 He held positions at Bell Laboratories, University of Washington, Carnegie Mellon, and Columbia, as well as sabbatical positions at Stanford, Berkeley, Princeton, California Institute of Technology, and Technical University, Munich.Traub was the author or editor of ten monographs and some 120 papers in computer science, mathematics, physics, finance, and economics.In 1959 he began his work on optimal iteration theory culminating in his 1964 monograph, which is still in print.