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Table of Contents

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

Chapter 2: Literature Review
2.1 Historical Development of Number Theory
2.2 Elliptic Curves in Number Theory
2.3 Modular Forms in Number Theory
2.4 Previous Research on Elliptic Curves and Modular Forms

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

Chapter 4: Discussion of Findings
4.1 Analysis of Elliptic Curves and Modular Forms
4.2 Implications of the Findings
4.3 Recommendations for Future Research

Chapter 5: Conclusion and Summary
5.1 Summary of Findings
5.2 Conclusion
5.3 Contributions to the Field
5.4 Recommendations for Further Study

Brief Overview of Thesis: Number Theory: Elliptic Curves and Modular Forms

Number theory is a branch of mathematics that deals with the study of integers and their properties. In recent years, the study of elliptic curves and modular forms has gained significant attention in the field of number theory. Elliptic curves are algebraic curves defined by cubic equations, while modular forms are complex functions that satisfy certain symmetry properties.

This thesis aims to explore the connections between elliptic curves and modular forms, and their applications in number theory. The research will involve a comprehensive literature review of the historical development of number theory, as well as an analysis of previous research on elliptic curves and modular forms.

The research methodology will involve data collection methods such as theoretical analysis and computational simulations. The findings of the study will be discussed in chapter four, where the implications of the research will be explored and recommendations for further study will be provided.

In conclusion, this thesis will provide a comprehensive overview of the relationship between elliptic curves and modular forms in number theory. The findings of the study will contribute to the advancement of knowledge in this field and provide valuable insights for future research.

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