Recent developments in Lie methods applied to various problems in optics and computer design are surveyed in this volume, based on lectures given and work done at the 1988 workshop held in Cocoyoc, Mexico. Topics discussed include perturbation expansions, the mathematical foundations of coherent optical computing, holographic image and interferometry, neural architecture for pattern recognition, recent progress in symbolic calculations with Lie structures together with applications, the operations of convolution and correlation of signals performed by optical means, wide-angle optics based on the Euclidean group of motions and its relation to the Heisenberg-Weyl approach to canonical quantization. Applications discussed include computer design, particle optics in the Superconducting Supercollider, and neural networks. Computational techniques are emphasized. This volume is an excellent introduction to a rather active field of research and can be recommended to graduate students as well as to researchers.

Marcos Moshinsky was born on 20 April 1921, in Kiev, Ukraine, and em- igrated to Mexico at the age of four. He began work at the Universidad N acional Aut6noma de Mexico on 1 January 1942, as a laboratory assis- tant working on the measurement of cosmic rays. He pursued his graduate studies at Princeton University, and wrote his thesis under the supervision of Professor Eugene Wigner. Since 1949, and in spite of many visits and temporary posts held abroad, Moshinsky has been based in Mexico. Through example and encouragement, Moshinsky may be credited to a large extent with the shaping of Mexican scientific research. He has di- rected 40 B. Sc. , M. Sc. , and Ph. D. theses, and published over 200 scientific articles and four books; he holds all the Mexican science prizes, and sev- eral international ones, being a member of 11 academies of learning. Talent and circumstance have placed Marcos Moshinsky at the origin of several of the enterprises of the Mexican and Latin American scientific communities: he was founding editor of the Revista Mexicana de F{sica from 1952 to 1967; the Escuela Latinoamericana de Fisica was initiated and five times organized by him in Mexico; he was founding member and later president of the Academia de la Investigaci6n Cientifica (1962-1963), the Sociedad Mexicana de Fisica (1967-1969), and the Centro Internacional de Fisica y Matematicas A plicadas (1986-), in Cuernavaca.