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Table of Contents:

Chapter 1: Introduction
1.1 Background of the Study
1.2 Problem Statement
1.3 Objectives of the Study
1.4 Significance of the Study
1.5 Limitations of the Study
1.6 Scope of the Study

Chapter 2: Literature Review
2.1 Overview of Galois Theory
2.2 Field Extensions and Their Properties
2.3 Historical Development of Galois Theory
2.4 Previous Studies on Galois Theory and Field Extensions

Chapter 3: Research Methodology
3.1 Overview of Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques

Chapter 4: Discussion of Findings
4.1 Analysis of Results
4.2 Comparison with Existing Literature
4.3 Implications for Theory and Practice

Chapter 5: Conclusion and Summary
5.1 Summary of Findings
5.2 Contributions to Knowledge
5.3 Recommendations for Future Research

Brief Overview on Thesis Galois Theory and Field Extensions:

Galois theory is a branch of abstract algebra that studies field extensions and their automorphisms. Field extensions are mathematical structures that extend the field of rational numbers to include new elements that are solutions to polynomial equations. Galois theory provides a systematic way to study these extensions and their symmetries.

In the thesis on Galois theory and field extensions, the researcher aims to explore the historical development of Galois theory, its key concepts, and its applications in mathematics and other fields. The study will also examine previous research on Galois theory and field extensions to identify gaps in the literature and propose new directions for future research.

Through a comprehensive literature review and empirical analysis, the research will contribute to the understanding of Galois theory and its significance in modern mathematics. The findings of the study will be discussed in detail in chapter four, highlighting the implications for theory and practice in the field of abstract algebra. Finally, the conclusion and summary in chapter five will provide a synthesis of the key findings and recommendations for future research in Galois theory and field extensions.

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