1. Introduction 2. Understanding Social Media Algorithms 2.1 Definition of Social Media Algorithms 2.2 How Algorithms Function 2.3 Evolution of Algorithms in Social Media 3. Political Polarization in the Digital Age 3.1 Defining Political Polarization 3.2 Historical Context and Trends 3.3 Role of Digital Media 4. Mechanisms of Public Opinion Formation 4.1 Psychological Factors in Opinion Formation 4.2 Influence of Media on Public Opinion 4.3 Social Media's Role in Opinion Dynamics 5. Algorithms and Political Polarization 5.1 Algorithmic Bias and Echo Chambers 5.2 Case Studies of Polarization 5.3 Potential Mitigating Strategies 6. Public Opinion Formation via Algorithms 6.1 Information Curation and Personalization 6.2 Filter Bubbles and Information Silos 6.3 Effects on Diverse Public Discourses 7. Case Studies and Empirical Research 7.1 Analysis of Real-world Incidents 7.2 Studies on Algorithmic Influence 7.3 Comparisons Across Platforms 8. Conclusions and Recommendations 8.1 Summary of Key Findings 8.2 Implications for Policy and Regulations 8.3 Future Research Directions
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