The increasing role of artificial intelligence to automate decision-making sparks concern about potential AI-based discrimination.
Matrices of small integers—innocuous as they may seem—can clearly provoke interesting behavior.
Joseph Teran spoke about the use of mathematical models for computer-generated imagery at AN18.
Gil Strang identifies continuous piecewise linear functions as powerful approximators in an effort to transform shallow learning into deep learning.
On the occasion of a birthday celebration, Walter Gautschi describes his interest in different research areas.
Nature can overcome the second law of thermodynamics and (nearly) exchange the temperatures of two substances.
Per-Gunnar Martinsson describes two randomized algorithms designed to help process large datasets in high-dimensional spaces.
2018 / xviii + 169 pages / Softcover / ISBN 978-1-611975-17-8 / List Price $59.00 / SIAM Member Price $41.30 / Order Code: CB91
Keywords: evolutionary game theory, voting theory, game theory, reductionist approach, invisible hand
The mathematical challenges coming from the social and behavioral sciences differ significantly from typical applied mathematical concerns. "Change," for instance, is ubiquitous, but without knowing the fundamental driving force, standard differential and iterative methods are not appropriate. Although differing forms of aggregation are widely used, a general mathematical assessment of potential pitfalls is missing. These realities provide opportunities to create new mathematical approaches.
These themes are described in an introductory, expository, and accessible manner by exploring new ways to handle dynamics and evolutionary game theory, to identify subtleties of decision and voting methods, to recognize unexpected modeling concerns, and to introduce new approaches with which to examine game theory. Applications range from avoiding undesired consequences when designing policy to identifying unanticipated voting (where the "wrong" person could win), nonparametric statistical, and economic "supply and demand" properties.
This book is intended for graduate students and researchers who are interested in learning about new mathematics of the social and behavioral sciences and for instructors who wish to develop appropriate undergraduate and graduate level courses.
About the Author
Donald G. Saari, a member of the National Academy of Sciences, is the Distinguished Professor of Mathematics and Economics and director of the Institute for Mathematical Behavioral Sciences at the University of California, Irvine. His research interests include the Newtonian N-body problem, the analysis of voting systems, and application of mathematics to the social and behavioral sciences.