Analysis of Game Theory Algorithms in Chess and Their Applications to Engineering Mathematics

1. Introduction 1.1 Background of Game Theory 1.2 Significance of Chess in Game Theory 1.3 Objectives of the Study 1.4 Structure of the Thesis 2. Overview of Game Theory 2.1 Definition and Basic Concepts 2.2 Historical Development 2.3 Key Algorithms in Game Theory 3. Algorithms in Chess 3.1 Minimax Algorithm 3.2 Alpha-Beta Pruning 3.3 Monte Carlo Tree Search 3.4 Comparison of Algorithms 4. Mathematical Foundations in Chess 4.1 Combinatorics in Chess Strategies 4.2 Probability in Chess Analysis 4.3 Optimization Techniques in Chess 5. Applications in Engineering Mathematics 5.1 Algorithmic Applications in Engineering 5.2 Control Systems Design 5.3 Network Optimization 6. Case Studies 6.1 Successful Implementations in Engineering 6.2 Comparative Analysis with Other Games 6.3 Challenges and Limitations 7. Future Directions 7.1 Emerging Algorithms in Game Theory 7.2 Potential Engineering Applications 7.3 Research Opportunities 8. Conclusion 8.1 Summary of Findings 8.2 Implications for Engineering 8.3 Final Thoughts and Recommendations