The theory of Boolean algebras was created in 1847 by the English mat- matician George Boole. He conceived it as a calculus (or arithmetic) suitable for a mathematical analysis of logic. The form of his calculus was rather di?erent from the modern version, which came into being during the - riod 1864-1895 through the contributions of William Stanley Jevons, Aug- tus De Morgan, Charles Sanders Peirce, and Ernst Schr] oder. A foundation of the calculus as an abstract algebraic discipline, axiomatized by a set of equations, and admitting many di?erent interpretations, was carried out by Edward...

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated...

There is at present a growing body of opinion that in the decades ahead discrete mathematics (that is, "noncontinuous mathematics"), and therefore parts of applicable modern algebra, will be of increasing importance. Cer- tainly, one reason for this opinion is the rapid development of computer science, and the use of discrete mathematics as one of its major tools. The purpose of this book is to convey to graduate students or to final-year undergraduate students the fact that the abstract algebra encountered pre- viously in a first algebra course can be used in many areas of applied...

IN 1959 I lectured on Boolean algebras at the University of Chicago. A mimeographed version of the notes on which the lectures were based circulated for about two years; this volume contains those notes, corrected and revised. Most of the corrections were suggested by Peter Crawley. To judge by his detailed and precise suggestions, he must have read every word, checked every reference, and weighed every argument, and I am lIery grateful to hirn for his help. This is not to say that he is to be held responsible for the imperfec- tions that remain, and, in particular, I alone am responsible for...

There is growing evidence that an amalgamation of systems theories and communication and information theories will become the leading conceptual model for addressing human behavior. In this book we have used a theoretical frame which focuses on the coding, storage, and movement of information within and among open systems. We believe this to be a productive working concept which allows the student of human behavior to avoid the mind/body dichotomy. This conceptual framework also allows the integration of the biologic and sociologic aspects of human behavior. Using this theoret ical model we...

The history of science is mostly written retrospec tively, a generation or two after the actual events being discussed. Science historians are now analyzing and evaluating the origins of evolutionary and genetical theory in the nineteenth century and a sort of "Darwin industry" seems to have grown up. A history of mammalian cytogenetics by one of the main participants is, hence, a very welcome change, since it has a vividness, an immediacy and a personal flavor which these scholarly tomes and the official biog raphies of scientists mostly lack. The life of the author, Chinese-born, T. C. Hsu,...

This text is an overall view of nematology because I believe the science should be treated as a unified discipline. The differences in the biological habits of nematodes do not justify the separation of plant nematologists and animal nematologists, since the separation is not a reflection of any difIerences inherent to nematodes. Therefore, the book is arranged with a format that in the beginning chapters illustrates the similarities and se quence of development of morphological characters among nematodes regardless of their biological habits. The later chapters illustrate the in tegration of...

Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra...

This book grew out of lectures on spectral theory which the author gave at the Scuola. Normale Superiore di Pisa in 1985 and at the Universite Laval in 1987. Its aim is to provide a rather quick introduction to the new techniques of subhar monic functions and analytic multifunctions in spectral theory. Of course there are many paths which enter the large forest of spectral theory: we chose to follow those of subharmonicity and several complex variables mainly because they have been discovered only recently and are not yet much frequented. In our book Pro pri6t6$ $pectrale$ de$ algebre$ de...