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TABLE OF CONTENTS

Chapter One: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Objectives of the Study
1.4 Research Questions
1.5 Significance of the Study
1.6 Limitations of the Study
1.7 Scope of the Study

Chapter Two: Literature Review
2.1 Overview of Combinatorial Game Theory
2.2 History of Nim and Sprague-Grundy Theory
2.3 Previous Studies on Nim and Sprague-Grundy Theory
2.4 Key Concepts in Nim and Sprague-Grundy Theory
2.5 Applications of Combinatorial Game Theory in Various Fields

Chapter Three: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques
3.4 Sampling Procedure
3.5 Ethical Considerations

Chapter Four: Discussion of Findings
4.1 Analysis of Nim Game Strategies
4.2 Evaluation of Sprague-Grundy Values in Game Theory
4.3 Comparison of Different Game Theoretic Approaches
4.4 Implications of Findings for Combinatorial Game Theory

Chapter Five: Conclusion and Summary
5.1 Summary of Key Findings
5.2 Contributions to the Field of Combinatorial Game Theory
5.3 Recommendations for Future Research
5.4 Conclusion

BRIEF OVERVIEW

Combinatorial Game Theory is a branch of mathematics that studies the strategic interactions of two players in games of perfect information. Nim and Sprague-Grundy Theory are classic examples of combinatorial games that have been extensively studied in the literature. Nim is a simple game where players take turns removing objects from piles, with the goal of being the last player to make a move. Sprague-Grundy Theory, on the other hand, assigns a mathematical value (called the Grundy number) to each position in a game, which can be used to determine the optimal strategies for winning.

This thesis aims to explore the principles of Nim and Sprague-Grundy Theory in depth, analyzing the strategies and mathematical concepts involved in these games. By conducting a literature review and applying research methodology, the study will delve into the history of these games, previous studies, key concepts, and practical applications in various fields. The findings from the analysis will be discussed in Chapter Four, examining the different strategies and approaches in Nim and Sprague-Grundy Theory.

In conclusion, this thesis will provide a comprehensive overview of Combinatorial Game Theory, focusing on Nim and Sprague-Grundy Theory. The research findings and insights generated from this study will contribute to the understanding and advancement of game theory in mathematics and related disciplines.

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