Aris's research fellowship was extended for a second year, but shortly afterward, in October 1956, Aris was informed of a lectureship opening at the University of Edinburgh. He took advantage of the opportunity, and left immediately for Edinburgh. University of Edinburgh lectureship Aris was on the faculty of the University of Edinburgh for two years, 1956–1958. While at Edinburgh, Aris wrote papers on his work at the University of Minnesota and at ICI. Having the lectureship position allowed Aris to gain experience lecturing to students. He also attended the lectures of, and interacted with, the chair of chemical technology at the University of Edinburgh, Kenneth Denbigh, who was a well-known thermodynamicist and an editor of the journal Chemical Engineering Science. University of Minnesota faculty Aris returned to Minneapolis in the summer of 1957 to continue his work on the stirred tank reactor problem. In August he became engaged to Claire Holman, and when he informed Amundson, Amundson offered him a faculty position at the University. Aris accepted the job, and began working as an assistant professor at the University of Minnesota in 1958. Aris had not formally received a Ph.D., but had registered three years earlier with the University of London, where he had earned his B.Sc., and which offered Ph.D. degrees by correspondence. A Ph.D. degree could be earned without following a strict preparation process; the individual needed to propose a research program after 3 years, select a committee of examiners, and submit a dissertation, and after an oral examination by and approval from the committee, the degree would be granted. Amundson had suggested Aris look into Richard Bellman's method of dynamic programming for his dissertation. Amundson informally served as Aris's advisor, and Aris completed his dissertation on the topic in 1960. His dissertation was published by the Academic Press in a series of which Bellman was the editor, and Bellman took note of the dissertation. Aris and Amundson visited Bellman at the Rand Corporation, where Bellman was working on economic models. The dynamic programming method had originally been developed for economics, but Bellman was attracted by applications in engineering, and the meeting led to a joint collaboration and a publication. Aris's research at the University of Minnesota focused on optimization, dynamic programming, control theory, Taylor diffusion, and computing engines. Aris also taught a graduate fluid mechanics course, and eventually wrote the book Vectors, tensors, and the basic equations