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The Computer from Pascal to von Neumann
In 1942, Lt. Herman H. Goldstine, a former mathematics professor, was stationed at the Moore School of Electrical Engineering at the University of Pennsylvania. It was there that he assisted in the creation of the ENIAC, the first electronic digital computer. The ENIAC was operational in 1945, but plans for a new computer were already underway. The principal source of ideas for the new computer was John von Neumann, who became Goldstine's chief collaborator. Together they developed EDVAC, successor to ENIAC. After World War II, at the Institute for Advanced Study, they built what was to become the prototype of the present-day computer. Herman Goldstine writes as both historian and scientist in this first examination of the development of computing machinery, from the seventeenth century through the early 1950s. His personal involvement lends a special authenticity to his narrative, as he sprinkles anecdotes and stories liberally through his text.
New and Full Moons 1001 B.C. to A.D. 1651
Originally pub. in 1973; reprinted in 1994. Presents tables giving the dates of all new and full moons during an historical era when these data were of considerable interest and importance. The longitudes of the moon at each of these times is also given, as is a consecutive enumeration of the conjunctions and a similar one of the oppositions. All dates are reckoned in the Julian calendar. These dates and times are calculated for an observer in Babylon, or equivalently Baghdad, since this location is fairly centrally located for the historians of the period. The time used is civil time and is based on a 24-hour clock with its origin at midnight. Since this vol. may be considered as a suppl. to Tuckerman's tables, all fundamental astronomical elements have been taken from them.
A History of Numerical Analysis from the 16th through the 19th Century
In this book I have attempted to trace the development of numerical analysis during the period in which the foundations of the modern theory were being laid. To do this I have had to exercise a certain amount of selectivity in choosing and in rejecting both authors and papers. I have rather arbitrarily chosen, in the main, the most famous mathematicians of the period in question and have concentrated on their major works in numerical analysis at the expense, perhaps, of other lesser known but capable analysts. This selectivity results from the need to choose from a large body of literature, and from my feeling that almost by definition the great masters of mathematics were the ones responsib...
A History of the Calculus of Variations from the 17th through the 19th Century
The calculus of variations is a subject whose beginning can be precisely dated. It might be said to begin at the moment that Euler coined the name calculus of variations but this is, of course, not the true moment of inception of the subject. It would not have been unreasonable if I had gone back to the set of isoperimetric problems considered by Greek mathemati cians such as Zenodorus (c. 200 B. C. ) and preserved by Pappus (c. 300 A. D. ). I have not done this since these problems were solved by geometric means. Instead I have arbitrarily chosen to begin with Fermat's elegant principle of least time. He used this principle in 1662 to show how a light ray was refracted at the interface between two optical media of different densities. This analysis of Fermat seems to me especially appropriate as a starting point: He used the methods of the calculus to minimize the time of passage cif a light ray through the two media, and his method was adapted by John Bernoulli to solve the brachystochrone problem. There have been several other histories of the subject, but they are now hopelessly archaic. One by Robert Woodhouse appeared in 1810 and another by Isaac Todhunter in 1861.
Routines of Substitution
This work is a historical and philosophical study of the programming work carried out by John von Neumann in the period 1945-8. At the heart of the book is an examination of a manuscript featuring the earliest known surviving example of von Neumann’s coding, a routine written in 1945 to ‘mesh’ two sequences of data and intended to be part of a larger program implementing the algorithm now known as mergesort. The text of the manuscript itself, along with a preliminary document describing the code he used to write this program, are reproduced as appendices. The program is approached in three chapters describing the historical background to von Neumann’s work, the significance of the sorting application itself, and the development of the EDVAC, the machine for which the program was written. The subsequent chapters widen the focus again, discussing the subsequent evolution of the program and the crucial topic of subroutines, before concluding by situating von Neumann’s work in a number of wider contexts. The book also offers a unifying philosophical interpretation of von Neumann’s approach to coding.
Banach, Frechet, Hilbert and Neumann Spaces
This book is the first of a set dedicated to the mathematical tools used in partial differential equations derived from physics. Its focus is on normed or semi-normed vector spaces, including the spaces of Banach, Fréchet and Hilbert, with new developments on Neumann spaces, but also on extractable spaces. The author presents the main properties of these spaces, which are useful for the construction of Lebesgue and Sobolev distributions with real or vector values and for solving partial differential equations. Differential calculus is also extended to semi-normed spaces. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers without restricting or generalizing the results.
The Origins of Digital Computers
My interest in the history of digital computers became an active one when I had the fortune to come across the almost entirely forgotten work of PERCY LUDGATE, who designed a mechanical program-controlled computer in Ireland in the early I ':ICC's. I undertook an investigation of his life and work, during which I began to realise that a large number of early developments, which we can now see as culminating in the modern digital computer, had been most undeservedly forgotten. Hopefully, historians of science, some of whom are now taking up the subject of the development of the computer and accumulating valuable data, particularly about the more recent events from the people concerned, will before too long provide us with comprehensive analytical accounts of the invention of the computer. The present book merely aims to bring together some of the more important and interesting written source material for such a history of computers. (Where necessary, papers have been translated into English, but every attempt has been made to retain the flavour of the original, and to avoid possibly misleading use of modern computing terminology.
Introduction to Interval Analysis
An update on the author's previous books, this introduction to interval analysis provides an introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB.
The Computer
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An Episodic History of Mathematics
A series of snapshots of the history of mathematics from ancient times to the twentieth century.
