
>
>
> ... which is a surprisingly complete survey of most of your
> basic undergraduate math, done very well.
>
>-- Owen
>
> Here is the table of contents:
>
> Contents
> 1 What is a Proof? 15
> 1.1 Propositions. 15
> 1.2 Axioms 19
> 1.3 LogicalDeductions . 20
> 1.4 ExamplesofProofs . 20
> 1.4.1 ATautology. 21
> 1.4.2 AProofbyContradiction . 22
> 2 Induction I 23
> 2.1 AWarmupPuzzle.. 23
> 2.2 Induction... 24
> 2.3 UsingInduction... 25
> 2.4 ADivisibilityTheorem... 28
> 2.5 AFaultyInductionProof.. 30
> 2.6 CourtyardTiling... 31
> 2.7 AnotherFaultyProof 33
> 3 Induction II 35
> 3.1 GoodProofsandBadProofs 35
> 3.2 APuzzle... 36
> 3.3 Unstacking.. 40
> 3.3.1 StrongInduction .. 40
> 3.3.2 AnalyzingtheGame 41
> 4 Number Theory I 45
> 4.1 ATheoryoftheIntegers .. 46
> 4.2 Divisibility.. 46
> 4.2.1 Turing’sCode(Version1.0) 47
> 4.2.2 TheDivisionAlgorithm .. 50
> 4.2.3 BreakingTuring’sCode .. 51
> 4.3 ModularArithmetic. 51
> 4.3.1 CongruenceandRemainders... 51
> 4.3.2 Factsaboutremandmod. 52
> 4.3.3 Turing’sCode(Version2.0) 54
> 4.3.4 CancellationModuloaPrime... 55
> 4.3.5 MultiplicativeInverses... 56
> 4.3.6 Fermat’sTheorem. 57
> 4.3.7 FindingInverseswithFermat’sTheorem 58
> 4.3.8 BreakingTuring’sCode—Again. 58
> 5 Number Theory II 61
> 5.1 DieHard... 61
> 5.1.1 DeathbyInduction. 62
> 5.1.2 AGeneralTheorem. 63
> 5.1.3 TheGreatestCommonDivisor.. 64
> 5.1.4 PropertiesoftheGreatestCommonDivisor... 65
> 5.2 TheFundamentalTheoremofArithemtic 67
> 5.3 ArithmeticwithanArbitraryModulus.. 68
> 5.3.1 RelativePrimalityandPhi. 68
> 5.3.2 GeneralizingtoanArbitraryModulus.. 70
> 5.3.3 Euler’sTheorem .. 71
> 6 Graph Theory 73
> 6.1 Introduction. 73
> 6.1.1 Definitions.. 74
> 6.1.2 SexinAmerica ... 74
> 6.1.3 GraphVariations .. 76
> 6.1.4 ApplicationsofGraphs .. 77
> 6.1.5 SomeCommonGraphs .. 77
> 6.1.6 Isomorphism 79
> 6.2 Connectivity. 80
> 6.2.1 ASimpleConnectivityTheorem . 80
> 6.2.2 DistanceandDiameter... 81
> 6.2.3 Walks. 83
> 6.3 AdjacencyMatrices. 83
> 6.4 Trees . 84
> 6.4.1 SpanningTrees ... 86
> 6.4.2 TreeVariations ... 87
> 7 Graph Theory II 89
> 7.1 ColoringGraphs... 89
> 7.1.1 k-Coloring.. 90
> 7.1.2 BipartiteGraphs .. 90
> 7.2 PlanarGraphs 91
> 7.2.1 Euler’sFormula... 93
> 7.2.2 ClassifyingPolyhedra ... 94
> 7.3 Hall’sMarriageTheorem.. 95
> 7.3.1 AFormalStatement 97
> 8 Communication Networks 99
> 8.1 CompleteBinaryTree 99
> 8.1.1 LatencyandDiameter ...100
> 8.1.2 SwitchSize .101
> 8.1.3 SwitchCount 101
> 8.1.4 Congestion .101
> 8.2 2-DArray ..103
> 8.3 Butterfly ...104
> 8.4 Benes ̆Network ...106
> 9 Relations 111
> 9.0.1 RelationsonO
