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Table of Contents:

Chapter One: Introduction
1.1 Background of the Study
1.2 Research Problem
1.3 Research Questions
1.4 Objectives of the Study
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 Topological Data Analysis
2.2 Principles of Applied Topology
2.3 Previous Studies on Topological Data Analysis
2.4 Applications of Topological Data Analysis
2.5 Current Trends in Applied Topology

Chapter Three: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques
3.4 Sampling Procedures
3.5 Ethical Considerations
3.6 Validity and Reliability

Chapter Four: Discussion of Findings
4.1 Analysis of Data
4.2 Interpretation of Results
4.3 Comparison with Literature
4.4 Implications for Practice
4.5 Recommendations for Future Research

Chapter Five: Conclusion and Summary
5.1 Summary of Findings
5.2 Conclusion
5.3 Contributions to Knowledge
5.4 Practical Implications
5.5 Suggestions for Further Research

Brief Overview:

Topological data analysis and applied topology are emerging fields that apply topological methods to analyze complex data sets. Topological data analysis focuses on understanding the shape and structure of data, while applied topology applies these principles to solve real-world problems in various fields such as biology, computer science, and engineering.

This thesis aims to explore the applications of topological data analysis and applied topology in different domains, examining the current trends and challenges in the field. The research methodology involves collecting and analyzing data using topological tools and techniques, with a focus on identifying patterns and relationships that may not be apparent using traditional statistical methods.

The findings of this study will contribute to advancing the understanding of how topological data analysis can be used to extract meaningful insights from complex data sets. The implications for practice include the potential for developing new algorithms and tools for data analysis, as well as improving decision-making processes in various industries.

In conclusion, this thesis provides a comprehensive overview of the principles and applications of topological data analysis and applied topology, highlighting the potential for further research and innovation in these exciting fields.

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