Here are 100 chapter titles for a book on Simulation, progressing from beginner to advanced, with a focus on the underlying mathematics:
I. Foundations (1-20)
- Introduction to Simulation: What and Why?
- Types of Simulation: Discrete-Event, Continuous, Hybrid
- Simulation Modeling: Concepts and Principles
- Mathematical Foundations: Probability and Statistics Review
- Random Variables and Distributions: Uniform, Exponential, Normal
- Probability Distributions: Poisson, Binomial, Gamma, and Others
- Random Number Generation: Linear Congruential Generators
- Pseudo-Random Numbers: Properties and Testing
- Random Variate Generation: Inverse Transform Method
- Random Variate Generation: Acceptance-Rejection Method
- Discrete-Event Simulation: Basic Concepts
- Entities, Attributes, and Activities: Modeling System Components
- Events and Event Scheduling: The Heart of DES
- Queuing Systems: Modeling Waiting Lines
- Queuing Theory: Mathematical Analysis of Queues (Brief Overview)
- Simulation Software: Tools for Building Models
- Model Validation and Verification: Ensuring Accuracy
- Input Data Analysis: Gathering and Fitting Distributions
- Output Analysis: Statistical Analysis of Results
- Review and Preview: Looking Ahead
II. Intermediate Techniques (21-40)
- Discrete-Event Simulation: Advanced Concepts
- Process Interaction Approach: Modeling Complex Systems
- Activity Scanning Approach: Alternative Modeling Perspective
- Three-Phase Approach: Combining Event and Activity Scanning
- Time Management in Simulation: Event Scheduling Algorithms
- Simulation Languages: GPSS, SIMAN, Arena, and Others
- Statistical Distributions in Simulation: Empirical Distributions
- Fitting Distributions to Data: Goodness-of-Fit Tests
- Chi-Square Test: Comparing Observed and Expected Frequencies
- Kolmogorov-Smirnov Test: Comparing Distributions
- Output Analysis: Confidence Intervals
- Replication and Runs: Obtaining Multiple Data Points
- Variance Reduction Techniques: Improving Simulation Efficiency
- Common Random Numbers: Reducing Variance in Comparisons
- Antithetic Variates: Exploiting Negative Correlation
- Control Variates: Using Related Variables to Reduce Variance
- Importance Sampling: Biasing the Simulation to Rare Events
- Model Calibration: Adjusting Model Parameters
- Sensitivity Analysis: Examining Model Response to Changes
- Review and Practice: Intermediate Techniques
III. Advanced Topics (41-60)
- Continuous Simulation: Modeling Dynamic Systems
- Differential Equations: The Basis of Continuous Simulation
- Numerical Integration: Solving Differential Equations
- Euler's Method: A Simple Numerical Integration Technique
- Runge-Kutta Methods: Higher-Order Accuracy
- System Dynamics: Modeling Feedback Loops
- Agent-Based Modeling: Simulating Interactions of Autonomous Agents
- Cellular Automata: Discrete Models with Local Interactions
- Hybrid Simulation: Combining Discrete and Continuous Elements
- Monte Carlo Simulation: Using Randomness to Solve Problems
- Markov Chains: Modeling Systems with Discrete States
- Markov Processes: Continuous-Time Markov Chains
- Queuing Networks: Complex Queuing Systems
- Jackson Networks: A Special Case of Queuing Networks
- Stochastic Processes: A General Framework for Random Phenomena
- Renewal Theory: Analyzing Events that Renew a System
- Time Series Analysis: Modeling and Forecasting Time-Dependent Data
- Stochastic Differential Equations: Modeling Random Systems with Calculus
- Brownian Motion: A Fundamental Stochastic Process
- Review and Practice: Advanced Topics
IV. Special Topics and Applications (61-80)
- Simulation in Manufacturing: Production Line Optimization
- Simulation in Logistics: Supply Chain Management
- Simulation in Healthcare: Hospital Operations and Patient Flow
- Simulation in Transportation: Traffic Flow and Network Design
- Simulation in Finance: Portfolio Management and Risk Analysis
- Simulation in Computer Science: Network Performance and Cloud Computing
- Simulation in Environmental Science: Climate Modeling and Pollution Dispersion
- Simulation in Social Sciences: Modeling Social Behavior and Interactions
- Simulation in Engineering: Product Design and System Optimization
- Simulation in Training and Education: Virtual Environments and Simulations
- Parallel and Distributed Simulation: Speeding Up Simulations
- High-Performance Computing for Simulation
- Cloud-Based Simulation: Scalable Simulation Environments
- Visualization and Animation: Communicating Simulation Results
- Virtual Reality and Simulation: Immersive Simulation Experiences
- Augmented Reality and Simulation: Blending Real and Simulated Worlds
- Data-Driven Simulation: Using Real-World Data to Drive Simulations
- Machine Learning and Simulation: Combining ML with Simulation
- Optimization and Simulation: Finding Optimal Solutions using Simulation
- Advanced Applications: A Survey
V. Deeper Dive and Extensions (81-100)
- Advanced Random Number Generation: Mersenne Twister and Other Algorithms
- Quasi-Random Numbers: Low-Discrepancy Sequences
- Advanced Random Variate Generation: Specialized Techniques
- Simulation Languages: Advanced Features and Programming
- Model Development Methodologies: Best Practices
- Verification and Validation: Advanced Techniques
- Output Analysis: Advanced Statistical Methods
- Design of Experiments: Optimizing Simulation Experiments
- Metamodeling: Building Models of Simulation Models
- Uncertainty Quantification: Assessing the Impact of Uncertainty
- Sensitivity Analysis: Advanced Techniques
- Optimization of Stochastic Systems: Stochastic Optimization
- Simulation-Based Optimization: Combining Simulation and Optimization
- Large-Scale Simulation: Challenges and Techniques
- Agent-Based Modeling: Advanced Topics
- System Dynamics: Advanced Topics
- Hybrid Simulation: Advanced Topics
- History of Simulation: A Detailed Account
- Open Problems and Future Directions in Simulation
- Research Topics in Simulation: A Guide for Exploration