Muutke küpsiste eelistusi

E-raamat: Mathematical Principles of the Internet, Two Volume Set

Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 110,49 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Mathematical Principles of the Internet, Two Volume SetSuurem pilt
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, these cover only a partial panorama and the key principles.

Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed.

In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.

Mathematical Principles of the Internet: Volume 1
Preface
xix
List of Symbols
xxix
Greek Symbols
xxxvii
Prologue
xxxix
1 Information Theory
1(100)
1.1 Introduction
3(1)
1.2 Entropy
4(3)
1.3 Mutual Information and Relative Entropy
7(4)
1.3.1 Mutual Information
7(2)
1.3.2 Relative Entropy
9(2)
1.4 Noiseless Coding for Memoryless Source
11(4)
1.4.1 Pair of Inequalities
12(2)
1.4.2 Shannon-Fano Coding Theorem
14(1)
1.5 Data Compression
15(17)
1.5.1 Huffman's Coding
16(5)
1.5.2 Arithmetic Coding
21(5)
1.5.3 Lempel-Ziv Coding
26(6)
1.6 Communication Channels
32(12)
1.6.1 Discrete Memoryless Channel
32(2)
1.6.2 Symmetric Channel
34(1)
1.6.3 Extension of a Discrete Memoryless Channel
35(1)
1.6.4 Basics of Coding and Decoding
36(2)
1.6.5 Noiseless Communication Channel Coding Theorem
38(3)
1.6.6 Noisy Communication Channel Coding Theorem
41(3)
1.7 Differential Entropy and Capacity of Communication Channels
44(8)
1.7.1 Differential Entropy
44(4)
1.7.2 Information Capacity Theorem
48(3)
1.7.3 Parallel Gaussian-Noise Communication Channels
51(1)
1.8 Rate Distortion Theory
52(14)
1.8.1 Quantization
52(1)
1.8.2 Rate Distortion Function
53(2)
1.8.3 Properties of Rate Distortion Function
55(3)
1.8.4 Representation of Independent Gaussian Random Variables
58(3)
1.8.5 Computation of Rate Distortion Function
61(5)
1.9 Network Information Theory
66(3)
1.9.1 Multi-access Gaussian Communication Channel
66(1)
1.9.2 Gaussian Broadcast Channels
67(2)
1.10 Maximum Entropy Principle
69(4)
1.10.1 Maximum-Likelihood Estimation
69(1)
1.10.2 Maximum Entropy Estimation
70(3)
Reference Notes
73(1)
Problems
74(23)
References
97(4)
2 Algebraic Coding Theory
101(72)
2.1 Introduction
103(2)
2.2 Basics of Coding Theory
105(7)
2.2.1 Information Rate
105(2)
2.2.2 Hamming Distance
107(1)
2.2.3 Decoding Rules
108(1)
2.2.4 Bounds on Codes
108(2)
2.2.5 Perfect Codes
110(1)
2.2.6 Error Probabilities
111(1)
2.3 Vector Spaces over Binary Field
112(1)
2.4 Linear Codes
113(8)
2.4.1 Basics of Linear Codes
114(4)
2.4.2 Minimum-Distance Decoding
118(3)
2.5 Cyclic Codes
121(5)
2.5.1 Basics of Cyclic Codes
121(2)
2.5.2 Check Polynomial and Parity-Check Matrix
123(1)
2.5.3 Encoding and Decoding Process
124(2)
2.6 Hamming Codes
126(4)
2.6.1 Basics of Hamming Codes
126(2)
2.6.2 Hamming Codes via Cyclic Codes
128(2)
2.7 Cyclic Redundancy Check Codes
130(2)
2.8 Reed-Muller Codes
132(5)
2.9 Bose-Chaudhuri-Hocquenghem Codes
137(10)
2.9.1 Binary BCH Codes
139(2)
2.9.2 Decoding of BCH Codes
141(6)
2.10 Reed-Solomon Codes
147(2)
2.11 Convolutional Codes
149(15)
2.11.1 Polynomial Representation
150(3)
2.11.2 Error-Correction and Distance Measures
153(1)
2.11.3 Matrix Representation
154(2)
2.11.4 Wyner-Ash Convolutional Codes
156(2)
2.11.5 Shift Registers
158(1)
2.11.6 Decoding
158(6)
2.12 Turbo Codes
164(1)
Reference Notes
165(1)
Problems
165(6)
References
171(2)
3 Cryptography
173(76)
3.1 Introduction
175(3)
3.2 Some Classical Ciphering Schemes
178(6)
3.2.1 The Shift Cipher
178(1)
3.2.2 The Affine Cryptosystem
179(1)
3.2.3 A Polyalphabetic Cipher
180(2)
3.2.4 The Hill Cipher
182(1)
3.2.5 The Permutation Cipher
183(1)
3.2.6 One-Time Pad
184(1)
3.3 Cryptanalysis
184(1)
3.4 Information-Theoretic Cryptanalysis
185(7)
3.4.1 Probabilistic Cryptosystem
185(2)
3.4.2 Perfect Secrecy
187(1)
3.4.3 Entropy
188(1)
3.4.4 Combination of Cryptosystems
188(1)
3.4.5 Unicity Distance
189(3)
3.5 Public-Key Cryptography
192(7)
3.5.1 The RSA Cryptosystem
193(4)
3.5.2 The El Gamal Cryptosystem
197(2)
3.6 Probabilistic Encryption
199(4)
3.7 Homomorphic Encryption
203(4)
3.7.1 Applications
204(1)
3.7.2 Algebraic Homomorphism
204(1)
3.7.3 Homomorphic Cryptosystems
205(2)
3.8 Digital Signatures
207(4)
3.8.1 The RSA Signature Scheme
208(1)
3.8.2 The El Gamal Signature Scheme
209(2)
3.9 Key Distribution
211(1)
3.10 Elliptic Curve Based Cryptosystems
212(6)
3.10.1 Elliptic Curve Based El Gamal Cryptosystem
213(2)
3.10.2 Menezes-Vanstone Elliptic Curve Cryptosystem
215(2)
3.10.3 Elliptic Curve Based Key Exchange Algorithm
217(1)
3.11 Hyperelliptic Curve Based Cryptosystem
218(2)
3.12 Hash Functions
220(1)
3.13 Authentication
221(3)
3.13.1 Identification
221(2)
3.13.2 Message Authentication
223(1)
3.14 The Data Encryption Standard
224(5)
3.14.1 The DES Algorithm
224(3)
3.14.2 Modes of Operation of DES
227(2)
3.15 The Advanced Encryption Standard
229(7)
3.15.1 Arithmetic Used in AES
229(2)
3.15.2 The AES Algorithm
231(1)
3.15.3 Different Layers
232(4)
3.16 Probabilistic Perspective on Cryptographic Security
236(6)
3.16.1 Basics of Probabilistic Security
236(3)
3.16.2 Security of a Symmetric-Key Cryptosystem
239(2)
3.16.3 Security of an Asymmetric-Key Cryptosystem
241(1)
Reference Notes
242(1)
Problems
243(2)
References
245(4)
4 Internet Traffic
249(52)
4.1 Introduction
251(2)
4.2 Self-Similarity in the LAN and Internet Traffic
253(1)
4.2.1 Self-Similarity in the LAN Traffic
253(1)
4.2.2 Self-Similarity in the Internet Traffic
254(1)
4.3 Power-Law Probability Distributions
254(2)
4.3.1 Pareto Distribution
255(1)
4.3.2 Zipf Distribution
255(1)
4.4 Modeling Highly Variable Measurements
256(3)
4.4.1 Heavy-Tailed Distributions
256(2)
4.4.2 Properties of Power-Law-Tailed Distributions
258(1)
4.5 Internet Traffic Modeling
259(9)
4.5.1 Self-Similar Processes
259(1)
4.5.2 Fractional Brownian Motion
260(4)
4.5.3 Second Order Self-Similarity
264(2)
4.5.4 Self-Similarity and the Hurst's Law
266(1)
4.5.5 Estimation of the Hurst Parameter
266(2)
4.6 Explanation of Self-Similarity in the Internet Traffic
268(6)
4.6.1 Notation and Assumptions
268(1)
4.6.2 Single Source Characterization
269(3)
4.6.3 Multiple Source Characterization
272(2)
4.7 Asymptotic Analysis of the R/S Statistic
274(4)
4.8 Transform Analysis of Fractional Brownian Motion
278(4)
4.8.1 Power Spectrum of the Increment of a FBMP
278(1)
4.8.2 Wigner-Ville Transform Technique
279(1)
4.8.3 Continuous Wavelet Transform Technique
279(2)
4.8.4 Discrete Wavelet Transform Technique
281(1)
4.9 Internet Traffic Modeling via Chaotic Maps
282(9)
4.9.1 Nonlinear Maps
284(4)
4.9.2 Sojourn Time Probability
288(1)
4.9.3 Asymptotic Spectral Analysis
289(2)
Reference Notes
291(1)
Problems
291(7)
References
298(3)
5 Dynamics, Control, and Management of Internet Congestion
301(94)
5.1 Introduction
303(2)
5.2 Congestion Control and Resource Allocation
305(2)
5.3 Network Basics
307(1)
5.4 The Transmission Control and Internet Protocols
308(4)
5.4.1 Transmission Control Protocol
308(3)
5.4.2 User Datagram Protocol
311(1)
5.4.3 Internet Protocol
311(1)
5.5 A Simple Periodic TCP Model
312(2)
5.6 Queue Management
314(8)
5.6.1 Passive Queue Management
314(1)
5.6.2 Active Queue Management
315(1)
5.6.3 Random Early Detection
315(7)
5.7 A Mean-Field Model of Multiple TCP/IP Connections
322(5)
5.7.1 Window-Size Evolution
323(1)
5.7.2 Differential Equation of the Queue Size
324(1)
5.7.3 Window-Size Probability Density Function
325(1)
5.7.4 Analysis of Stable System
325(2)
5.8 Traffic Rate, Congestion Management, and Stability
327(11)
5.8.1 Traffic Rate Control and Fairness
328(4)
5.8.2 Congestion Control via Feedback and Its Stability
332(3)
5.8.3 Max-Min Fair Algorithms
335(3)
5.9 Traffic Management via Packet Scheduling and Regulation
338(4)
5.9.1 Generalized Processor Sharing
339(1)
5.9.2 Packetized Generalized Processor Sharing Scheme
340(1)
5.9.3 Leaky Bucket for Traffic Regulation
341(1)
5.10 Network Calculus
342(6)
5.10.1 Mathematical Preliminaries
343(2)
5.10.2 Basic Concepts
345(1)
5.10.3 Fundamental Bounds
346(2)
5.11 Multiple Access of Communicating Medium
348(9)
5.11.1 Medium Access Control Techniques
348(6)
5.11.2 CSMA/CD Model
354(2)
5.11.3 CSMA/CA Model
356(1)
5.12 Stochastic Geometry of Wireless Networks
357(15)
5.12.1 Basics of Wireless Technology
357(3)
5.12.2 Preliminaries on Stochastic Modeling
360(2)
5.12.3 Interference Model
362(4)
5.12.4 A Combination Model for Path Loss and Fading
366(2)
5.12.5 Outage Probability
368(1)
5.12.6 Transmission Capacity
369(3)
Reference Notes
372(1)
Problems
373(18)
References
391(4)
6 Queueing Theory
395(74)
6.1 Introduction
397(1)
6.2 Terminology and Notation
398(3)
6.3 Little's Law
401(1)
6.4 Steady-State Probabilities
402(2)
6.5 Birth-and-Death Process Based Queueing Systems
404(11)
6.5.1 Exponentially Distributed Random Variable
404(1)
6.5.2 Birth-and-Death Process Description of a Queue
405(1)
6.5.3 M/M/infinity Queue
406(1)
6.5.4 M/M/c/c Queue
407(1)
6.5.5 M/M/1 Queue
408(2)
6.5.6 M/M/1/K Queue
410(2)
6.5.7 M/M/c Queue
412(2)
6.5.8 M/M/1/K/K Queue
414(1)
6.6 Non-Poisson Queues
415(20)
6.6.1 D/D/1 Queue
416(1)
6.6.2 M/G/1 Queue
416(5)
6.6.3 G/M/1 Queue
421(6)
6.6.4 G/M/c Queue
427(3)
6.6.5 G/G/1 Queue
430(5)
6.7 Priority Queueing Systems
435(3)
6.7.1 Single Server Nonpreemptive Priorities
436(2)
6.7.2 Multiserver Nonpreemptive Priorities
438(1)
6.8 Queueing Networks
438(6)
6.8.1 Open Queueing Networks
439(1)
6.8.2 Closed Queueing Networks
440(4)
6.9 Bounds and Approximations
444(6)
6.9.1 Heavy Traffic Approximations
444(2)
6.9.2 Approximations for Multiserver Queues
446(1)
6.9.3 G/G/1 Queue Bounds
447(1)
6.9.4 Diffusion Approximation
448(2)
6.10 Application of Large Deviation Techniques
450(8)
6.10.1 Theory of Effective Bandwidths
451(4)
6.10.2 Queue with Large Buffer
455(3)
Reference Notes
458(1)
Problems
458(9)
References
467(2)
7 Stochastic Structure of the Internet and the World Wide Web
469(98)
7.1 Introduction
471(1)
7.2 Metrics to Characterize Random Graphs
472(1)
7.3 Experimental Evidence
473(4)
7.3.1 Macroscopic Structure of the World Wide Web
475(1)
7.3.2 A Kappa-shell Decomposition of the Internet Topology
475(2)
7.4 Some Important Metrics Revisited
477(5)
7.4.1 Degree Distribution
477(3)
7.4.2 Clustering Coefficient
480(2)
7.4.3 Betweenness
482(1)
7.5 Classical Random Graph Theory
482(4)
7.6 Study of Random Graphs via z-Transforms
486(7)
7.6.1 Phase Transition
486(1)
7.6.2 Average Path Length
487(1)
7.6.3 Clustering Coefficient of the Random Graph
488(1)
7.6.4 Distribution of Component Sizes
488(2)
7.6.5 Examples
490(3)
7.7 The Kappa-core of a Random Graph
493(6)
7.8 Graph Spectra
499(2)
7.8.1 Graph with Poissonian Degree Distribution
499(1)
7.8.2 Graph with Power-Law Degree Distribution
500(1)
7.9 Small-World Networks
501(3)
7.10 Network Evolution Models
504(10)
7.10.1 Barabasi and Albert Model
505(2)
7.10.2 A Variant of the Barabasi and Albert Model
507(1)
7.10.3 A Generalization of Barabasi and Albert Model
508(2)
7.10.4 Intrinsic Vertex Weight Model
510(3)
7.10.5 Web Graph Evolution Model
513(1)
7.11 Hyperbolic Geometry of Networks
514(8)
7.11.1 Relevant Hyperbolic Geometry
514(1)
7.11.2 Modeling Complex Networks
515(4)
7.11.3 Popularity-Similarity Network Dynamics
519(3)
7.12 Search Techniques on Networks
522(9)
7.12.1 Application of SVD Techniques
523(1)
7.12.2 Detailed Network Search
524(5)
7.12.3 Random and Guided Search on the Network
529(2)
7.13 Virus Epidemics and Immunization in the Internet
531(5)
7.13.1 A Model of Spread of Epidemic
531(4)
7.13.2 Immunization Process
535(1)
7.14 Error and Attack Tolerance of Networks
536(4)
7.14.1 Error Tolerance
537(1)
7.14.2 Attack Tolerance
538(2)
7.15 Congestion in a Stochastic Network
540(2)
7.15.1 Network with Equally-Busy Nodes
541(1)
7.15.2 Scale-Free Networks
541(1)
7.16 Exponential Random Graph Models
542(4)
Reference Notes
546(1)
Problems
547(14)
References
561(6)
8 Graph-Theoretic Algorithms
567(100)
8.1 Introduction
569(1)
8.2 Shortest Path Algorithms
569(9)
8.2.1 Bellman-Ford Shortest Path Algorithm
570(1)
8.2.2 Dijkstra's Shortest Path Algorithm
571(3)
8.2.3 All-Pairs Shortest Path Algorithms
574(4)
8.3 Special Path Algorithms
578(11)
8.3.1 K Shortest Paths Algorithm
578(2)
8.3.2 Routing with Transit-Times and Constraints
580(4)
8.3.3 Disjoint Paths Algorithm
584(5)
8.4 Algebraic Path Techniques
589(8)
8.4.1 Semirings and Dioids
589(3)
8.4.2 Applications
592(2)
8.4.3 Prebimonoids
594(3)
8.5 Geographic Routing in Hyperbolic Space
597(5)
8.5.1 Greedy Embeddings
597(1)
8.5.2 Applicable Hyperbolic Geometry
598(3)
8.5.3 Greedy Embedding in Hyperbolic Space
601(1)
8.6 Minimum Spanning Tree Algorithms
602(5)
8.6.1 Janiik's Algorithm
604(1)
8.6.2 Kruskal's Algorithm
605(2)
8.7 Connectivity of a Graph
607(2)
8.8 Network Reliability
609(8)
8.8.1 Access Network Reliability
610(2)
8.8.2 Mesh Network Reliability
612(5)
8.9 Maximum Flows and Minimum Cost Flows
617(20)
8.9.1 Maximum Flows
618(10)
8.9.2 Minimum Cost Flows
628(9)
8.10 Network Coding
637(14)
8.10.1 A Communication Network Model
640(1)
8.10.2 Linear Network Coding
641(3)
8.10.3 Properties of Linear Network Coding
644(2)
8.10.4 Throughput Improvement
646(5)
8.11 Design of Communication Networks
651(3)
Reference Notes
654(1)
Problems
654(9)
References
663(4)
9 Game Theory and the Internet
667(68)
9.1 Introduction
669(1)
9.2 Game Theory
670(31)
9.2.1 Preliminaries
671(1)
9.2.2 Strategic-Form Games
672(18)
9.2.3 Extensive-Form Games
690(7)
9.2.4 Repeated Games
697(4)
9.3 Selfish Routing
701(10)
9.3.1 Braess' Paradox
701(2)
9.3.2 Routing Model
703(6)
9.3.3 Technique to Reduce the Price of Anarchy
709(2)
9.4 A Selfish Task Allocation Model
711(5)
9.5 A Repeated Game
716(1)
9.6 Algorithmic Mechanism Design
717(6)
9.6.1 Preliminaries
718(2)
9.6.2 Vickrey-Groves-Clarke Mechanism
720(1)
9.6.3 Examples
721(2)
Reference Notes
723(1)
Problems
724(7)
References
731(4)
10 Internet Economics
735(44)
10.1 Introduction
737(1)
10.2 Scope of Economics
738(1)
10.3 Internet Technology, Costs, and Pricing
738(2)
10.4 A Qualitative Economic Model of the Internet
740(1)
10.5 Network Resources, Congestion, and Pricing
741(4)
10.5.1 Social Welfare and Capacity
741(1)
10.5.2 Competitive Market Pricing
742(3)
10.5.3 Pricing without Usage Fees
745(1)
10.6 Service Differentiation
745(3)
10.7 Time-Dependent Pricing and Bandwidth Trade-Off
748(3)
10.7.1 Basic Model
748(1)
10.7.2 Nash Equilibrium of the Game
749(1)
10.7.3 Social Welfare Function
750(1)
10.7.4 Revenue Maximization
751(1)
10.8 Auctions
751(5)
10.8.1 Vickrey Auction
752(1)
10.8.2 Generalized Vickrey Auction
753(3)
10.9 Application of Coalitional Game Theory
756(8)
10.9.1 Basics of Coalitional Game Theory
756(5)
10.9.2 ISP Settlement
761(3)
10.10 Bargaining Games
764(3)
Reference Notes
767(1)
Problems
767(9)
References
776(3)
11 Data Mining and Knowledge Discovery
779(148)
11.1 Introduction
781(1)
11.2 Basics of Knowledge Discovery Process and Data Mining
782(6)
11.2.1 Knowledge Discovery Process
782(1)
11.2.2 Elements of Data Mining
783(3)
11.2.3 Data Mining as a Learning Process
786(2)
11.3 Clustering
788(16)
11.3.1 Proximity Measures
790(2)
11.3.2 m-Means Clustering
792(2)
11.3.3 Hierarchical Clustering
794(1)
11.3.4 Model-Based Clustering
795(5)
11.3.5 Fuzzy Clustering
800(2)
11.3.6 Cluster Validity Measures
802(2)
11.4 Association Rules and Sequential Pattern Mining
804(15)
11.4.1 Basic Concepts of Association Rules
805(2)
11.4.2 Necessity of an Efficient Algorithm
807(1)
11.4.3 The Apriori Algorithm
808(8)
11.4.4 Sequential Pattern Mining
816(3)
11.5 Metric Classification
819(21)
11.5.1 Bayesian Classifier
820(3)
11.5.2 Support Vector Machines
823(7)
11.5.3 Nearest-Neighbor Classification
830(1)
11.5.4 Artificial Neural Network
831(9)
11.6 Nonmetric Classification
840(10)
11.6.1 Decision Tree Induction
841(4)
11.6.2 Rule-Based Induction
845(5)
11.7 Classification via Ensemble Methods
850(6)
11.7.1 Bagging
851(1)
11.7.2 Boosting
852(4)
11.8 Rough Sets
856(13)
11.8.1 Basics
856(4)
11.8.2 Reduct and Core
860(5)
11.8.3 Decision System
865(2)
11.8.4 Decision Rules
867(2)
11.9 High-Dimensional Data
869(2)
11.10 Statistical Techniques
871(3)
11.10.1 Prediction via Regression Analysis
871(2)
11.10.2 Principal Component Analysis
873(1)
11.11 Social Network Analysis
874(12)
11.11.1 Node Centrality
874(4)
11.11.2 Node-Group Centrality
878(1)
11.11.3 Node Similarity
879(2)
11.11.4 Linking Structure
881(1)
11.11.5 Community Detection
882(4)
11.12 Hidden Markov Model
886(14)
11.12.1 Model Description and the Problems
886(3)
11.12.2 Probability Evaluation
889(3)
11.12.3 Decoding of State Sequence
892(1)
11.12.4 Model Evaluation
893(7)
11.13 Kalman Filtering
900(9)
11.13.1 Stochastic Dynamical System
901(1)
11.13.2 Filtering Scheme
902(4)
11.13.3 A Probabilistic Perspective on Kalman Filtering
906(3)
Reference Notes
909(1)
Problems
910(12)
References
922(5)
12 Quantum Computation, Communication, and Cryptography
927(78)
12.1 Introduction
929(1)
12.2 Quantum Mechanics
930(12)
12.2.1 Preliminaries
930(3)
12.2.2 Pure and Mixed States, and Density Operator
933(4)
12.2.3 Evolution of a Quantum System
937(1)
12.2.4 Observables
938(1)
12.2.5 Postulates of Quantum Mechanics
939(1)
12.2.6 Heisenberg's Uncertainty Principle
940(1)
12.2.7 Quantum Operations
940(2)
12.2.8 Quantum Entanglement
942(1)
12.3 Quantum Computing Elements
942(6)
12.3.1 Boolean Gates and Circuits
942(2)
12.3.2 Quantum Bits and Registers
944(1)
12.3.3 Quantum Gates and Circuits
945(3)
12.3.4 No-Cloning Theorem
948(1)
12.4 What is Quantum Computation?
948(1)
12.5 Models of Computation
949(9)
12.5.1 Deterministic Turing Machine
950(4)
12.5.2 Nondeterministic Turing Machine
954(1)
12.5.3 Probabilistic Turing Machine
955(2)
12.5.4 Quantum Turing Machine
957(1)
12.6 Quantum Algorithms
958(14)
12.6.1 Deutsch's Problem and Algorithm
959(2)
12.6.2 Deutsch-Josza's Problem and Algorithm
961(2)
12.6.3 Shor's Factorization Algorithm
963(5)
12.6.4 Grover's Search Algorithm
968(4)
12.7 Quantum Information Theory
972(3)
12.8 Quantum Communication Theory
975(4)
12.8.1 Data Compression
975(1)
12.8.2 Typical Subspaces
976(1)
12.8.3 Fidelity
977(2)
12.8.4 Schumacher's Noiseless Channel Coding Theorem
979(1)
12.9 Quantum Error-Correction
979(6)
12.9.1 Difficulties Encountered
980(1)
12.9.2 Types of Errors
980(1)
12.9.3 Basics of Quantum Error-Correction
981(3)
12.9.4 A Bound on Quantum Error-Correcting Codes
984(1)
12.9.5 Shor's Nine-Qubit Code
984(1)
12.9.6 Barenco's Three-Qubit Code
985(1)
12.10 Quantum Cryptography
985(7)
12.10.1 Classical Cryptographic Communication
985(1)
12.10.2 Modern Cryptographic Communication
986(1)
12.10.3 Quantum Cryptographic Communication
986(6)
Reference Notes
992(1)
Problems
992(10)
References
1002(3)
Index
1005
Mathematical Principles of the Internet: Volume 2
Preface
xv
List of Symbols
xxv
Greek Symbols
xxxiii
1 Number Theory
1(44)
1.1 Introduction
3(1)
1.2 Sets
3(5)
1.2.1 Set Operations
5(2)
1.2.2 Bounded Sets
7(1)
1.2.3 Interval Notation
7(1)
1.3 Functions
8(4)
1.3.1 Sequences
8(1)
1.3.2 Permutation Mappings
9(1)
1.3.3 Permutation Matrices
10(1)
1.3.4 Unary and Binary Operations
11(1)
1.3.5 Logical Operations
11(1)
1.4 Basic Number-Theoretic Concepts
12(8)
1.4.1 Countability
12(1)
1.4.2 Divisibility
12(1)
1.4.3 Prime Numbers
12(1)
1.4.4 Greatest Common Divisor
13(4)
1.4.5 Continued Fractions
17(3)
1.5 Congruence Arithmetic
20(13)
1.5.1 Chinese Remainder Theorem
23(1)
1.5.2 Moebius Function
24(2)
1.5.3 Euler's Phi-Function
26(2)
1.5.4 Modular Arithmetic
28(2)
1.5.5 Quadratic Residues
30(2)
1.5.6 Jacobi Symbol
32(1)
1.6 Cyclotomic Polynomials
33(2)
1.7 Some Combinatorics
35(2)
1.7.1 Principle of Inclusion and Exclusion
35(1)
1.7.2 Stirling Numbers
36(1)
Reference Notes
37(1)
Problems
37(5)
References
42(3)
2 Abstract Algebra
45(90)
2.1 Introduction
47(1)
2.2 Algebraic Structures
47(16)
2.2.1 Groups
48(4)
2.2.2 Rings
52(1)
2.2.3 Subrings and Ideals
53(2)
2.2.4 Fields
55(2)
2.2.5 Polynomial Rings
57(5)
2.2.6 Boolean Algebra
62(1)
2.3 More Group Theory
63(3)
2.4 Vector Spaces over Fields
66(4)
2.5 Linear Mappings
70(1)
2.6 Structure of Finite Fields
71(15)
2.6.1 Construction
73(3)
2.6.2 Minimal Polynomials
76(3)
2.6.3 Irreducible Polynomials
79(1)
2.6.4 Factoring Polynomials
80(1)
2.6.5 Examples
81(5)
2.7 Roots of Unity in Finite Field
86(1)
2.8 Elliptic Curves
87(13)
2.8.1 Elliptic Curves over Real Fields
90(5)
2.8.2 Elliptic Curves over Finite Fields
95(1)
2.8.3 Elliptic Curves over Zp, p > 3
96(3)
2.8.4 Elliptic Curves over GF2n
99(1)
2.9 Hyperelliptic Curves
100(17)
2.9.1 Basics of Hyperelliptic Curves
100(2)
2.9.2 Polynomials, Rational Functions, Zeros, and Poles
102(3)
2.9.3 Divisors
105(6)
2.9.4 Mumford Representation of Divisors
111(6)
2.9.5 Order of the Jacobian
117(1)
Reference Notes
117(1)
Problems
118(14)
References
132(3)
3 Matrices and Determinants
135(68)
3.1 Introduction
137(1)
3.2 Basic Matrix Theory
137(7)
3.2.1 Basic Matrix Operations
139(1)
3.2.2 Different Types of Matrices
140(2)
3.2.3 Matrix Norm
142(2)
3.3 Determinants
144(4)
3.3.1 Definitions
144(2)
3.3.2 Vandermonde Determinant
146(1)
3.3.3 Binet-Cauchy Theorem
146(2)
3.4 More Matrix Theory
148(4)
3.4.1 Rank of a Matrix
148(1)
3.4.2 Adjoint of a Square Matrix
149(1)
3.4.3 Nullity of a Matrix
149(1)
3.4.4 System of Linear Equations
150(1)
3.4.5 Matrix Inversion Lemma
151(1)
3.4.6 Tensor Product of Matrices
151(1)
3.5 Matrices as Linear Transformations
152(3)
3.6 Spectral Analysis of Matrices
155(3)
3.7 Hermitian Matrices and Their Eigenstructures
158(3)
3.8 Perron-Frobenius Theory
161(4)
3.8.1 Positive Matrices
162(1)
3.8.2 Nonnegative Matrices
163(2)
3.8.3 Stochastic Matrices
165(1)
3.9 Singular Value Decomposition
165(3)
3.10 Matrix Calculus
168(3)
3.11 Random Matrices
171(6)
3.11.1 Gaussian Orthogonal Ensemble
171(2)
3.11.2 Wigner's Semicircle Law
173(4)
Reference Notes
177(1)
Problems
177(24)
References
201(2)
4 Graph Theory
203(40)
4.1 Introduction
205(1)
4.2 Undirected and Directed Graphs
205(4)
4.2.1 Undirected Graphs
206(1)
4.2.2 Directed Graphs
207(2)
4.3 Special Graphs
209(2)
4.4 Graph Operations, Representations, and Transformations
211(4)
4.4.1 Graph Operations
211(1)
4.4.2 Graph Representations
212(2)
4.4.3 Graph Transformations
214(1)
4.5 Plane and Planar Graphs
215(3)
4.6 Some Useful Observations
218(2)
4.7 Spanning Trees
220(6)
4.7.1 Matrix-Tree Theorem
220(2)
4.7.2 Numerical Algorithm
222(2)
4.7.3 Number of Labeled Trees
224(1)
4.7.4 Computation of Number of Spanning Trees
225(1)
4.7.5 Generation of Spanning Trees of a Graph
225(1)
4.8 The Kappa-core, Kappa-crust, and Kappa-shell of a Graph
226(2)
4.9 Matroids
228(4)
4.10 Spectral Analysis of Graphs
232(3)
4.10.1 Spectral Analysis via Adjacency Matrix
232(3)
4.10.2 Laplacian Spectral Analysis
235(1)
Reference Notes
235(1)
Problems
236(5)
References
241(2)
5 Geometry
243(106)
5.1 Introduction
245(1)
5.2 Euclidean Geometry
246(5)
5.2.1 Requirements for an Axiomatic System
246(1)
5.2.2 Axiomatic Foundation of Euclidean Geometry
247(2)
5.2.3 Basic Definitions and Constructions
249(2)
5.3 Circle Inversion
251(3)
5.4 Elementary Differential Geometry
254(9)
5.4.1 Mathematical Preliminaries
254(2)
5.4.2 Lines and Planes
256(1)
5.4.3 Curves in Plane and Space
257(6)
5.5 Basics of Surface Geometry
263(8)
5.5.1 Preliminaries
263(2)
5.5.2 First Fundamental Form
265(2)
5.5.3 Conformal Mapping of Surfaces
267(1)
5.5.4 Second Fundamental Form
268(3)
5.6 Properties of Surfaces
271(13)
5.6.1 Curves on a Surface
272(6)
5.6.2 Local Isometry of Surfaces
278(1)
5.6.3 Geodesics on a Surface
279(5)
5.7 Prelude to Hyperbolic Geometry
284(8)
5.7.1 Surfaces of Revolution
285(2)
5.7.2 Constant Gaussian Curvature Surfaces
287(1)
5.7.3 Isotropic Curves
288(1)
5.7.4 A Conformal Mapping Perspective
289(3)
5.8 Hyperbolic Geometry
292(12)
5.8.1 Upper Half-Plane Model
293(2)
5.8.2 Isometrics of Upper Half-Plane Model
295(2)
5.8.3 Poincare Disc Model
297(4)
5.8.4 Surface of Different Constant Curvature
301(1)
5.8.5 Tessellations
301(1)
5.8.6 Geometric Constructions
302(2)
Reference Notes
304(1)
Problems
304(42)
References
346(3)
6 Applied Analysis
349(108)
6.1 Introduction
351(1)
6.2 Basic Analysis
351(11)
6.2.1 Point Sets
352(1)
6.2.2 Limits, Continuity, Derivatives, and Monotonicity
352(4)
6.2.3 Partial Derivatives
356(2)
6.2.4 Jacobians, Singularity, and Related Topics
358(1)
6.2.5 Hyperbolic Functions
359(1)
6.2.6 Ordinary Differential Equations
360(2)
6.3 Complex Analysis
362(9)
6.3.1 Coordinate Representation
363(1)
6.3.2 De Moivre's and Euler's Identities
364(1)
6.3.3 Limits, Continuity, Derivatives, and Analyticity
365(1)
6.3.4 Contours or Curves
366(1)
6.3.5 Conformal Mapping
367(1)
6.3.6 Integration
367(1)
6.3.7 Infinite Series
368(1)
6.3.8 Lagrange's Series Expansion
369(1)
6.3.9 Saddle Point Technique of Integration
369(2)
6.4 Cartesian Geometry
371(2)
6.4.1 Straight Line and Circle
371(1)
6.4.2 Conic Sections
372(1)
6.5 Moebius Transformation
373(5)
6.6 Polynomial Properties
378(10)
6.6.1 Roots of a Polynomial
378(1)
6.6.2 Resultant of Two Polynomials
378(4)
6.6.3 Discriminant of a Polynomial
382(1)
6.6.4 Bezout's Theorem
383(5)
6.7 Asymptotic Behavior and Algorithmic-Complexity Classes
388(5)
6.7.1 Asymptotic Behavior
388(4)
6.7.2 Algorithmic-Complexity Classes
392(1)
6.8 Vector Algebra
393(2)
6.8.1 Dot Product
393(1)
6.8.2 Vector Product
394(1)
6.9 Vector Spaces Revisited
395(8)
6.9.1 Normed Vector Space
396(1)
6.9.2 Complete Vector Space
396(2)
6.9.3 Compactness
398(1)
6.9.4 Inner Product Space
399(1)
6.9.5 Orthogonality
400(2)
6.9.6 Gram-Schmidt Orthogonalization Process
402(1)
6.9.7 Projections
402(1)
6.9.8 Isometry
403(1)
6.10 Fourier Series
403(6)
6.10.1 Generalized Functions
404(1)
6.10.2 Conditions for the Existence of Fourier Series
405(1)
6.10.3 Complex Fourier Series
406(1)
6.10.4 Trigonometric Fourier Series
407(2)
6.11 Transform Techniques
409(20)
6.11.1 Fourier Transform
409(4)
6.11.2 Laplace Transform
413(3)
6.11.3 Mellin Transform
416(2)
6.11.4 Wigner-Ville Transform
418(1)
6.11.5 Wavelet Transform
419(3)
6.11.6 Hadamard Transform
422(1)
6.11.7 Discrete Fourier Transform
423(6)
6.12 Faa di Bruno's Formula
429(2)
6.13 Special Mathematical Functions
431(3)
6.13.1 Gamma and Incomplete Gamma Functions
431(1)
6.13.2 Beta Function
432(1)
6.13.3 Riemann's Zeta Function
432(1)
6.13.4 Polylogarithm Function
433(1)
6.13.5 Bessel Function
433(1)
6.13.6 Exponential Integral
433(1)
6.13.7 Error Function
434(1)
Reference Notes
434(1)
Problems
435(18)
References
453(4)
7 Optimization, Stability, and Chaos Theory
457(82)
7.1 Introduction
459(1)
7.2 Basics of Optimization Theory
460(5)
7.2.1 Convex and Concave Functions
460(3)
7.2.2 Convex Sets
463(2)
7.3 Inequalities
465(3)
7.4 Elements of Linear Programming
468(5)
7.4.1 Hyperplanes
468(1)
7.4.2 Farkas' Alternative
469(1)
7.4.3 Primal and Dual Problems
469(4)
7.5 Optimization Techniques
473(18)
7.5.1 Taylor's Series of Several Variables
473(1)
7.5.2 Minimization and Maximization of a Function
474(3)
7.5.3 Nonlinear Constrained Optimization
477(1)
7.5.4 Optimization Problem with Equality Constraints
478(3)
7.5.5 Optimization Problem with Inequality Constraints
481(6)
7.5.6 Nonlinear Optimization via Duality Theory
487(4)
7.6 Calculus of Variations
491(3)
7.7 Stability Theory
494(14)
7.7.1 Notions Used in Describing a System
494(5)
7.7.2 Stability Concepts
499(9)
7.8 Chaos Theory
508(8)
7.8.1 Preliminaries
509(2)
7.8.2 Characterization of Chaotic Dynamics
511(3)
7.8.3 Examples of Chaotic Maps
514(2)
Reference Notes
516(1)
Problems
517(18)
References
535(4)
8 Probability Theory
539(70)
8.1 Introduction
541(1)
8.2 Axioms of Probability Theory
542(2)
8.3 Random Variables
544(2)
8.4 Average Measures
546(2)
8.4.1 Expectation
547(1)
8.4.2 Common Second Order Expectations
548(1)
8.5 Independent Random Variables
548(1)
8.6 Transforms and Moment Generating Functions
549(2)
8.6.1 z-Transform
549(1)
8.6.2 Moment Generating Function
550(1)
8.7 Examples of Some Distributions
551(8)
8.7.1 Discrete Distributions
552(1)
8.7.2 Continuous Distributions
553(4)
8.7.3 Multivariate Gaussian Distribution
557(2)
8.8 Some Well-Known Results
559(5)
8.8.1 Well-Known Inequalities
559(2)
8.8.2 Law of Large Numbers
561(1)
8.8.3 Gaussian Central Limit Theorem
562(2)
8.9 Generalized Central Limit Theorem
564(9)
8.9.1 Characteristic Function
564(1)
8.9.2 Infinitely Divisible Distributions
565(4)
8.9.3 Stable Distributions
569(4)
8.10 Range Distribution
573(2)
8.10.1 Joint Distribution of U and V
573(1)
8.10.2 Distribution of Range
574(1)
8.10.3 A Property of the Average Value of Range
574(1)
8.11 Large Deviation Theory
575(5)
8.11.1 A Prelude via Saddle Point Technique
576(1)
8.11.2 Cramer and Bahadur-Rao Theorems
577(3)
Reference Notes
580(1)
Problems
580(26)
References
606(3)
9 Stochastic Processes
609(70)
9.1 Introduction
611(1)
9.2 Terminology and Definitions
611(2)
9.3 Measure Theory
613(3)
9.3.1 Sigma-Algebra, Measurable Sets, and Measurable Space
613(1)
9.3.2 Borel Sets
614(1)
9.3.3 Measure
614(1)
9.3.4 Measurable Function
615(1)
9.4 Examples of Stochastic Processes
616(9)
9.4.1 Poisson Process
616(3)
9.4.2 Shot Noise Process
619(3)
9.4.3 Gaussian Process
622(1)
9.4.4 Brownian Motion Process
622(1)
9.4.5 Gaussian White Noise Process
623(1)
9.4.6 Brownian Motion and Gaussian White Noise
624(1)
9.5 Point Process
625(10)
9.5.1 Poisson Point Process
628(2)
9.5.2 Laplace Functional
630(2)
9.5.3 Marked Point Process
632(2)
9.5.4 Transformation of Poisson Point Processes
634(1)
9.6 Renewal Theory
635(7)
9.6.1 Ordinary Renewal Process
635(2)
9.6.2 Modified Renewal Process
637(1)
9.6.3 Alternating Renewal Process
638(2)
9.6.4 Backward and Forward Recurrence-Times
640(1)
9.6.5 Equilibrium Renewal Process
641(1)
9.6.6 Equilibrium Alternating Renewal Process
641(1)
9.7 Markov Processes
642(19)
9.7.1 Discrete-Time Markov Chains
643(7)
9.7.2 Continuous-Time Markov Chains
650(8)
9.7.3 Continuous-Time Markov Processes
658(3)
Reference Notes
661(1)
Problems
662(15)
References
677(2)
Index
679
Nirdosh Bhatnagar works, both in the academia and industry in Silicon Valley, California, USA. He is the author of several papers and reports. Nirdosh earned an MS in operations research, and MS and PhD in electrical engineering, all from Stanford University, Stanford, California.
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97813513792122e.html
Märksõnad: