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Table of Contents:

Chapter 1: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Research Questions
1.4 Significance of the Study

Chapter 2: Literature Review
2.1 Overview of Number Theory
2.2 Algebraic Number Theory
2.3 Analytic Number Theory
2.4 Previous Studies on Number Theory
2.5 Gaps in the Literature

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 Data
4.2 Comparison of Algebraic and Analytic Number Theory
4.3 Implications of Findings

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

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Thesis Overview:

Number theory is a branch of mathematics that deals with the properties and relationships of numbers, particularly integers. There are two main branches of number theory: algebraic number theory and analytic number theory.

Algebraic number theory focuses on studying number fields, which are extensions of the rational numbers obtained by adjoining roots of polynomials with integer coefficients. It also deals with algebraic structures such as rings of integers, ideal class groups, and units in number fields. Analytic number theory, on the other hand, utilizes tools from analysis and complex analysis to study the distribution of prime numbers, the Riemann zeta function, and other number-theoretic functions.

This thesis aims to provide a comprehensive overview of both algebraic and analytic number theory, exploring their similarities, differences, and applications in modern mathematics. By conducting a thorough literature review, analyzing data, and discussing findings, this project seeks to contribute to the existing body of knowledge in number theory and provide insights for future research in the field.

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