Number Theory for Beginners

In the summer quarter of 1949, I taught a ten-weeks introductory course on number theory at the University of Chicago; it was announced in the catalogue as "e;Alge- bra 251"e;. What made it possible, in the form which I had planned for it, was the fact that Max Rosenlicht, now of the University of California at Berkeley, was then my assistant. According to his recollection, "e;this was the first and last time, in the his tory of the Chicago department of mathematics, that an assistant worked for his salary"e;. The course consisted of two lectures a week, supplemented by a weekly "e;laboratory period"e; where students were given exercises which they were. asked to solve under Max's supervision and (when necessary) with his help. This idea was borrowed from the "e;Praktikum"e; of German universi- ties. Being alien to the local tradition, it did not work out as well as I had hoped, and student attendance at the problem sessions so on became desultory. v vi Weekly notes were written up by Max Rosenlicht and issued week by week to the students. Rather than a literal reproduction of the course, they should be regarded as its skeleton; they were supplemented by references to stan- dard text-books on algebra. Max also contributed by far the larger part of the exercises. None of ,this was meant for publication.