(Fox, Phyllis) Milne-Thompson, L. M. | The Calculus of Finite Differences

Second edition of this classic in applied mathematics, originally published in 1933. With the ownership signature of computer scientist Phyllis Fox and the date January 31, 1956, indicating that Fox purchased this volume while working on the numerical solution of partial differential equations for UNIVAC.

During the late 1940s Phyllis Fox (1923 - ) earned undergraduate degrees in mathematics and electrical engineering and worked as an operator for GE’s differential analyser. In 1949 she obtained her master’s in electrical engineering at MIT, writing a program for the school’s unfinished vacuum tube computer the Whirlwind I. Fox then earned her doctorate in mathematics at MIT, supervised by the prominent applied mathematician Chia-Chiao Lin (1916-2013).

As Fox explained to an interviewer from the Society for Industrial and Applied Mathematics in 2005, between 1954 and 1958 she worked at the Courant Institute, an Atomic Energy Commission-funded department of the City University of New York. “[Richard] Courant ran it, but Courant, Kurt O. Friedrichs, Levy, all these famous, really, applied mathematicians were there, and I got a job. As what, I don’t know. But I wasn’t really a fluid dynamicist. They had bought a computer, a Univac. Now, none of these applied mathematicians really wanted to bother with the machine, but a physicist named Bob Richtmyer who came out of AEC and Los Alamos was there. He was interested in doing computations on the Univac... At that time, the main problem thing they were looking for was controlled thermonuclear. Now this isn’t the bomb. The controlled fusion, of course, is the source of all power, if you can make it work. Fine. Theoretically it was clean, and an infinite source of power, once you got it going. And the Russians were probably working on it, so it was very secret. But of course, the technique would apply also to Teller and his bomb. I wasn’t in the abstract analysis part of the research, but I helped with the computer probably, and some of the analysis of the equations involved, because I had that experience from MIT.”

After leaving CUNY, Fox worked on the DYNAMO programming language and the first LISP interpreter and manual, taught at the Newark College of Engineering, and consulted for Bell Labs until her retirement in 1984.

The author of the present volume, Louis Melville Milne-Thomson (1891-1974), was a professor at the Royal Naval College at Greenwich who made significant contributions to applied mathematics, including the Milne-Thomson circle theorem and the Milne-Thomson method for finding a holomorphic function. He was particularly concerned with “making mathematics accessible to the beginner or non-specialist” and in 1933 “published the first of several textbooks. The Calculus of Finite Differences was based on his own experience of making tables and, in its preface, he states that one motivation for writing it was the lack of other texts suitable for his students” (ODNB).