This research program is involved with the invention and use of computer-oriented numerical, algebraic and hardware techniques applied to problems in physics. The area of application is in Quantum Electrodynamics: high order corrections to the anomalous magnetic moment of the electron. This quantity is known both theoretically and experimentally to extremely high precision. The continuing computational program, in cooperation with experimental work done elsewhere, seeks to improve the precision with which this quantity is known so as to improve our values for some of the fundamental constants as well as to provide a valuable touchstone for the testing of theories of fundamental particles. The demanding nature of these calculations requires the invention of new numerical techniques, the creation and application of very powerful symbolic algebra programs, and the design and building of novel computing engines.