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计算的本质 版权信息
- ISBN:9787523206591
- 条形码:9787523206591 ; 978-7-5232-0659-1
- 装帧:平装-胶订
- 册数:暂无
- 重量:暂无
- 所属分类:>>
计算的本质 内容简介
计算,实际上是解决问题的过程。人们希望用计算机能找到解决一切问题的方法,因此在计算领域建立了算法理论和算法模型,并根据各种问题提出具体算法。而计算的复杂性是现代数学中*令人着迷的领域之一。本书通过几个经典的计算问题:哥尼斯堡七桥问题、汉密尔顿路径问题、整数分解和国际象棋问题,浅探计算的魅力。
计算的本质 目录
Figure Credits
Preface
1 Prologue
1.1 CrossingBridges
1.2 IntractableItineraries
1.3 Playing ChessWith God
1.4 What LiesAhead
Problems
Notes
2 The Basics
2.1 Problems and Solutions
2.2 Time,Space,and Scaling
2.3 Intrinsic Complexity
2.4 The Importance ofBeingPolynomial
2.5 TractabilityandMathematicalInsight
Problems
Notes
3 Insights and Algorithms
3.1 Recursion
3.2 Divide and Conquer
3.3 DynamicProgramming
3.4 GettingThere FromHere
3.5 When Greedis Good
3.6 FindingaBetterFlow
3.7 Flows,Cuts,and Duality
3.8 Transformations andReductions
Problems
Notes
4 NeedlesInaHaystack:theClassNP
4.1 Needles andHaystacks
4.2 AT0ur 0fNP
4.3 Search。Existence,andNondeterminism
4.4 Knots and Primes
Problems
Notes
5 WhO is the Hardest One of All?NP-Completeness
5.1 Ⅵmen 0ne Problem CapturesThemAll
5.2 Circuits andFormulas
5.3 DesigningReductions
5.4 Completeness as aSurprise
5.5 The BoundaryBetween EasyandHard
5.6 Finally,Hamfltonian path
Problems
Notes
6 The Deep Question:P vs.NP
6.1 WhatifP=NP
6.2 UpperBounds are Easy,LowerBoundsAre Hard
6.3 Diagonalization andthe Time Hierarchy
6.4 PossibleWbrlds
6.5 NaturalProofs
6.6 Problemsinthe Gap
6.7 Nonconstructive PrOOfs
6.8 The RoadAhead
Problems
Notes
7 The Grand Unified Theory of Computation
7.1 Babbage~Vision and Hilbert's Dream
7.2 Universalityand Undecidabnit、
7.3 BuildingBlocks:Recursive Functions
7.4 Formis Function:the A—Calculus
7.5 Turing'sApplied Philosophy
7.6 ComputationEverywhere
Problems
Notes
8 Memory,Paths,and Games
8.1 Wlelcometothe State Space
8.2 ShowMe TheWay
8.3 LandNL.Completeness
8.4 Middle.First Search and Nondeterministic Space
8.5 Y0u Cant GetThereFromHere
8.6 PSPACE,Games,and Quantified SAT
8.7 Games People Play
8.8 Symmetric Space
Problems
Notes
9 Optimization and Approximation
9.1 Three Flavors ofOptimization
9.2 Approximations
9.3 Inapproximability
9.4 Jewels andFacets:LinearProgramming
9.5 Throughthe Looking-Glass:Duality
9.6 SolvingbyBalloon:InteriorPointMethods
9.7 Huntingwitll EggsheHs
9.8 A1gorithmic Cubism
9.9 Trees,Tours,andPolytopes
9.10 SolvingHard ProblemsinPractice
Problems
Notes
10 Randomized Algorithms
10.1 FoilingtheAdversary
10.2 111e SmallestCut
10.3 The Satisfied Drunkard:WalkSAT
10.4 Solvingin Heaven.Projectingto Earth
10.5 GamesAgainsttheAdversary
10.6 Fingerprints,HashFunctions,andUniqueness
10.7 The Roots ofIdentity
10.8 Primalit、
10.9 Randomized ComplexityClasses
Problems
Notes
11 Interacflon and Pseudorandomness
11.1 TheTale ofArthurandMerlin
11.2 The Fable ofthe Chess Master
11.3 ProbabilisticallyCheckable Proofs
11.4 Pseudorandom Generators and Derandomization
Problems
Nores
12 Random Walks and Rapid Mixing
12.1 A Random、^mkin Physics
12.2 The Approachto Equfl~rium
12.3 EquflibriumIndicators
12.4 Coupling
....
12.5 Coloring aGraph.Randomly
12.6 BuryingAncientHistory:CouplingfromthePast
12.7 The Spectral Gap
12.8 FlOWS ofProbabnity:Conductance
12.9 Expanders
12.10 MixinginTime andSpace
Problems
Notes
13 Counting,Sampling,and StatisflcM Physics
13.1 SpanningTrees andthe Determinant
13.2 PerfectMatchings andthe Permanent
13.3 The ComplexityofCounting
13.4 From Countingto Sampling.and Back
13.5 RandomMatchings andApproximatingthePermanent
13.6 P1anal:Graphs andAsymptotics onLattices
13.7 SolvingtheIsingModel
Problems
Notes
14 When Formulas Freeze:Phase Transitons in Computation
14.1 Experiments and Coniectures
14.2 Random Graphs,Giant Components,and Cores
14.3 Equations of Motion:Algorithmic Lower Bounds
14.4 Magic Moments
14.5 The Easiest Hard
展开全部
计算的本质 作者简介
(美)克里斯托弗·摩尔(Cristopher Moore),美国著名计算机学家、数学家和物理学家,他是美国圣塔菲研究所的常任教授,并且是美国数学学会和美国物理学会的杰出会士。 (德)斯蒂芬·默滕斯(Stephan Mertens),德国马格德堡大学的理论物理学家,也是美国圣塔菲研究所的外聘教授。
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