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Birkhauser Boston, Inc., will publish a series of carefully selected mono graphs in the area of mathematical modeling to present serious applications of mathematics for both the undergraduate and the professional audience. Some of the monographs to be selected and published will appeal more to the professional mathematician and user of mathematics, serving to familiarize the user with new models and new methods. Some, like the present monograph, will stress the educational aspect and will appeal more to a student audience, either as a textbook or as additional reading. We feel that this first volume in the series may in itself serve as a model for our program. Samuel Goldberg attaches a high priority to teaching stu dents the art of modeling, that is, to use his words, the art of constructing useful mathematical models of real-world phenomena. We concur. It is our strong conviction as editors that the connection between the actual problems and their mathematical models must be factually plausible, if not actually real. As this first volume in the new series goes to press, we invite its readers to share with us both their criticisms and their constructive suggestions.
List of contents
1. A Power Index for Individuals and Coalitions.- 1.1 Introduction.- 1.2 Coalitions and characteristic function of a game.- 1.3 Shapley value to a player.- 1.4 Shapley-Shubik power index.- 1.5 Some illustrative examples.- 1.6 Applications and other measures of power.- 2. How Many People Have Ever Lived?.- 2.1 Introduction.- 2.2 A birth-death stochastic process.- 2.3 Determination of the mean population size.- 2.4 Fitting an exponential curve.- 2.5 Population data and results.- 3. Management of Research Projects.- 3.1 Introduction.- 3.2 Problem 1.- 3.3 Problem 2.- 3.4 Bibliographic notes.- 4. Stochastic Learning Models.- 4.1 Introduction.- 4.2 The experiment and the model.- 4.3 Consequences of the model.- 4.4 Extensions and further reading.- 5. Glottochronology.- 5.1 Introduction.- 5.2 A "death" process for words.- 5.3 Comparing cognates in two languages.- 6. Probability Models for Mobility.- 6.1 The basic BKM Markov model.- 6.2 The Stayer-Mover model.- 6.3 Further modifications.- 7. Recall From Memory.- 7.1 Introduction.- 7.2 The model.- 7.3 Outline of the analysis.- 7.4 The derivation of Pn(t).- 7.5 Final remarks and additional references.- Postscript..- Index. 115.
