This Festschrift volume in honour of Prof. E R Caianiello contains invited papers of eminent scientists who have worked in the several areas to which Prof. Caianiello has given seminal contributions: quantum field theory, foundations of quantum mechanics and maximal acceleration (Vol. 1); neural nets, general systems theory and various topics of cybernetics (Vol. 2). The wide range of topics covered shows the fruitfulness of a higher unifying perspective on seemingly diverse subjects.

Almost all theories of fundamental interactions are nowadays based on the gauge concept. Starting with the historical example of quantum electrodynamics, we have been led to the successful unified gauge theory of weak and electromagnetic interactions, and finally to a non abelian gauge theory of strong interactions with the notion of permanently confined quarks. The. early theoretical work on gauge theories was devoted to proofs of renormalizability, investigation of short distance behaviour, the discovery of asymptotic freedom, etc . . , aspects which were accessible to tools extrapolated from renormalised perturbation theory. The second phase of the subject is concerned with the problem of quark confinement which necessitates a non-perturbative understanding of gauge theories. This phase has so far been marked by the introduc tion of ideas from geometry, topology and statistical mechanics in particular the theory of phase transitions. The 1979 Cargese Institute on "Recent Developments on Gauge Theories" was devoted to a thorough discussion of these non-perturbative, global aspects of non-abelian gauge theories. In the lectures and seminars reproduced in this volume the reader wilf find detailed reports on most of the important developments of recent times on non perturbative gauge fields by some of the leading experts and innovators in this field. Aside from lectures on gauge fields proper, there were lectures on gauge field concepts in condensed matter physics and lectures by mathematicians on global aspects of the calculus of variations, its relation to geometry and topology, and related topics.

Over the past three decades R.E. Kalman has been one of the most influential personalities in system and control theory. His ideas have been instrumental in a variety of areas. This is a Festschrift honoring his 60th birthday. It contains contributions from leading researchers in the field giving an account of the profound influence of his ideas in a number of areas of active research in system and control theory. For example, since their introduction by Kalman in the early 60's, the concepts of controllability and observability of dynamical systems with inputs, have been the corner stone of the great majority of investigations in the field.

This four-volume work represents the most comprehensive documentation and study of the creation of general relativity. Einstein’s 1912 Zurich notebook is published for the first time in facsimile and transcript and commented on by today’s major historians of science. Additional sources from Einstein and others, who from the late 19th to the early 20th century contributed to this monumental development, are presented here in translation for the first time. The volumes offer detailed commentaries and analyses of these sources that are based on a close reading of these documents supplemented by interpretations by the leading historians of relativity.

Contains 11 modules consist of a number of activities designed to demonstrate the use of the history of mathematics in the teaching of mathematics. Objectives of the Modules: To enable students to develop a much richer understanding of mathematics and its applications by viewing the same phenomena from multiple mathematical perspectives; To enable students to understand the historical background and connections among historical ideas leading to the development of mathematics; To enable students to see how mathematical concepts evolved over periods of time; To provide students with opportunities to apply their knowledge of mathematics to various concrete situations and problems in a historical context; To develop in students an appreciation of the history connected with the development of different mathematical concepts; To enable students to recognize and use connections among mathematical ideas; To enable students to understand how mathematical ideas interconnect and build on one another to produce a coherent whole; To lead students to recognize and apply mathematics in contexts outside of mathematics.--Publisher.

Heredity: knowledge and power -- Generation, reproduction, evolution -- Heredity in separate domains -- First syntheses -- Heredity, race, and eugenics -- Disciplining heredity -- Heredity and molecular biology -- Gene technology, genomics, postgenomics: attempt at an outlook.

The essays in this book provide the first comprehensive treatment of the concept of revolution in mathematics. In 1962 an exciting discussion of revolutions in the natural sciences was prompted by the publication of Kuhn's The Structure of Scientific Revolutions. A fascinating but little knownoffshoot of this debate was begun in the USA in the mid-1970s: can the concept of revolutions be applied to mathematics as well as science? Michael Crowe declared that revolutions never occur in mathematics, while Joseph Dauben argued that there have been mathematical revolutions and gave someexamples.The original papers of Crowe, Dauben, and Mehrtens are reprinted in this book, together with additional chapters giving their current views. To this are added new contributions from nine further experts in the history of mathematics who each discuss an important episode and consider whether it was arevolution.This book is an excellent reference work and an ideal course text for both graduate and undergraduate courses in the history and philosophy of science and mathematics.

Galileo Galilei (1564–1642), his life and his work have been and continue to be the subject of an enormous number of scholarly works. One of the con- quences of this is the proliferation of identities bestowed on this gure of the Italian Renaissance: Galileo the great theoretician, Galileo the keen astronomer, Galileo the genius, Galileo the physicist, Galileo the mathematician, Galileo the solitary thinker, Galileo the founder of modern science, Galileo the heretic, Galileo the courtier, Galileo the early modern Archimedes, Galileo the Aristotelian, Galileo the founder of the Italian scienti c language, Galileo the cosmologist, Galileo the Platonist, Galileo the artist and Galileo the democratic scientist. These may be only a few of the identities that historians of science have associated with Galileo. And now: Galileo the engineer! That Galileo had so many faces, or even identities, seems hardly plausible. But by focusing on his activities as an engineer, historians are able to reassemble Galileo in a single persona, at least as far as his scienti c work is concerned. The impression that Galileo was an ingenious and isolated theoretician derives from his scienti c work being regarded outside the context in which it originated.