The field of mathematical psychology began in the 1950s and includes both psychological theorizing, in which mathematics plays a key role, and applied mathematics, motivated by substantive problems in psychology. Central to its success was the publication of the first Handbook of Mathematical Psychology in the 1960s. The psychological sciences have since expanded to include new areas of research, and significant advances have been made in both traditional psychological domains and in the applications of the computational sciences to psychology. Upholding the rigor of the first title in this field to be published, the New Handbook of Mathematical Psychology reflects the current state of the field by exploring the mathematical and computational foundations of new developments over the last half-century. This first volume focuses on select mathematical ideas, theories, and modeling approaches to form a foundational treatment of mathematical psychology.

1 Selected concepts from probability

2 Probability, random variables, and selectivity

3 Functional equations

4 Network analysis

5 Knowledge spaces and learning spaces

6 Evolutionary game theory

7 Choice, preference, and utility: probabilistic and deterministic representations

8 Discrete state models of cognition

9 Bayesian hierarchical models of cognition

1 0 Model evaluation and selection

Review

'This volume, the first of several, is a welcome effort to systematize the mathematical ideas and foundational issues that characterize modern developments in mathematical psychology. A highly readable resource for anyone interested in theory as it relates to the psychological and cognitive sciences.' Richard C. Atkinson, President Emeritus of the University of California and Professor Emeritus of Psychological and Cognitive Sciences at the University of California, San Diego

'These two volumes are a valuable contribution to mathematical psychology; partly representing important summaries of special branches, partly pushing the forefront of research towards new horizons. They should be read by all working in special fields, but also by students who are striving for a general point of view. We are looking forward to the third volume.' Reinhard Suck, Journal of Mathematical Psychology

'Containing substantial chapters detailing applications of mathematics to a wide range of topics in behavior and cognition, written by leading scholars in the field, and updated to reflect current trends and new developments, the New Handbook is destined to become an essential resource for students and experienced researchers alike.' Philip L. Smith, Editor-in-Chief, Journal of Mathematical Psychology

About the Authors

Hans Colonius is Professor of Psychology at Carl V. Ossietzky Universität Oldenburg, Germany.

Ehtibar N. Dzhafarov is Professor of Psychological Sciences at Purdue University, Indiana.

William H. Batchelder is Professor of Cognitive Sciences at the University of California, Irvine.

Jay Myung is Professor of Psychology at Ohio State University.