The next year Mac Lane put group theory first, and set theory (Boolean algebra ) last! That was characteristic of his freshness, his initiative, and his lack of respect for conformity but it came as a slight shock to me at the time. When I taught "modern algebra" in "Math 6" the first time, in 1937- 38, I began with sets and ended with groups. Our collaboration involved some compromises.
My conservative inclusion of material from the then traditional "college algebra" and "theory of equations" courses (Bôcher, Dickson, Fine ) may have helped with its initial success, as did my recognition that Galois theory used vector spaces. His problems and his organization of linear algebra were especially timely. Mac Lane had had much more teaching experience than I, and I think the popularity of our book owes more to him than to me. Although my course was well attended, I was much more research-oriented than teaching-oriented. He returned to Harvard in 1938, the year after I had given a course in modern algebra on the undergraduate level for the first time. My father recognized Mac Lane's exceptional qualities, and got him invited as a Benjamin Peirce Instructor in 1934- 1936.
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