Mathematical and Computational Methods for Complex Social Systems.

Format:

Book

Author/Creator:

Brooks, Heather Z.

Contributor:

Feng, Michelle.

Porter, Mason A.

Series:

Proceedings of Symposia in Applied Mathematics Series

Proceedings of Symposia in Applied Mathematics Series ; v.80

Language:

English

Subjects (All):

Social systems--Mathematical models.

Social systems.

Social systems--Research--Methodology.

Physical Description:

1 online resource (180 pages)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, 2026.

Summary:

The spread of memes and misinformation on social media, political redistricting, gentrification in urban communities, pedestrian movement in crowds, and the dynamics of voters are among the many social phenomena that researchers investigate in the field of complex systems. In the study of complex social systems, there is often also societal relevance to improving our understanding of how individuals interact with each other and their environment, giving rise to collective group dynamics. The mathematical and computational study of complex social systems relies on and motivates the development of methods in many topics, including mathematical modeling, data analysis, network science, and topology and geometry. This volume is a collection of diverse articles about complex social systems. This collection includes both (1) survey and tutorial articles that introduce complex social systems and methods to study them and (2) manuscripts with original research that highlight a variety of mathematical areas and applications. This book introduces the study of complex social systems to a broad mathematical audience. It will particularly appeal to people who are interested in applied mathematics.

Contents:

Cover

Half-title page

Title page

Copyright

Contents

Preface

1. Introduction

2. Summary of the articles in this volume

3. Conclusion

References

A primer on data-driven modeling of complex social systems

2. Some resources on modeling

3. Some perspectives on data and models

4. Challenges, choices, and creativity in data-driven modeling

5. Illustrative case studies

6. Conclusions

Acknowledgments

A model for wealth concentration: From a discrete system to a PDE

2. Discrete model

3. Continuum limit

4. Sensitivity analysis

5. Discussion

Appendix A.

Appendix B.

Appendix C.

A non-expert's introduction to data ethics for mathematicians

2. Data ethics, the mathematics community, and mathematical-science education

3. A few efforts related to data ethics, society, and social good

4. Research replication and ethics, open data and code, the tension between privacy and open data and code, and some controversy

5. Ethical principles and other considerations in the scientific use of human data

6. Some research and lay articles that are relevant to data ethics and data privacy

7. Conclusion

Acknowledgements

Uncertainty in criminal justice algorithms: Simulation studies of the Pennsylvania Additive Classification Tool

2. The PACT

3. Simulation experiments and sensitivity analysis

4. Fairness

6. Conclusion

A tutorial on networks of social systems: A mathematical modeling perspective

Introduction

1. Mathematical representations of networks

2. Properties of social networks

3. Overview and conclusions

References.

Interpreting topology in the context of social science

1. Intuition

2. Definitions and useful theorems

3. Tutorial

4. Conclusion

Selected published titles in this series

Back Cover.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-8024-7