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Stationary processes and prediction theory
540
Book
of purely scientific problems and subjects of specific interest to the communications engineer. Each chapter follows the very admirable practice of commencing with a definition, in terms which can be understood by nonspecialists, of the subject matter to be dis-
NOTES
[J. F. I.
cussed. The book contains a number of excellent photographs and easily-comprehensible diagrams which considerably enhance its value. M. A. POMERANTZ Bartol Research Foundation
BOOK NOTES STATIONARY PROCESSES AND PREDICTION THEORY, by Harry Furstenberg. 283 pages, 7 X 10in. Princeton, Princeton University Press, 1960. Price, $5.00 (paper). In Study 44 of the Annals of Mathematics series, the author's main concern is with sequences derived from Markoff sequences. His thesis--that such sequences are statistically predictable--is developed in nine chapters covering stochastic processes and sequences, stochastic semigroups, Markoff processes and subprocesses, inductive functions and their relation to Markoff processes, continuous predictability and statistical predictability. The final chapter deals with projective inductive functions and prediction. The author's main concern is not to prove theorems, but "to show how certain concepts . . . may be used to systematically analyze various stationary processes and their sample sequences." AN INTRODUCTIONTO THE THEORY OF NUMBERS, by Ivan Niven and Herbert S. Zuckerman. 250 pages, 6 X 9 in. New York, John Wiley & Sons, Inc., 1960. Price, $6.25. Using a topical rather than an historical approach, the authors present a reasonably complete introduction to the theory of numbers. The first part of the book, on basic concepts, is more detailed than the final chapters, where more specialized material is presented. Intended as a test for a one-year course for seniors or beginning graduate students, the book may be used in a shorter course, since many of the chapters are independent of each other. The problems are varied from simple numerical ones to those dealing with development of theory. Sample subjects treated are the partition function, the distribution of primes, asymptotic density, Diophantlne equations, Farey equations and congruences.
STABILIZATION OF FREE RADICALS AT LOW TEMPERATURES, edited by A. M. Bass and H. P. Broida. 110 pages, illustrations, 6 X 9 in. Washington, U. S. Government Printing Office, 1960. Price, $1.50. The three-year (1956--1959) program in free radical research at the National Bureau of Standards is reviewed in this monograph. Nine papers and all extensive bibliography comprise this volume. One paper describes the organization of the program, seven are papers presented at a 1959 symposium, and the other is a summary of that symposium. Subjects covered include physical and chemical processes in trapped radical systems, experimeutal aspects of the NBS program, lowtemperature chemistry, production of trapped radicals, properties of radical-trapping solids, concentrations of trapped radicals, and interactions between trapped species and the matrix. SEMINAR ON TRANSFORMATION GROUPS, by Armand Borel. 245 pages, 7 X 10 in. Princeton, Princeton University Press, 1960. Price, $4.50 (paper). Borel has contributed ten of the sixteen chapters comprising this volume 46 in the Annals of Mathematics Studies; four other authorities complete the roster of contributors - - G . Bredon, E. E. Floyd, D. Montgomery and R. PalMs. The volume, consisting primarily of notes from a seminar held at the Institute for Advanced Study in 1958 and 1959, gives all exposition of some basic theorems and of results obtained by cohomological methods in the theory of compact Lie groups of transformations. The reader is assumed to know basic theory of transformation groups and algebraic topology.
Book
of purely scientific problems and subjects of specific interest to the communications engineer. Each chapter follows the very admirable practice of commencing with a definition, in terms which can be understood by nonspecialists, of the subject matter to be dis-
NOTES
[J. F. I.
cussed. The book contains a number of excellent photographs and easily-comprehensible diagrams which considerably enhance its value. M. A. POMERANTZ Bartol Research Foundation
BOOK NOTES STATIONARY PROCESSES AND PREDICTION THEORY, by Harry Furstenberg. 283 pages, 7 X 10in. Princeton, Princeton University Press, 1960. Price, $5.00 (paper). In Study 44 of the Annals of Mathematics series, the author's main concern is with sequences derived from Markoff sequences. His thesis--that such sequences are statistically predictable--is developed in nine chapters covering stochastic processes and sequences, stochastic semigroups, Markoff processes and subprocesses, inductive functions and their relation to Markoff processes, continuous predictability and statistical predictability. The final chapter deals with projective inductive functions and prediction. The author's main concern is not to prove theorems, but "to show how certain concepts . . . may be used to systematically analyze various stationary processes and their sample sequences." AN INTRODUCTIONTO THE THEORY OF NUMBERS, by Ivan Niven and Herbert S. Zuckerman. 250 pages, 6 X 9 in. New York, John Wiley & Sons, Inc., 1960. Price, $6.25. Using a topical rather than an historical approach, the authors present a reasonably complete introduction to the theory of numbers. The first part of the book, on basic concepts, is more detailed than the final chapters, where more specialized material is presented. Intended as a test for a one-year course for seniors or beginning graduate students, the book may be used in a shorter course, since many of the chapters are independent of each other. The problems are varied from simple numerical ones to those dealing with development of theory. Sample subjects treated are the partition function, the distribution of primes, asymptotic density, Diophantlne equations, Farey equations and congruences.
STABILIZATION OF FREE RADICALS AT LOW TEMPERATURES, edited by A. M. Bass and H. P. Broida. 110 pages, illustrations, 6 X 9 in. Washington, U. S. Government Printing Office, 1960. Price, $1.50. The three-year (1956--1959) program in free radical research at the National Bureau of Standards is reviewed in this monograph. Nine papers and all extensive bibliography comprise this volume. One paper describes the organization of the program, seven are papers presented at a 1959 symposium, and the other is a summary of that symposium. Subjects covered include physical and chemical processes in trapped radical systems, experimeutal aspects of the NBS program, lowtemperature chemistry, production of trapped radicals, properties of radical-trapping solids, concentrations of trapped radicals, and interactions between trapped species and the matrix. SEMINAR ON TRANSFORMATION GROUPS, by Armand Borel. 245 pages, 7 X 10 in. Princeton, Princeton University Press, 1960. Price, $4.50 (paper). Borel has contributed ten of the sixteen chapters comprising this volume 46 in the Annals of Mathematics Studies; four other authorities complete the roster of contributors - - G . Bredon, E. E. Floyd, D. Montgomery and R. PalMs. The volume, consisting primarily of notes from a seminar held at the Institute for Advanced Study in 1958 and 1959, gives all exposition of some basic theorems and of results obtained by cohomological methods in the theory of compact Lie groups of transformations. The reader is assumed to know basic theory of transformation groups and algebraic topology.