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It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. It contained a brief but essentially com- plete account of the main features of classfield theory, both local and global and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I included such a treatment of this topic.
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Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by Chevalley, of pre-war vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very well. None of ,this was meant for publication.内容简介 The first part of this volume is based on a course taught at Princeton University in 1961-62 at that time, an excellent set of notes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Max also contributed by far the larger part of the exercises.
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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. v vi Weekly notes were written up by Max Rosenlicht and issued week by week to the students. 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. This idea was borrowed from the "e Praktikum"e of German universi- ties. asked to solve under Max's supervision and (when necessary) with his help. The course consisted of two lectures a week, supplemented by a weekly "e laboratory period"e where students were given exercises which they were. 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. 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. 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.