This text by a master in the field covers recursive convergence, recursive and relative continuity, recursive and relative differentiability, the relative integral, elementary functions, and transfinite ordinals. 1961 edition.

Recursive Algebra, Analysis and Combinatorics

Recursive Frame Analysis (RFA) is a qualitative research method for mapping and analyzing change-oriented conversation. Cybernetician and therapist Bradford Keeney invented RFA over twenty years ago as a means of discerning and indicating the bare bones organization of real-time therapeutic performance. This book revisits some of Keeney's original ideas while providing a more exhaustive theoretical foundation for RFA, a thorough exploration of its practical application as a research tool, and several detailed analyses of therapy sessions.

This is a revised version of the 1984 book of the same name but considerably modified and enlarged to accommodate the developments in recursive estimation and time series analysis that have occurred over the last quarter century. Also over this time, the CAPTAIN Toolbox for recursive estimation and time series analysis has been developed at Lancaster, for use in the MatlabTM software environment (see Appendix G). Consequently, the present version of the book is able to exploit the many computational routines that are contained in this widely available Toolbox, as well as some of the other routines in MatlabTM and its other toolboxes. The book is an introductory one on the topic of recursive estimation and it demonstrates how this approach to estimation, in its various forms, can be an impressive aid to the modelling of stochastic, dynamic systems. It is intended for undergraduate or Masters students who wish to obtain a grounding in this subject; or for practitioners in industry who may have heard of topics dealt with in this book and, while they want to know more about them, may have been deterred by the rather esoteric nature of some books in this challenging area of study.

In Capital Theory and Equilibrium Analysis and Recursive Utility, Robert Becker and John Boyd have synthesized their previously unpublished work on recursive models.

Multiple complex pathways, characterized by interrelated events and c- ditions, represent routes to many illnesses, diseases, and ultimately death. Although there are substantial data and plausibility arguments suppo- ing many conditions as contributory components of pathways to illness and disease end points, we have, historically, lacked an e?ective method- ogy for identifying the structure of the full pathways. Regression methods, with strong linearity assumptions and data-basedconstraints onthe extent and order of interaction terms, have traditionally been the strategies of choice for relating outcomes to potentially complex explanatory pathways. However, nonlinear relationships among candidate explanatory variables are a generic feature that must be dealt with in any characterization of how health outcomes come about. It is noteworthy that similar challenges arise from data analyses in Economics, Finance, Engineering, etc. Thus, the purpose of this book is to demonstrate the e?ectiveness of a relatively recently developed methodology—recursive partitioning—as a response to this challenge. We also compare and contrast what is learned via rec- sive partitioning with results obtained on the same data sets using more traditional methods. This serves to highlight exactly where—and for what kinds of questions—recursive partitioning–based strategies have a decisive advantage over classical regression techniques.

This book has grown out of a set of lecture notes prepared originally for a NATO Summer School on "The Theory and Practice of Systems ModelLing and Identification" held between the 17th and 28th July, 1972 at the Ecole Nationale Superieure de L'Aeronautique et de L'Espace. Since this time I have given similar lecture courses in the Control Division of the Engineering Department, University of Cambridge; Department of Mechanical Engineering, University of Western Australia; the University of Ghent, Belgium (during the time I held the IBM Visiting Chair in Simulation for the month of January, 1980), the Australian National University, and the Agricultural University, Wageningen, the Netherlands. As a result, I am grateful to all the reci pients of these lecture courses for their help in refining the book to its present form; it is still far from perfect but I hope that it will help the student to become acquainted with the interesting and practically useful concept of recursive estimation. Furthermore, I hope it will stimulate the reader to further study the theoretical aspects of the subject, which are not dealt with in detail in the present text. The book is primarily intended to provide an introductory set of lecture notes on the subject of recursive estimation to undergraduate/Masters students. However, the book can also be considered as a "theoretical background" handbook for use with the CAPTAIN Computer Package.