Mathematical and Algorithmic Foundations of the Internet 1st Edition by Fabrizio Luccio, Linda Pagli, Graham Steel ISBN 1439831386 9781439831380

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Product details:

ISBN 10:       1439831386
ISBN 13: 978-1439831380
Author:         Fabrizio Luccio, Linda Pagli, Graham Steel

To truly understand how the Internet and Web are organized and function requires knowledge of mathematics and computation theory. Mathematical and Algorithmic Foundations of the Internet introduces the concepts and methods upon which computer networks rely and explores their applications to the Internet and Web. The book offers a unique approach to mathematical and algorithmic concepts, demonstrating their universality by presenting ideas and examples from various fields, including literature, history, and art.

Progressing from fundamental concepts to more specific topics and applications, the text covers computational complexity and randomness, networks and graphs, parallel and distributed computing, and search engines. While the mathematical treatment is rigorous, it is presented at a level that can be grasped by readers with an elementary mathematical background. The authors also present a lighter side to this complex subject by illustrating how many of the mathematical concepts have counterparts in everyday life.

The book provides in-depth coverage of the mathematical prerequisites and assembles a complete presentation of how computer networks function. It is a useful resource for anyone interested in the inner functioning, design, and organization of the Internet.

Mathematical and Algorithmic Foundations of the Internet 1st Table of contents:

Part I: Introduction to Mathematical Foundations

Chapter 1: The Internet and the Role of Mathematics

• Overview of the Internet Architecture
• Mathematical Models of the Internet
• The Role of Algorithms in Network Operations
• Introduction to Graph Theory in Networking

Chapter 2: Basic Mathematical Tools for Networking

• Set Theory and Logic for Network Design
• Probability and Statistics for Traffic Modeling
• Linear Algebra for Network Analysis
• Fundamentals of Discrete Mathematics

Chapter 3: Graph Theory and Network Topology

• Basic Concepts in Graph Theory
• Types of Graphs in Networking (e.g., Directed, Undirected)
• Network Topology and its Mathematical Representation
• Applications of Graph Theory in Routing and Network Design

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Part II: Network Algorithms and Protocols

Chapter 4: Routing Algorithms

• Introduction to Routing Protocols
• Shortest Path Algorithms (Dijkstra’s, Bellman-Ford, etc.)
• Routing in Large-Scale Networks
• Distributed Algorithms for Routing

Chapter 5: Congestion Control and Flow Algorithms

• The Problem of Congestion in Networks
• Flow Control Algorithms (TCP, UDP, etc.)
• Mathematical Models for Flow Control
• Queueing Theory and Traffic Modeling

Chapter 6: Network Optimization Algorithms

• Linear Programming for Network Optimization
• Optimization of Network Traffic and Resource Allocation
• Algorithms for Load Balancing
• Network Cost Minimization Algorithms

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Part III: Mathematical Models for Network Security and Reliability

Chapter 7: Cryptography and Secure Communication

• The Role of Mathematics in Cryptography
• Symmetric vs. Asymmetric Cryptography
• Public Key Infrastructure (PKI)
• Mathematical Foundations of Encryption Algorithms (RSA, AES, etc.)

Chapter 8: Network Reliability and Fault Tolerance

• Mathematical Models for Fault Tolerance
• Redundancy and Error Correction Techniques
• Algorithms for Reliable Data Transmission
• Monitoring and Maintenance Algorithms

Chapter 9: Game Theory and Security in Networked Systems

• Introduction to Game Theory
• Strategic Interaction in Internet Security
• Network Attacks and Defense Strategies
• Game Theoretic Models for Network Security

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Part IV: Advanced Mathematical and Algorithmic Techniques

Chapter 10: Distributed Algorithms for Large-Scale Networks

• Algorithms for Distributed Systems
• Consensus and Synchronization Problems
• Fault-Tolerant Distributed Algorithms
• Practical Applications of Distributed Algorithms

Chapter 11: Machine Learning in Networking

• Mathematical Foundations of Machine Learning
• Machine Learning Algorithms for Network Traffic Analysis
• Network Optimization with Artificial Intelligence
• Real-World Applications of AI in Networking

Chapter 12: The Future of Mathematical and Algorithmic Internet Foundations

• Emerging Trends in Network Algorithms
• Quantum Computing and its Impact on Internet Security
• Mathematical Challenges in Next-Generation Networks
• The Role of Algorithms in the Internet of Things (IoT)

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